JP5577946B2 - Manufacturing process evaluation method, its evaluation apparatus, and its program - Google Patents

Description

  The present invention relates to a manufacturing process evaluation method, an evaluation apparatus thereof, and a program thereof.

  In order to increase the overall processing capacity of a manufacturing process composed of a plurality of processes, there is a method for evaluating each process constituting the manufacturing process. For example, it is an evaluation method using a bottleneck process that restricts the entire processing capability of the manufacturing process from among the manufacturing processes.

  In the evaluation method as described above, the bottleneck process is found using the average value of the processing capacity of each process constituting the manufacturing process, and the overall processing capacity is increased by improving the bottleneck process. Such an idea of improving and operating the manufacturing process by paying attention to the bottleneck process is referred to as constraint theory (TOC: theory of constraints).

"The Goal-What is the Ultimate Purpose of a Company", Eliyah Goldrat, Diamond

  If there is a variation in the processing capability of a single process, the single process with the variation may affect the processing capability of the entire process even if it is not regarded as a bottleneck process. In the constraint theory, it is not targeted for improvement except for the bottleneck process. Therefore, it is not possible to evaluate the influence of processes other than the bottleneck process on the processing capability of the entire process.

  The manufacturing process evaluation method, the evaluation apparatus, and the program for solving the above-described problems are as follows.

(1) A manufacturing process evaluation apparatus having a plurality of single processes,
A storage unit for storing an average and a standard deviation of values indicating the processing capacities of the plurality of unit processes;
A processing unit for calculating a probability distribution function of the manufacturing process;
With
The processor is
Calculating a probability distribution function of each of the plurality of single steps using an average and a standard deviation of values indicating the processing capabilities of the plurality of single steps stored in the storage unit; Calculating the first probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions;
Accepting an input to change the average and / or standard deviation of values indicating the processing capability of one single step among the plurality of single steps to a value that improves the processing capability of the single step, and processing capability of the single step There comprising a probability distribution function of the modified average and / or standard deviation to calculate the probability distribution function of the previous SL one single step using a calculated pre SL one single step to enhance the plurality of Calculating the second probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the single process;
Evaluating the manufacturing process having the plurality of processes by comparing a first probability distribution function and a second probability distribution function of the manufacturing process;
An evaluation apparatus characterized by that.
(2) The evaluation apparatus according to (1), further including a display unit, which displays a first probability distribution function and a second probability distribution function of the manufacturing process.
(3) The storage unit stores single process cost data indicating a correspondence relationship between the processing capacity of the single process and the cost data required to improve the processing capacity,
The processing unit selects, based on the single cost data, a single process that is a target for changing an average and / or standard deviation of values indicating the processing capacity to a value that improves the processing capacity of the single process (1). ) Or the evaluation device according to (2).
(4) A method for evaluating a manufacturing process having a plurality of unit processes, wherein the information processing apparatus
Reading an average and standard deviation of values indicating the processing capability of each of the plurality of single steps from the storage unit of the information processing device, calculating a probability distribution function of each of the plurality of single steps, and Calculating the first probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the process;
Accepting an input to change the average and / or standard deviation of values indicating the processing capability of one single step among the plurality of single steps to a value that improves the processing capability of the single step, and processing capability of the single step There comprising a probability distribution function of the modified average and / or standard deviation to calculate the probability distribution function of the previous SL one single step using a calculated pre SL one single step to enhance the plurality of Calculating the second probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the single process;
An evaluation method comprising: evaluating a manufacturing process having the plurality of processes by comparing a first probability distribution function and a second probability distribution function of the manufacturing process.
(5) The evaluation method according to (4), wherein the first probability distribution function and the second probability distribution function of the manufacturing process are displayed on the display unit of the information processing apparatus.
(6) The storage unit stores single process cost data indicating a correspondence relationship between the processing capacity of the single process and the cost data for improving the processing capacity,
The information processing apparatus includes:
Based on the elemental cost data, select a single process which is the subject to change the average and / or standard deviation of the values indicating the processing capacity to a value that improves the processing capacity of the single step (4) or (5 ) Evaluation method.
(7) A program for evaluating a manufacturing process having a plurality of unit processes,
Reading an average and standard deviation of values indicating the processing capability of each of the plurality of single steps from the storage unit of the information processing device, calculating a probability distribution function of each of the plurality of single steps, and Calculating the first probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the process;
Accepting an input to change the average and / or standard deviation of values indicating the processing capability of one single step among the plurality of single steps to a value that improves the processing capability of the single step, and processing capability of the single step There comprising a probability distribution function of the modified average and / or standard deviation to calculate the probability distribution function of the previous SL one single step using a calculated pre SL one single step to enhance the plurality of Calculating the second probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the single process;
Evaluating the manufacturing process having the plurality of processes by comparing a first probability distribution function and a second probability distribution function of the manufacturing process;
A program that causes an information processing apparatus to execute processing.
(8) Displaying the first probability distribution function and the second probability distribution function of the manufacturing process on the display unit of the information processing apparatus,
The program according to (7), which causes an information processing apparatus to execute processing.
(9) The storage unit stores single process cost data indicating a correspondence relationship between the processing capacity of the single process and the cost data required to improve the processing capacity,
Based on the single unit cost data, selecting a single step that is a target for changing the average and / or standard deviation of the value indicating the processing capability to a value that improves the processing capability of the single step,
The program according to (7) or (8), which causes the information processing apparatus to execute processing.

  In one aspect, the present invention has an effect of evaluating the influence of a single process having variations on the processing capability of the entire process.

FIG. 1 is a diagram illustrating an example of a manufacturing process. FIG. 2 is a diagram illustrating an example of a continuous rolling process. FIG. 3 is a diagram for explaining the influence of a single process having variations in processing time on the entire process. FIG. 4 is a diagram illustrating an example of a processing time of a manufacturing process including two processes having the same average processing time. FIG. 5 is a diagram showing the relationship between the average value of the processing time of the manufacturing process shown in FIG. 4 and the actual processing time. FIG. 6 is a diagram illustrating an example of a cumulative distribution function indicating single processes with variations in processing time. FIG. 7 is a diagram illustrating an example of the processing time of a manufacturing process including two processes having different average processing times. FIG. 8 is a diagram illustrating a synthesis example of a probability distribution of processing capability. FIG. 9 is a diagram illustrating an example of evaluating the overall capability by superposing a plurality of steps using a cumulative distribution function. FIG. 10 is a diagram comparing the total synthesis processing time when the standard deviation of the processing time is large and small with respect to the average value of the processing time. FIG. 11 is a diagram illustrating an example of estimating the total processing time distribution by superimposing unbalanced multi-step capability with different capacities using the actual distribution of processing times. FIG. 12A is a diagram illustrating a probability distribution indicating the processing capability of the single processes A to C. FIG. FIG. 12B is a diagram illustrating a probability distribution indicating the processing capability of the entire process. FIG. 12C is a diagram illustrating a probability distribution indicating the processing capability of the entire process after the improvement of the single process. FIG. 13 is a diagram illustrating an example of an information processing apparatus. FIG. 14 is a diagram illustrating an example of data stored in the storage unit. FIG. 15 is a diagram illustrating an example of single process cost data. FIG. 16 is a diagram illustrating an example of evaluation of a manufacturing process. FIG. 17 is a diagram illustrating an example of changing the processing capability of a single process.

  Hereinafter, [1] manufacturing process, [2] evaluation using real number verification result of manufacturing process, [3] statistical evaluation of manufacturing process, [4] evaluation of improvement contribution to whole process of single process, [5] evaluation The embodiment will be described in order by dividing the apparatus into [6] manufacturing process evaluation process flow.

  In the manufacturing process [1], the types of manufacturing processes including single processes with variations in processing capability and examples of specific manufacturing processes will be described. The evaluation [2] using the real number verification result of the manufacturing process and the statistical evaluation [3] of the manufacturing process describe an evaluation method for judging the manufacturing process by the processing ability of the single unit capacity. Improvement contribution evaluation [4] of a single process to the whole process explains the contribution that the improvement of the processing capacity of the single process gives to the processing capacity of the whole process. In the evaluation apparatus [5], an apparatus for executing the evaluation method [3] or [4] will be described. In the evaluation process flow [6] of the manufacturing process, the evaluation method [3] or [4] performed by the evaluation apparatus [5] will be described. ] Will be described.

[1] Manufacturing Process First, the manufacturing process will be described. The manufacturing process generally includes a single process having a variation in processing capability. Note that the variation in processing capacity is, for example, a variation in processing time per product if the manufacturing process uses solids as a product, and a flow rate per time in a manufacturing process that does not use solids as a product. Variation. In the manufacturing process, there is also a discrete process in which a solid product is processed according to a bill of materials and combined to manufacture a product. In addition, the manufacturing process includes a continuous process in which a fluid such as liquid or gas is chemically reacted to be changed to another fluid. Further, the manufacturing process includes a combination of the above continuous process and a discrete process.

  Manufacturing processes with varying processing capabilities include, for example, (a) a processing process for manufacturing parts by processing raw materials, (b) a machining process for machining parts, and (c) an assembly process for assembling products from the parts. There is. Hereinafter, the steps (a) to (c) will be outlined.

  (A) As a processing step of processing a raw material to manufacture a part, for example, there is an iron manufacturing process of an ironworks. The ironmaking process at a steel mill is composed of a iron making process, a steel making process, a rolling process, and the like. The iron making process is a process in which iron ore, which is a natural resource, and coke are chemically reacted at a high temperature in a blast furnace, and pig iron, which is iron obtained by removing oxygen from the iron ore, is taken out. Since the product in the iron making process is pig iron which is a high-temperature liquid, it becomes pig iron at a predetermined flow rate. For example, as the amount of iron ore charged into the blast furnace changes, the iron making process varies in processing capacity.

  The steel making process is a process for producing “steel” which is viscous and tough iron by removing impurities such as carbon, phosphorus, sulfur and silicon contained in pig iron by a converter. In the steel making process, molten steel from which impurities have been removed by a converter is poured into a continuous casting machine and cast into a predetermined shape, thereby producing a steel piece whose side has been solidified. Since the product in the steel making process is a steel piece whose side surface is solidified, it becomes a predetermined amount of steel piece. For example, the steelmaking process varies in processing capacity due to the change in the amount of pig iron introduced into the converter.

  The rolling process is a process in which a steel slab is sandwiched between rolls and extended to be thinned to a predetermined thickness. For example, since the roll passing time of the steel slab is changed by changing the size and amount of the steel slab to be input into the rolling process, the processing capacity of the rolling process varies. As an example of the process, the continuous rolling process will be described later with reference to FIG.

  (B) As for the machining process for machining parts, for example, an automobile factory has a machining process for machining and manufacturing automobile parts. The machining is performed by a human operating a drilling machine that drills holes, a lathe that performs cutting with a tool called a fixed tool, or automatic machining is performed using an automatic lathe or the like. In the machining process, the processing capability varies due to individual differences depending on the person operating.

  (C) Assembling processes for assembling products from parts include, for example, assembling engines from cylinders, piston rods, cam chains, etc., which are engine parts, assembling computers from processors and memories, structures and heat insulating materials. There are various things such as the process of assembling a house from such members. In the assembly process, the processing capability varies due to individual differences among humans.

  As described above, many of the manufacturing processes have variations in processing capability. However, in the constraint theory and the like, an average value is used in verification of processing capability, so that it is treated as having no variation. However, as will be described later, when the processing capability of each process that actually configures the manufacturing process is verified, it can be seen that each process has a variation that affects the entire process.

  FIG. 1 is a diagram illustrating an example of a manufacturing process. The manufacturing process 100 shown in FIG. 1 has n (n is a natural number) unit processes. The manufacturing process 100 is, for example, any one of the above-described processes (a) to (c).

  In the first step, a raw material is received and a series of steps are executed, and the nth step outputs a product. Each single process is connected to another single process.

  Also, tanks that serve as buffers between single processes and intermediate inventory facilities such as warehouses are not arranged. In the case where each single process is provided with a transportation facility such as a conveyor, the conveyor does not operate so as to accumulate a conveyed product and operates at a constant speed, and therefore does not function as a buffer. In this way, if there is an intermediate inventory between single processes, the variation in the processing capacity of the single process will not affect the entire process due to the intermediate inventory, so the effect of the varying single processes on the processing capacity of the entire process is clear. It is because it does not become.

  FIG. 2 is a diagram illustrating an example of a continuous rolling process. The continuous rolling process 100a shown in FIG. 2 includes a yard process 10a, a cutting process 20a, a reheating process 30a, a rolling process 40a, and a cooling process 50a. The continuous rolling process 100a is a process of manufacturing various steel products such as a thick plate, a thin plate, a shape steel, and a steel pipe from the steel piece manufactured in the steel making process.

  Yard process 10a is a process of conveying a steel piece from a slab yard to a rolling mill that performs a continuous rolling process.

  The cutting step 20a is a step of cutting a steel piece conveyed from the slab yard by gas cutting or the like. In a cutting process, it cuts into the steel piece of the predetermined dimension for rolling by the following rolling process 40a.

  The reheating step 30a is a step of reheating the cut steel piece. In the reheating step, the steel slab is recrystallized by raising the steel slab to the recrystallization temperature or higher. The recrystallization temperature also varies depending on the material and the degree of processing, which is the rate of change of the plate thickness. For example, the recrystallization temperature is lower as the steel slab has a higher degree of work and the recrystallization temperature is higher as the steel slab has a lower degree of work. Thus, since the reheating process 30a has different heating temperatures depending on the material or degree of processing, the processing time varies.

  The rolling process 40a is a process for processing a steel piece into a product having a predetermined shape by applying force to the steel piece and forging it. In the rolling step 40a, a steel slab is rolled by a rough rolling mill 41a and a finish rolling mill 42a. In the rolling process 40a, the roughing mill 41a and the finish rolling mill 42a process the steel slab into a predetermined shape such as a plate, a rod, or a pipe by passing the steel slab between the rolls of the machines. In addition, in the rolling process 40a, since the hardness of a material and a work degree differ with sizes etc., the processing time of the rough rolling mill 41a and the finishing mill 42a differs. Thus, the rolling process 40a varies in processing time because the heating temperature varies depending on the material or the degree of processing.

  The cooling step 50a is a step of cooling the steel piece. In the cooling step 50a, accelerated cooling is performed after rolling to change the structure of the steel slab and increase the strength or toughness of the steel slab. In the cooling step 50a, a hot labeler 51a that corrects the shape of the steel slab and an injection nozzle that injects a cooling medium are provided on the upper and lower surfaces of the steel slab that is restrained by a plurality of restraining roll pairs and transported on the transport line. The steel slab is cooled by the cooling device 52a.

[2] Evaluation Using Mounting Verification Result of Manufacturing Process As described with reference to FIGS. 1 and 2, the manufacturing process has variations in processing time. The entire process consisting of single processes with variations in processing time is affected by variations in the processing time of single processes.

FIG. 3 is a diagram for explaining the influence of a single process having variations in processing time on the entire process. The processing times of the two single processes A and B correspond to the cumulative distribution function 211 shown in FIG. The vertical axis of the cumulative distribution function 211 is the probability that processing time will occur, and the horizontal axis is a random variable z determined by the following equation 1.
z = (processing time x−average value μ of processing time) / standard deviation σ. ... Formula 1

  It is assumed that the probability that the single process A and the single process B perform processing with the average value of the processing time is “0.5” as indicated by an arrow 212. Here, since the processes that occur in the single process A and the single process B are independent events, the probabilities P (201) and P (202) in which a certain processing time occurs in the single process A and the single process B, and the single processes A and The probability P (203) that a certain processing time occurs in the entire process composed of the single process B is expressed by the following Expression 2.

  P (203) = P (201) × P (202) Equation 2

Therefore, as indicated by an arrow 213 shown in FIG. 3, the probability that the entire process performs processing with an average value of processing time is 0.5 × 0.5 = 0.25. Thus, the average time for the entire process consists of a single step with a variation in the processing time is longer than the predicted be that the average time constraints theory. Therefore, when there are variations in processing time in the single processes constituting the manufacturing process, the process that affects the processing time of the entire manufacturing process cannot be determined by the average value of the processing time of the single processes in the constraint theory.

  Hereinafter, the influence of the variation in the processing time of the single process on the processing time of the entire manufacturing process will be described using a real number verification result.

[2.1] Processing capacity of a manufacturing process composed of two single processes with the same average processing time FIG. 4 shows a manufacturing process composed of two single processes with the same average processing time. It is a figure which shows an example of the process time of a process. The histograms 201 and 202 shown in FIG. 4 are histograms showing the processing capabilities of the single process A and the single process B, respectively. There is no buffer between the single process A and the single process B, and the single process A and the single process B are independent processes.

  The histogram 203 is a histogram showing the overall processing capability that is the processing capability of the single step A and the single step B as a whole.

As shown in the histogram 201, the average μ of the processing time per product, which is the processing capability of the single process A, is 151 seconds. As shown in the histogram 202, the average μ of the processing time per product, which is the processing capability of the single process B, is 148 seconds. The standard deviation σ of the processing time per product of the single process A is 52, and the standard deviation σ of the processing time per product of the single process B is 48 .

  The single process A and the single process B do not correspond to the bottleneck process because the processing capabilities are almost equal and balanced. The average processing time per product of the entire process should be the average processing time of the single process A and the single process B in the concept of constraint theory, but in reality, the average processing time of the entire process is 178 seconds, which is longer than the average value of the processing time of the single process A and the single process B.

  FIG. 5 is a diagram showing the relationship between the average value of the processing time of the entire process shown in FIG. 4 and the processing time of the single process. The average value increase rate (Δμ / μ) on the vertical axis of the graph 204 shown in FIG. 5 is a ratio between the average value μ203 of the processing time of the histogram 203 and the average value μ201 of the processing time of the histogram 201 as the entire process. is there. Δμ represents the difference between the average value μ203 of the processing time of the histogram 203 and the average value μ201 of the processing time of the histogram 201, which is the entire process. When the average value μ203 of the processing time of the histogram 203 as the entire process is the same as the average value μ of the processing time of the histogram 201, the average value increase rate (Δμ / μ) becomes 0%, and the average processing time of the histogram 203 The average value increase rate (Δμ / μ) increases as the value μ becomes larger than the average of the processing times μ of the histogram 201, that is, as the result becomes different from the constraint theory.

  The dimensionless variation (σ / average μ) of the single process, which is the horizontal axis of the graph 204, is a value obtained by dividing the standard deviation σ 201 of the processing time of the histogram 201 by the average value μ 201 of the processing time of the histogram 201. The dimensionless variation and the average value increase rate have the relationship shown in Formula 3A.

  Δμ / μ = 0.56 × (σ / μ) Equation 3A

  That is, if the standard deviation σ of a single process is increased, the difference in the processing time of the entire process is increased in proportion to 0.56 times the standard deviation σ. For example, when the non-dimensional variation is “30%”, the average value increase rate is “17%”. Therefore, the following expressions 3B and 3C can be derived from the expression 3A.

Processing time of entire process = processing time of single process × (1 + 0.56σ) Equation 3B
When 1 >> (0.56σ) ² Total processing capacity = average of single processing capacity × (1−0.56σ) Equation 3C
σ: Standard deviation of processing time for a single process

  As shown in Equation 3C, it can be seen that the non-dimensional variation increases and the processing capability of the entire manufacturing process decreases as the standard deviation with respect to the average processing time increases. Further, as shown in the section “0.56σ”, a little more than half of the time standard deviation% with respect to the average value of the processing capability of a single process affects the processing time of the entire process.

[2.2] Processing capacity of a manufacturing process composed of two processes with different average processing times FIG. 6 shows an example of processing capacity of a manufacturing process composed of two processes with different average processing times. FIG. The histograms 221 and 222 shown in FIG. 6 are histograms showing the processing times of the single process C and the single process D. The histogram 223 is a histogram of the entire process including the single process C and the single process D.

As shown in the histogram 221, the average μ of the processing time per product, which is the processing capability of the single process C, is 150 seconds. As shown in the histogram 222, the average μ of the processing time per product, which is the processing capability of the single process D, is 117 seconds. The standard deviation σ of the processing time per product of the single process C is 50, and the standard deviation σ of the processing time per product of the single process D is 38 .

  The single process C and the single process D have different processing capabilities, and the single process C shown in the histogram 221 is a bottleneck process with a long processing time. The average processing time per product, which is the processing capability of the entire process composed of the single process C and the single process D, should be the same processing time as the single process C in terms of the constraint theory. The average value of the processing time of the entire process is 163 seconds, which is longer than the average value of the processing time of the single process C.

  FIG. 7 is a diagram illustrating an example of the influence of the processing capability of a single process on the processing capability of the entire process. The bottleneck process described with reference to FIG. 7 corresponds to the single process C, and the non-bottleneck process corresponds to the single process D. The overall process corresponds to an overall process composed of a single process C and a single process D. Also, the graph 224 shown in FIG. 7 is generated using histograms 221 and 222 showing the single process C and the single process D shown in FIG.

  The capability reduction rate, which is the vertical axis of the graph 224, is a value obtained by dividing the difference between the average total processing time of the entire process and the average processing time of the bottleneck process by the average processing time of the bottleneck process. In constraint theory, the average processing time for the entire process should be the same as the average processing time for the bottleneck process. Therefore, if the capability reduction rate increases, unlike the constraint theory, it indicates that the processing time of the entire process is longer than the bottleneck process.

The capability difference φ on the horizontal axis of the graph 224 is a value obtained by dividing the difference in processing time between the bottleneck process and the non-bottleneck process by the processing time of the bottleneck process . A small capability difference φ indicates that the processing capability of the non-bottleneck process has decreased, and a large capability difference φ indicates that the processing capability of the non-bottleneck process is high.

  From the histograms 221 and 222 shown in FIG. 6, data having non-dimensional variations of 10%, 20%, 30%, 40%, and 50% were selected. From the selected data, the ability reduction rate was obtained when the ability difference was 0%, 10%, 20%, 30%, and 40%, and the data was plotted on the graph 224.

From the graph 224, the following has been found to improve the throughput of the entire process.
(Result 1) The processing capability of the entire process is improved by reducing the variation of the single process.
(Result 2) When the processing capability of the bottleneck cannot be changed, the processing capability of the non-bottleneck process is increased and the processing capability of the entire process is improved. In other words, even if the capability of the non-bottleneck process is improved, the processing capability of the entire process is improved. Neither of the above (Result 1) and (Result 2) can be derived from the constraint theory.
This will be described below.

A straight line 225 obtained by complementing the plot data of the graph 224 indicates the relationship between the capability decrease rate and the capability difference when the variation% obtained by dividing the standard deviation by the average value is 30%. The straight line 225 indicates that the larger the “x”, which is the difference in capacity between the bottleneck process and the non-bottleneck process, is proportional to 0.4 times the difference in capacity, the processing time of the entire process and the bottleneck process. It shows that “y”, which is the difference from the processing time, becomes smaller. In addition, as shown in the above result (2), in the straight line 225, even if the non-bottleneck process is improved so that the capacity difference is 40%, the overall processing capacity reduction rate is improved to “0”. it can be seen that it is. The primary function 226 represents a linear 225 this and, Formula 3B, the equation 3C, the following equation 4 is derived.

Processing time of entire process = processing time of single bottleneck process × (1 + 0.56σ × (1−φ / 0.4)) Equation 4A
When 1 >> (0.56σ · (1-φ / 0.4)) ² , the processing capacity of the entire process = the average of the processing capacity of the single bottleneck process × (1−0.56σ × (1−φ / 0.4) ) ... Formula 4B

[3] Statistical evaluation of manufacturing process [2] Evaluation method of overall ability of manufacturing process having variation by statistical method based on formulation method based on evaluation using real number verification result of manufacturing process shown above Will be explained. In this evaluation method, if there is a precondition indicating the processing capability of a single process such as an average or standard deviation, the relationship between the overall processing capability of the manufacturing process and the single processing capability can be accurately presented.

[3.1] Series steps with average processing time (1) General solution concept The following describes the general solution concept. There are n groups of independent events with a normal probability distribution with mean values μ (1) to μ (n) and standard deviations σ (1) to σ (n), and the number of samples in each group is equally large enough Shall. Samples one by one arbitrarily from each population at this time by n pieces taken out, the or the maximum value is any probability distribution (mean and standard deviation), find general solutions.

In general, the cumulative distribution function is expressed by F (chi), the cumulative distribution function of the maximum value independent of n random variables is defined as G (χ), G (χ ) is represented by Equation 5 below.

G (χ) = {F (χ)} ⁿ Expression 5

  From Equation 5, the average value and the standard deviation σ are calculated.

The normal distribution is shown by the following formula 6.
Normal distribution φ (χ) = 1 / √2πσ · exp (− (χ−μ) ² / 2σ ² ) Equation 6

The distribution of the maximum value is shown by the following formulas 7 to 10.
Total cumulative distribution function G (χ) = {Φ ((χ−μ) / σ)} ^{n in the} whole process Equation 7
Probability density function g (χ) = n {Φ ((χ−μ) / σ)} ⁽ⁿ⁻¹⁾ φ ((χ−μ) / σ) / σ Expression 8
μ [x _(n) ] = μ + e ₁ σ (e ₁ is an increasing function with respect to n) Equation 9
σ [x _(n) ] = e ₂ σ ² (e ₂ is a decreasing function with respect to n) Equation 10

(2) Specific example showing probability distribution of entire process Next, a specific example showing the probability distribution of the entire process will be described using the above general solution.

(I) shows an example of taking out two from a population of n = 2 in case the standard normal distribution _{f (χ) = 1 / √2π} · exp (-χ 2/2).
When average μ (1) = μ (2) = 0, standard deviation σ (1) = σ (2) = 1, and n = 2, the average value e ₁ and variance e _{2 of the} entire process consisting of two processes. Is shown below.

_{f (χ) = exp (-χ} 2/2) × {1 + erf (χ / √2)} / √2π ··· formula 11
e ₁ = ∫χf _(χ) dx = 1 / √π = 0.56419
e ₂ = ∫χ ² f _(χ) dx− (∫χf _(χ) dx) ² = 1−1 / π = 0.6817

In the example using the above-described real number verification result, when the average value μ of processing time of a single process μ = 150 and the standard deviation σ = 50, the average processing time is μ [x _(n) ] = 150 + 0.5642 × 50 = 178, and the standard deviation is σ [x _(n) ] ^0.5 = (0.6817) ^0.5 × 50 = 41, which is consistent with the real number verification result.

The maximum value distribution is G (χ) = F (χ) ² and the inverse function of the cumulative distribution function is Finv (χ). When F (χ) = 0.5 in the standard normal distribution, Value = average) and the following general solution is obtained.
Average value of all processes e ₁ : e ₁ = Finv function (0.5 ^{1 / n} ) Equation 12
Standard deviation of entire process √e ₂ = Finv function [{G function ₍₁₎ } ^{1 / n} ] −e _1.

Next, using the general solution of e1 and √e2 described above, an equation showing the probability distribution of the processing capability of the entire process is shown algebraically.
S1: First, a cumulative distribution function F (z) is drawn using z = (χ−μ) / σ, which is a random variable that standardizes a sample. χ is a value indicating processing capability such as processing time, μ is an average value, and σ is a standard deviation.
S2: Next, a combined cumulative distribution function G (z), in which a plurality of F (z) are superimposed and combined, is drawn. At this time, G (z) = F1 (z) * F2 (z) * .. Fn (z), and G (z) = F (z) n for the same distribution form.

The positive function of the cumulative distribution function of the standard normal distribution and the inverse function of the cumulative distribution function of the standard normal distribution are equations that can be used in algebraic analysis, so the average value e _{1 of} the entire process consisting of two steps, The standard deviation √e ₂ is expressed as follows using Equations 12 and 13.
Average value of two steps e ₁ = Finv function (0.5 ^0.5 ) = 0.545
Standard deviation of two steps √e ₂ = Finv function [{G function ₍₁₎ } ^0.5 ] −e ₁ = 0.8418

Moreover, the average value e _{1 of} the whole process consisting of _two steps and the standard deviation √e ₂ of the whole process consisting of three steps are expressed as follows using Equations 12 and 13.
Average value of 3 steps e ₁ : Finv (0.5 ^1/3 ) = 0.919
Standard deviation of 3 steps √e ₂ : Finv [G ₍₁₎ ^1/3 ] −Finv (0.5 ^1/3 ) = 0.703

  Similarly, when the number of processes is increased, (n, e1, √e2) is calculated using (12, 0.998, 0.727), (5, 1.129, 0.697), (6, 1.231, 0.674),...

Thus, e ₁ and √e ₂ can be calculated from the number n of processes constituting the entire process.

FIG. 8 is a diagram illustrating a synthesis example of a probability distribution of processing capability. The graph 231 shows a cumulative distribution function F (z) of a standard normal distribution, a combined cumulative distribution function F (z) ^{2 obtained} by combining two cumulative distribution functions F (z), and three cumulative distribution functions F ( F (z) ³ , which is a combined cumulative distribution function obtained by combining z), and e ₁ and √e ₂ are shown.

The graph 231 shows probability density functions corresponding to F (z), F (z) ² , and F (z) ³ , respectively.

The overall ability of n processes in which the average values are almost equal and the processing time is balanced and continuous is expressed by the following expressions 14 and 15. The overall average capacity is Gμ, the variation is σ _G , the unit average capacity Fμ, and the variation is σ _F.

Gμ = Fμ + e ₁ σ _F Equation 14
σ _G = √e ₂ · σ _F Equation 15
However, e ₁ = Finv function (0.5 ^{1 / n} ), √e ₂ = Finv function [{G function ₍₁₎ } ^{1 / n} ] −e ₁

Particularly when n = 2, as shown by 233 in FIG. 8, e ₁ = 1 / √π = 0.56419, and as shown by 234 in FIG. 8, √e ₂ = √ (1-1 / π) = 0.8256.

  Thus, the cumulative distribution function when a plurality of cumulative distribution functions are multiplied using the standard normal distribution cumulative distribution function is shown. Assuming that the single process shown in FIG. 1 is a cumulative distribution function of a standard normal distribution, it can be seen that the entire process composed of a plurality of single processes can be statistically calculated.

[3.2] Evaluation of continuous total capacity of two processes with unbalanced processing time Algebraic calculation analysis of continuous total capacity evaluation of two processes with unbalanced processing time as well as series processes with average processing time A method will be described.

Take out n processes (for example, 2 processes) from the continuous processes, and make the average value μ _(n) and variation σ _{F (n)} of each single processing capacity (processing time) known, and the average value of the total capacity processing time A method for obtaining μ and variation σ _G is shown below.

When the single processing time is balanced (Fμ ₍₁₎ = Fμ (2)... = Fμ _(n) ) (the average value is almost equal), the processing time of the entire consecutive n processes is expressed by the following equation 16, It is expressed by Equation 17. The average value of the entire processing time is Gμ, the variation σ _G , and the average value of the single processing time is Fμ, and the variation σ _F.

Gμ = Fμ + e ₁ σ _F Equation 16
σ _G = √e ₂ · σ _F Equation 17
However, e ₁ = Finv function (0.5 ^{1 / n} ), √e ₂ = Finv function [{G function ₍₁₎ } ^{1 / n} ] −e ₁

When n = 2, e ₁ = 1 / √π = 0.56419, √e ₂ = √ (1-1 / π) = 0.8256

Further, the variation σ of the population distributed with O ≦ has a strong correlation with the average value μ, and when it can be expressed as k · σ _F = F (k = 2 to 3), the following general formula 18 Is obtained.

Gμ = Fμ (1 + e ₁ / k) Equation 18
When n = 2, Gμ = (1.188 to 1.226) · Fμ, σ _G = (0.8256) · σ _F

  Formulation is possible as described above, and estimation calculation using real numbers is possible. For example, when the average processing capacity of the entire process is set to 100, it can be determined that the two single processing capacities should be about 118 to 122.

Note that, as described in Expression 13 and Expression 14, e ₁ and √e ₂ can be calculated from the number n of processes constituting the entire process. That is, (1 + e ₁ / k) in Expression 18 can be calculated from the number of steps n. Equation 19 below is a variation of Equation 18.

Fμ = Gμ / (1 + e ₁ / k) = Equation 19

  In order to obtain a desired overall processing capacity Gμ, it is possible to calculate from Equation 19 how much the processing capacity Fμ of a single process should be.

  Next, a method for estimating the overall processing time distribution by unbalanced multi-step capability superposition with different capabilities using a processing time distribution function will be described with reference to FIG.

  FIG. 9 is a diagram illustrating an example of evaluating the overall capability by superposing a plurality of steps using a cumulative distribution function. A graph 241 illustrated in FIG. 9 represents a cumulative distribution function, and a graph 242 represents a probability density function.

  Graphs 241 and 242 show three distribution functions of Ga, Gb, and Gc as single function processing time distribution functions, and mean μ and standard deviation σ are (150, 50), (135, 45), ( 120, 40). Ga, Gb, and Gc were calculated by the above formula 14.

Two successive steps (a → a, a → b, a → c) are polymerized to represent GA synthesis = Ga × Ga, GB synthesis = Ga × Gb, and GC synthesis = Ga × Gc, as shown in FIG. It becomes a solid line distribution.

The GA synthesis is in a state where the processing time is balanced, and agrees with 150 + 0.5642 × 50 = 177 from the formula. As shown in FIG. 9, in the case of the GA synthesis, G = 177 seconds ((177−150) / 150 = 18% worse than 150 seconds). (Relative to 150 seconds, (169-150) /150=12.7Pasento worsening) G = 169 seconds in the case of G B synthesis becomes. In the case of GC synthesis, G = 161 seconds (compared to (161-150) /150=7.3% compared to 150 seconds).

  In this way, the cumulative distribution function when a plurality of cumulative distribution functions are multiplied using a cumulative distribution function that is not a standard normal distribution is shown. If it is assumed that the single process shown in FIG. 1 is the cumulative distribution function shown in FIG. 9, it can be seen that the overall process composed of a plurality of single processes can be statistically calculated.

[3.3] Capability unbalance General purpose general capacity evaluation in multiple steps FIG. 10 shows a case where the standard deviation of the processing time is large (1/2 of the average value) and a case where the standard deviation of the processing time is small (average) It is the figure which compared the whole synthetic | combination processing time of 1/6) of the value. A graph 251 shown in FIG. 10 shows a process in which the processing time is different when the standard deviation of the processing time is ½ of the average value, and a graph 252 shows a case where the standard deviation of the processing time is ６ of the average value. The process from which processing time differs is shown.

  In the overall capability evaluation, the average overall capability after synthesis is deteriorated by the standard deviation σ as well as the single process capability processing time average value. When the standard deviation σ is suppressed to about 1/6 of the average value μ (graph 252), the bottleneck average value can be evaluated almost as usual due to the effect of less than 10% of the processing capacity of the bottleneck single unit process. When the variation is as large as ½ of the average (graph 251), the processing time is inevitably deteriorated by a maximum of 28%.

  As described above, it was shown that the entire process can be calculated even when a plurality of processes having different processing times are multiplied.

  FIG. 11 is a diagram illustrating an example of estimating the total processing time distribution by superimposing unbalanced multi-step capability with different capacities using the actual distribution of processing times.

  As an actual example, the actual distribution (graph 261) of each process single time of the acceptance process to the yard, which is one of the steelmaking processes, the rolling process, and the secondary processing process (cutting), and the time distribution that approximates the normal distribution for each similar material For both (graph 262), the combined time distributions were compared. As shown in the results 263 and 264, the processing time average value after the synthesis is expressed with almost no difference.

  Furthermore, the calculated combined processing time distribution and the observed actual processing time distribution agree well.

[4] Evaluation of improvement contribution to the whole process of the single process There are three distribution functions of the single process time, Fa (z), Fb (z), and Fc (z), and the average μ and the standard deviation σ are respectively (ΜFa, σFa), (μFb, σFb), (μFc, σFc). As described above, the combined cumulative distribution function G of the processing time of the entire process can be expressed as G = Fa × Fb × Fc, and the average value μG and standard deviation σG of the cumulative distribution function can be obtained. Table 1 below shows the processing time and standard deviation of each of the single steps A, B, and C.

FIG. 12A is a diagram illustrating a cumulative distribution function indicating the processing capability of the single processes A to C and the entire process. In FIG. 12A, the distribution function of the single process before improvement is Fa (z), Fb (z), and Fc (z). The distribution function of the improved single process is FA (z), F B (z), and F C (z). The distribution function of the entire process in which FA (z) after improvement, Fb (z) before improvement, and Fc (z) are synthesized is indicated by Au. The distribution function of the overall process of synthesizing the improved FB (z) and the uncorrected Fa (z) and Fc (z) is indicated by Bup. The distribution function of the overall process of synthesizing FC (z) after improvement and Fa (z) and Fb (z) before improvement is indicated by Cup. “Synthesis” is a distribution function of the entire process in which Fa (z), Fb (z), and Fc (z) are synthesized.

FIG. 12B is a diagram illustrating a probability density function indicating the processing capability of the single processes A to C and the entire process. FIG. 12C is a diagram illustrating a probability distribution indicating the processing capability of the entire process after the improvement of the single process. The average value μ and the standard deviation σ of the processing time of each of the single processes A, B, and C are as shown in FIGS. 12A to 12C , and the average value of the processing time of the entire process (black dotted line in the figure) ( μG, σG) = (169, 39).

  Here, the improvement contribution to the whole process capacity when the single process capacity of any of the single processes A to C could be improved by 10% was evaluated. As a result, it becomes like Table 2 shown below.

  That is, if the average value μFa of the process time of the process A, which is a bottleneck process, is improved from 150 (s) to 135 (s), the average value μG of the process time of the entire process is changed from 169 (s) to 161 (s). The rate is 4.9%. When the average value μFb of the processing time of the process B is improved from 130 (s) to 117 (s), the average value μG of the processing time of the entire process is changed from 169 (s) to 164 (s), and the improvement rate is 3.9%. Become. When the average value μFc of the processing time of the process C is improved from 110 (s) to 99 (s), the average value μG of the processing time of the entire process is changed from 169 (s) to 167 (s), and the improvement rate is 1.1%. Become. Thus, the process capability of the entire process can be improved even in processes B and C that are not bottleneck processes.

  Moreover, when it is going to improve the processing time of the whole process, for example, 3%, the process A and the process B can improve 3% by raising the improvement rate 10%, respectively. It can be accurately evaluated that the improvement rate of 10% is impossible. By such an evaluation, when a change occurs in the single process capability, the capability change can be estimated in advance and reflected in the production plan, or a priority measure for improving productivity can be estimated in advance.

  As shown in Table 2, when the costs required for 10% capacity improvement in Process A and Process B are “100” and “50” respectively, priority is given to improving Process B, which is not a bottleneck process. Reasonable judgment is possible. For example, the single process to be improved is determined from the single process cost per 1% improvement rate of the entire process.

[5] Evaluation Device Hereinafter, a hardware configuration of an information processing device as an evaluation device for evaluating a manufacturing process having a plurality of steps will be described.

  FIG. 13 is a diagram illustrating an example of a hardware configuration of the information processing apparatus. As illustrated in FIG. 13, the information processing apparatus 500 includes a processing unit 510, a memory access control unit 516, a storage unit 520, a communication unit 530, a secondary storage device 540, a drive device 550, and an I / O controller 560. The information processing apparatus 500 is further connected to the input unit 570 and the display unit 580 via the I / O controller 560.

  The processing unit 510 is a device that loads the data from the storage unit 520 by executing the program 990 stored in the storage unit 520, calculates the loaded data, and stores the calculation result in the storage unit 520. The processing unit 510 is, for example, a CPU (Central Processing Unit). For example, the processing unit 510 executes the program 990 to generate a synthetic cumulative distribution and a probability density function as shown in FIGS. 8 to 12 and evaluate the manufacturing process.

  The memory access control unit 516 is a unit that loads data from the storage unit 520 to the processing unit 510, stores data received from the processing unit 510 in the storage unit 520, and the like.

  The I / O controller 560 is a device that controls connection between the processing unit 510 and other units. The I / O controller 560 operates according to a standard such as AGP (Accelerated Graphics Port) or PCI Express (Peripheral Component Interconnect Express), for example.

  The storage unit 520 is a device that stores data and a program 990. The processing unit 510 can access the storage unit 520 without going through the I / O controller 560. The storage unit 520 is, for example, a DRAM (Dynamic Random Access Memory). Data stored in the storage unit 520 will be described later with reference to FIG.

  The secondary storage device 540 is a device that can store the program 990 and data stored in the storage unit 520 and can retain information even when power is not supplied. The secondary storage device 540 is a disk array using a magnetic disk, an SSD (Solid State Drive) using a flash memory, or the like.

  The communication unit 530 is connected to the network 400 as a communication path, and transmits / receives data between the information processing apparatus 500 and another information processing apparatus connected to the network 400. The communication unit 530 is, for example, a NIC (network interface controller).

  The drive device 550 is a device that reads and writes a storage medium 590 such as a floppy (registered trademark) disk, a CD-ROM (Compact Disc Read Only Memory), a DVD (Digital Versatile Disc), and the like. The drive device 550 includes a motor that rotates the storage medium 590, a head that reads and writes data on the storage medium 590, and the like. Note that the storage medium 590 can store the program 990. The drive device 550 reads the program 990 from the storage medium 590 set in the drive device 550. The processing unit 510 stores the program 990 read by the drive device 550 in the storage unit 520 or the secondary storage device 540.

  The input unit 570 is a keyboard that outputs an input signal, which is text information such as characters and numbers, to the processing unit 510, a mouse for selecting an image displayed on the display unit 580, and the like.

  The display unit 580 is a display device such as a Liquid Crystal Display (LCD), for example. The processing unit 510 outputs a display drive signal for driving the display unit 580 to the display unit 580 via the I / O controller 560. The display unit 580 displays an image of the combined cumulative distribution and probability density function shown in FIGS. 8 to 11 according to the display drive signal.

  The information processing apparatus 500 can be connected to a data collection apparatus 600 that can grasp the processing time distribution of a single process via the network 400 and store single process processing capacity data 910 (described later) in the storage unit 520. Therefore, the information processing apparatus 500 can estimate the entire processing capability of the manufacturing process by offline simulation.

  Further, in the production process having a structure having a plurality of continuous multi-stage processes, the information processing apparatus 500 transmits a control signal to the control device 700 that performs processing line distribution by estimating the consistent capability of each line in advance. It can also be used for simple control.

[5.1] Data Stored in Storage Unit FIG. 14 is a diagram illustrating an example of data stored in the storage unit. The storage unit 520 stores single process throughput data 910, overall process throughput data 920, single process cost data 930, and a program 990.

The single-step process capability data 910 is data indicating the single-step process capability, such as histograms 201 and 202 shown in FIG. 4 and histograms 221 and 222 shown in FIG. It is measurement data of processing capacity.

  The overall process capacity data 920 is data generated by the processing unit 510 executing the manufacturing process evaluation process from the single process capacity process data 910. The overall process throughput data 920 is data for specifying the throughput of the overall process based on an average value and standard deviation such as the combined cumulative distribution and probability density function shown in FIGS.

  The single process cost data 930 is data indicating a correspondence relationship between the processing capacity of the single process and the cost data for improving the processing capacity of the single process.

FIG. 15 is a diagram illustrating an example of single process cost data. The unit process cost data 930 includes, for example, a process name column 931 and a cost column 933. In the process name column 931, for example, the name of the single process shown in FIG. 2 is registered, and in the cost column 933, an increase in the average value of the processing capability “5%, 10%, 15%, 20%,. ... ”, The cost corresponding to the increase in processing capacity for the process of the same entry input in the process name column 931 is registered. The NA in the cost column 933 indicates “not applicable”. In the relational expression column 935, an equation indicating the relation between the processing capability R of the single process and the cost is registered.

  When improving the processing capacity of the entire process, for example, the cost of increasing the processing capacity of the reheating process 30a by 30% and the cost of increasing the processing capacity of the rolling process 40a by 5% may be higher. In such a case, the processing unit 510 can improve the processing capability of the entire process at a low cost by increasing the processing capability of a single process that is less costly.

  The program 990 is a program for causing the processing unit 510 to perform manufacturing process evaluation processing.

[6] Manufacturing Process Evaluation Process Flow An example of the manufacturing process evaluation process will be described with reference to FIGS. 16 and 17. FIG. 16 is a diagram illustrating an example of a manufacturing process evaluation process. First, the processing unit 510 reads the single process capability data 910 stored in the storage unit 520 (S1001). The processing unit 510 multiplies the processing capabilities of the read single processes to generate overall process processing capacity data 920 (S1002) . The multiplication of the data is, for example, a synthesis of a probability function such as a cumulative distribution function or a probability density function shown in FIGS. Next, the processing unit 510 displays the entire process capacity data 920 on the display unit 580 (S1003). The overall process capacity data 920 for displaying an image on the display unit 580 is, for example, the overall process capacity shown in FIGS. The information processing apparatus 500 can present the average value and standard deviation of a single process that affects the processing capability of the entire process to the user by screen display.

Next, the processing unit 510 changes the processing capability of the single process (S1004). In this step, the user of the information processing apparatus 500 may change the average or standard deviation of the single process to be operated by looking at the overall process capacity data displayed on the screen in step S1003. In addition, the process may be automatically performed by the processing unit 510. If the processing unit 510 is carried out automatically, changing the capacity of a single step is shown in Figure 17 as S1101~S110 2.

  FIG. 17 is a diagram illustrating an example of changing the processing capability of a single process. As shown in FIG. 17, the processing unit 510 calculates the processing capacity of the entire process by increasing the average processing capacity of each single process (S1101). The process is, for example, the process described with reference to FIGS. 12A to 12C.

  The processing unit 510 determines a single process that contributes to the improvement of the processing capability of the entire process at the minimum cost (S1102). For example, the processing unit 510 refers to the relational expression column 935 of the single process cost data 930 to refer to the single process cost per 1% of the improvement rate of the entire process. Then, the processing unit 510 calculates the processing capability of a single process necessary for the processing capacity improvement rate of the entire process (for example, the improvement rate shown in FIG. 12C) and the single process cost at that time. In this way, the processing unit 510 determines a single process that contributes to improving the processing capability of the entire process at the minimum cost.

  In step S1005 shown in FIG. 16, the processing unit 510 calculates the overall process capacity data 920 using the single process capacity changed in S1004 (S1005), and the overall process capacity data 920 is displayed on the display unit 580. The screen is displayed (S1006). The overall process capacity data 920 for displaying an image on the display unit 580 is, for example, the overall process capacity shown in FIGS. The information processing apparatus 500 can present the average value and standard deviation of a single process that affects the processing capability of the entire process to the user by screen display.

  Next, the processing unit 510 calculates the processing capability of the entire process using the processing capability of the single process changed in S1004, and the processing capability of the entire process is desired in comparison with the overall process processing capability calculated in S1005. It is determined whether or not the processing capacity is reached. If the desired processing capability is reached (YES in S1007), the processing unit 510 ends the processing. If the desired processing capacity is not reached (No in S1007), the processing unit 510 repeats S1004. By such repeated processing, when the amount of processing capacity to be changed in S1004 is small, the desired overall processing capacity can be reached by gradually increasing the processing capacity to be changed in S1004.

10a Yard process 20a Cutting process 30a Reheating process 40a Rolling process 41a Rough rolling mill 42a Finishing mill 50a Cooling process 100 Manufacturing process 100a Continuous rolling process 400 Network 500 Information processing apparatus 510 Processing unit 516 Memory access control unit 520 Storage unit 530 Communication Unit 540 Secondary storage device 550 Drive device 560 I / O controller 570 Input unit 580 Display unit 590 Storage medium 910 Single process process capability data 920 Overall process process capability data 930 Single process cost data 990 program

Claims (9)

An evaluation device for a manufacturing process having a plurality of unit processes,
A storage unit for storing an average and a standard deviation of values indicating the processing capacities of the plurality of unit processes;
A processing unit for calculating a probability distribution function of the manufacturing process;
With
The processor is
Calculating a probability distribution function of each of the plurality of single steps using an average and a standard deviation of values indicating the processing capabilities of the plurality of single steps stored in the storage unit; Calculating the first probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions;
Accepting an input to change the average and / or standard deviation of values indicating the processing capability of one single step among the plurality of single steps to a value that improves the processing capability of the single step, and processing capability of the single step There comprising a probability distribution function of the modified average and / or standard deviation to calculate the probability distribution function of the previous SL one single step using a calculated pre SL one single step to enhance the plurality of Calculating the second probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the single process;
Evaluating the manufacturing process having the plurality of processes by comparing a first probability distribution function and a second probability distribution function of the manufacturing process;
An evaluation apparatus characterized by that.   The evaluation apparatus according to claim 1, further comprising: a display unit configured to display a first probability distribution function and a second probability distribution function of the manufacturing process. The storage unit stores single process cost data indicating a correspondence relationship between the processing capacity of the single process and cost data related to the improvement of the processing capacity,
The processing unit selects, based on the single unit cost data, a single step that is a target for changing an average and / or standard deviation of values indicating the processing capability to a value that improves the processing capability of the single step. The evaluation apparatus according to 1 or 2. A method for evaluating a manufacturing process having a plurality of single processes, wherein the information processing apparatus
Reading an average and standard deviation of values indicating the processing capability of each of the plurality of single steps from the storage unit of the information processing device, calculating a probability distribution function of each of the plurality of single steps, and Calculating the first probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the process;
Accepting an input to change the average and / or standard deviation of values indicating the processing capability of one single step among the plurality of single steps to a value that improves the processing capability of the single step, and processing capability of the single step There comprising a probability distribution function of the modified average and / or standard deviation to calculate the probability distribution function of the previous SL one single step using a calculated pre SL one single step to enhance the plurality of Calculating the second probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the single process;
An evaluation method comprising: evaluating a manufacturing process having the plurality of processes by comparing a first probability distribution function and a second probability distribution function of the manufacturing process.   The evaluation method according to claim 4, wherein the first probability distribution function and the second probability distribution function of the manufacturing process are displayed on a display unit of the information processing apparatus. The storage unit stores single process cost data indicating a correspondence relationship between the processing capacity of the single process and cost data related to the improvement of the processing capacity,
The information processing apparatus includes:
6. The single process, which is a target for changing the average and / or standard deviation of the value indicating the processing capability to a value that improves the processing capability of the single process, is selected based on the single cost data. Evaluation method. A program for evaluating a manufacturing process having a plurality of unit processes,
Reading an average and standard deviation of values indicating the processing capability of each of the plurality of single steps from the storage unit of the information processing device, calculating a probability distribution function of each of the plurality of single steps, and Calculating the first probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the process;
Accepting an input to change the average and / or standard deviation of values indicating the processing capability of one single step among the plurality of single steps to a value that improves the processing capability of the single step, and processing capability of the single step There comprising a probability distribution function of the modified average and / or standard deviation to calculate the probability distribution function of the previous SL one single step using a calculated pre SL one single step to enhance the plurality of Calculating the second probability distribution function of the manufacturing process by taking the product of the respective probability distribution functions of the single process;
Evaluating the manufacturing process having the plurality of processes by comparing a first probability distribution function and a second probability distribution function of the manufacturing process;
A program that causes an information processing apparatus to execute processing. Displaying the first probability distribution function and the second probability distribution function of the manufacturing process on the display unit of the information processing apparatus;
8. The program according to claim 7, which causes an information processing apparatus to execute processing. The storage unit stores single process cost data indicating a correspondence relationship between the processing capacity of the single process and cost data related to the improvement of the processing capacity,
Based on the single unit cost data, selecting a single step that is a target for changing the average and / or standard deviation of the value indicating the processing capability to a value that improves the processing capability of the single step,
The program according to claim 7 or 8, which causes the information processing apparatus to execute processing.

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