AU764823B2 - Method of estimating precision of apparatus - Google Patents
Method of estimating precision of apparatus Download PDFInfo
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- AU764823B2 AU764823B2 AU32249/99A AU3224999A AU764823B2 AU 764823 B2 AU764823 B2 AU 764823B2 AU 32249/99 A AU32249/99 A AU 32249/99A AU 3224999 A AU3224999 A AU 3224999A AU 764823 B2 AU764823 B2 AU 764823B2
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- precision
- variance
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- 238000000034 method Methods 0.000 title claims description 14
- 238000004364 calculation method Methods 0.000 claims description 3
- 238000012360 testing method Methods 0.000 description 11
- 238000005259 measurement Methods 0.000 description 6
- NINIDFKCEFEMDL-UHFFFAOYSA-N Sulfur Chemical compound [S] NINIDFKCEFEMDL-UHFFFAOYSA-N 0.000 description 3
- 239000005864 Sulphur Substances 0.000 description 2
- 238000000540 analysis of variance Methods 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 238000010224 classification analysis Methods 0.000 description 1
- 238000013145 classification model Methods 0.000 description 1
- 239000003245 coal Substances 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000013401 experimental design Methods 0.000 description 1
- 238000002156 mixing Methods 0.000 description 1
- 239000002245 particle Substances 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 229910052717 sulfur Inorganic materials 0.000 description 1
- 239000011593 sulfur Substances 0.000 description 1
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Description
S F Ref: 465934
AUSTRALIA
PATENTS ACT 1990 COMPLETE SPECIFICATION FOR A STANDARD PATENT
ORIGINAL
Name and Address of Applicant: Actual Inventor(s): Address for Service: Invention Title: Gregory Gould 30 Clairmont Avenue Thornwood New York 10594 UNITED STATES OF AMERICA Gregory Gould Spruson Ferguson, Patent Attorneys Level 33 St Martins Tower, 31 Market Street Sydney, New South Wales, 2000, Australia Method of Estimating Precision of Apparatus The following statement is a full description of this invention, including the best method of performing it known to me/us:- 5845 MAY. 24. 1999 3:49PM LADAS PARRY NY 1 212 246 8959 NO. 0519 P. 2 METHOD OF ESTIMATING PRECISION OF APPARATUS With the development of apparatus enabling automatic analysis of various substances, such as the nuclear analyzer, there is a need for estimating the precision of such apparatus. The current accepted manner of doing this is the labor intensive batch mode bias test using a three instrument Grubbs Estimators experimental design to obtain estimates of instrument precision and bias.
This test is based on the laws of propagation of error. By making simultaneous measurements with three "instruments" and appropriate mathematical manipulation of sums and differences of these measurements, one can obtain estimates of the variance of measurement precision associated with each of the three "instruments" for the batch size used for the test. Two of the "instruments" comprise instruments made by conventional sampling and testing and the third "instrument" is the measurements made by the particular instrument being tested. The Grubbs Estimators procedure does not separate instrument precision from product variability.
15 It provides an estimate only of over-all precision and the estimated precision is batch size specific, product variability specific, particle size distribution specific, and bulk density specific. This approach also lacks instancy and immediacy of results.
The applicant's method of estimating the precision of an apparatus avoids the drawbacks of the Grubbs Estimators test technique and provides 20 additionally an estimate of the fourth source of variance, namely, product variability.
This is accomplished by taking successive pairs of information obtained by the analyzer and calculating the index of provision from said pairs. As used herein said successive pairs of information shall include overlapping or non-overlapping data, and each member of said successive pairs of information may consist of various combinations (such as averages, medians, mean squares, and the like) of multiple data items.
This calculation may be performed in accordance with the following formula: Va d In Where Va variance of precision of a single member of a pair d difference between members of pairs MAY. 24. 1999 3:49PM LADAS PARRY NY 1 212 246 8959 NO. 0519 P. 3 -2n number of differences.
The invention will be described with respect to the estimation of the precision of an on-line nuclear analyzer. However, it should be understood that the invention is applicable to any piece of apparatus which produces a continuous stream of information. This perhaps can best be illustrated by an application of the method to the estimation of the precision of a gamma metrics model 1812 C on-line nuclear analyzer installed in the coal blending facility of Central Illinois Lighting Company.
By practicing the method of the present invention, precision estimates of the measurements made by the on-line nuclear analyzer, and estimates of product variability (variance) on-the-fly in real time from the information generated by the analyzer. It is also possible to make continuous assessment of bias relative to physical samples collected by a mechanical sampling system. In the case of the Central Illinois Lighting Company (Cilco), the batch-mode bias test was comprised of thirty batches. The batches averaged slightly over 42 minutes of flow and ranged 15 from a lowof 36 minutes to a high of 50 minutes. Table I shows what the flow in terms of one minute ash observations look like during the Cilco test (see column 1), Sas well as a classical single classification Model I Analysis of Variance calculation of the estimated one minute index of precision expressed in terms of the statistical parameter known as a variance.
o MAY. 24. 19.99 3:150PM LADAS PARRY NY- 1212 246 8959 NO. 0519 P. 4 3- Cilco Test Batch No.1 As Received ash Stratum. Reading A Reading B RowSum RowSum 2 A 2 B 2 1 8.1256 7.1 125 15.2381 232.1997 66.02538 50.58766 2 8.3013 6.0229 .14.3242 205.1827 68.9116 36.2753 3 7.5154 7.8518 15.3672 236.1508 56.4812 61.6508 4 7.7123 7.4551 15.1674 230.0500 59.4796 55.5785 6.4899 6-3351 12.8250 164.4806 42.1188 40.1335 6 7.8400 7.7831 15.6231 244.0813 61.4656 60.5766 7 5.4034 6.6789 12.0823 145.9820 29-1967 44.6077 8 7.2469 6.9645 14-2114 201.9639 52.5176 48.5043 9 8.1800 7.1952 15.3752 236.3968 66.9124 51.7709 10 712414 8.0728 15.3142 234.5247 52.4379 65.1701 11 6.9948 4.6114 11.6062 134.7039 48.9272 21.2650 12 7.2861 7.1645 14.4506 208.8198 53.0873 51.3301 13' 6.8290 7.22S3 14.0543 197.5233 46.6352 52.2050 14 8.8405 8.8031 17.6436 311.2966 78.1544 77.4946 15 5.9030 7.6675- 13.5705 .184.1585 34.8454 58.7906 16 7.9576 6.3456 14.3032 204.5815 63.3234 40.2666 17 6.1167 8.9458 15.0625 226.8789 37.4140 80.0273 18 7.4928 5.2926 12.7854 163.4665 56.1421 28.0116 19 6.1381 7.2661 13.4042 179..6726 37.6763 52.7962 6.4099 7.0312 13.4411 180.6632 41.0868 49.4378 21 6.5962 6.2539 12.8501 165.1251 43.5099 39.1113 n 21 N Sum 150.6209 148.0789 298.6998 4287.9024 1096.3487 1065.5914 Z X 298.6998 V 2161'.9401.
MAY. 24. 1999 3: 50PM LADAS PARRY NY 1 212.246 8959 NO. 0519 P. a a a. a.
a Cilco Test Batch No.1 As Received ash Stratum Reading A Reading B RowSumn RowSUM 2 A 2 B2 (X XY 89221.5705
SX)
2 /N cf 2124.3231 RowSum 2 /2 cf 19-6281_____ Total 37.6170 ANALYSIS OF VARIANCE SS df Ms Estimate Between Stratum 19.6281 .20 0.9814 Vi-t2Vpd Within Stratum 17.9889 21 0.8566 Vi 10 Total 3.70 41 0.1248 2Vpd 0.0624 Vpd 15 While the average was around the range varied from around 4% to 11%.
Taking this range to represent 4 standard deviations, the coefficient of variation would be about 25%. Referring to Table 1, using 30 batches with the analyzed data sorted into 2.
minute strata of adjoining 1 minute readings for each of the determinations "as received ash" and "as received sulphur" arc set forth. Next, a single classification analysis of variance was performed. on each batch as shown in Table I from which was obtained the within strata valance. The within'strata variance is a pooled variance, the average variance estimate of a single member of a pair for that batch. For batch number, 1, this value for as received ash was 0.8566.
Table 2 is a tabulation of the estimates of instrument precision variance for each of the 30 batches for ash and sulphur on an as received basis.
1MAY. 24. 19,99 3:50PM LADAS PARY NY 1 212 246 8959 NO. 0519 P. 6 a.
a a.
a.
a a.
a
A
a a a Replicate Observations Within Stratum Variances As Rc'd As Rec'd Ash Sul 10.8566 0.0210 2 1.0060 0.0201 3 0.8535* 0.0191 4 0.6141 0.0261 0.6815 0.0273 6 0.6470 0.0162 7 0.6306 0.0256 8 0.9097 0.0184 9 1-1224 0-0245 0.9097 0.0199 I11 1.4831 0.0392 12 0.9257 0.0282 13 1.0058 0.0247 14 1.4279 0.0372 is 1.0612 0.0240 16 0.3843 0.0342 17 0.7617 0.0167 18 0.4258 0.0298 19 0.8091 0.0111 0.7882 0.01 12 21 0.6335' 0.0137 22 0.8406 0.0251 23 0.5937 0.0285 24 0.7421 0.0199 0.9272 0.0233 26 0.6296 0,0420 'MAY. .24. 19.9 9 3:150PM LADAS PARRY NY 1 212 246 8959 NO. 0519 P. 7 -6a a.
a.
a. a a a a a a a.
a a .a Replicate Observations Within Stratum Variances As Rc'd As Ree'd Ash Sul 27 1.3545 0.0264 28 0.5717 0.0499 29 1.0281 0.0344 0.5880 0.0194 max 1.4831 009 Min 0.3843 0.0111 Avg 0.8404 0.0252 The grand average at the foot of each column is the full test estimate of the instrument average precision variance of a single member of a pair. A comparison with the values obtained by the Grubbs Estimators immediately shows the implication of applicant's invention. expressed. in terms of measurement precision. Applying the Grubbs Estimators 15 Procedure to exactly the same data, the following results were obtained.
Grubbs Statified Estimators Replicate F Determination Observations Ratio As ecdAsh 0.311 0.142 4.80 As Rec Sulfur .0.034 0.025 1.85 it is noted that on-average of the Grubbs Estimators test results might be expected to yield variance estimates as much as 300% larger than that obtained by applicant's invention.
Claims (3)
1. A method of estimating the precision of an apparatus that generates a continuous stream of information, internally or externally, which comprises dividing said information into successive pairs of said information and then calculating the index of precision, and then evaluating said index of precision against a benchmark such as a standard value, a specification, or a contract requirement.
2. The method of claim 1, wherein the apparatus is an on-line nuclear analyzer.
3. The method of claim 2, where the calculation is performed in accordance with the following formula: Va= d 2 fn Where Va variance of precision of a single member of a pair d difference between members of pairs n number of differences. S4. A method of estimating the precision of an apparatus substantially as hereinbefore described. S *o Dated 25 May, 1999 Gregory Gould Patent Attorneys for the Applicant/Nominated Person SPRUSON FERGUSON i. I I .I II
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| AU32249/99A AU764823B2 (en) | 1999-05-26 | 1999-05-26 | Method of estimating precision of apparatus |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| AU32249/99A AU764823B2 (en) | 1999-05-26 | 1999-05-26 | Method of estimating precision of apparatus |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| AU3224999A AU3224999A (en) | 2000-11-30 |
| AU764823B2 true AU764823B2 (en) | 2003-08-28 |
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Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| AU32249/99A Ceased AU764823B2 (en) | 1999-05-26 | 1999-05-26 | Method of estimating precision of apparatus |
Country Status (1)
| Country | Link |
|---|---|
| AU (1) | AU764823B2 (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5072387A (en) * | 1989-12-20 | 1991-12-10 | Chevron Research And Technology Company | Method for determining a transit time for a radioactive tracer |
| US5492547A (en) * | 1993-09-14 | 1996-02-20 | Dekalb Genetics Corp. | Process for predicting the phenotypic trait of yield in maize |
| US5864633A (en) * | 1996-05-17 | 1999-01-26 | Therma-Wave, Inc. | Method and apparatus for optical data analysis |
-
1999
- 1999-05-26 AU AU32249/99A patent/AU764823B2/en not_active Ceased
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5072387A (en) * | 1989-12-20 | 1991-12-10 | Chevron Research And Technology Company | Method for determining a transit time for a radioactive tracer |
| US5492547A (en) * | 1993-09-14 | 1996-02-20 | Dekalb Genetics Corp. | Process for predicting the phenotypic trait of yield in maize |
| US5492547B1 (en) * | 1993-09-14 | 1998-06-30 | Dekalb Genetics Corp | Process for predicting the phenotypic trait of yield in maize |
| US5864633A (en) * | 1996-05-17 | 1999-01-26 | Therma-Wave, Inc. | Method and apparatus for optical data analysis |
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| Publication number | Publication date |
|---|---|
| AU3224999A (en) | 2000-11-30 |
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