AU3224999A - Method of estimating precision of apparatus - Google Patents

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 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. 19.99 3: 49PM LADAS PARRY NY 1 212 246 8959 NO. 0519 P. 2 MIETHOD 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 "instument" is the measurements made by the particular instrument being tested. The Grubbs Estimators procedure does not separate instrument precision from product variability, It provides an estimate only of over-all precision and the estimated precision is batch size specific, product variability specific, particle size distribution specific, anid 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 suiccessive 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 2 In Where Va variance of precision of a single member of a pair d =difference between members of pairs M~AY. 2 4. 19 9 9 3: 49PM~ LADAS PARRY NY 1 212 245 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 low of 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), as 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.

00 0 00..

0 MAY. 24. 19,99 3:150PM LADAS PARRY NY 1 212 246 8959 NO. 0519 P. 4 -3 L Cilco Test Batch No.1 As Received ash Stratumn Reading A Reading B RowSum RowSumz 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 7.2414 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 6.82 90 7.2253 14.0543 197.5233 46.6352 52.2050 14 8.8405 8.8031 17.6436 311.2966 78-1544 77.4946 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 42 Sum 150.6209 148.0789 298.6998 4287.9024 1096.3487 106.51 7- X 298.6998 yxa 2161.9401 MAY, 24. 19.99 3:15 0PM LADAS PARRY NY 1 212 246 8959 NO. 0519 P. -4- Cilco Test Batch No. As Received ash Stratum Reading A -Reading B RowSuni RowSum 2 A 2

B

2 (X X 89221.5705 (~X)fN =cf 2124.3231 RowSum 2 /2 cf Total 37.6170 ANALYSIS OF VARIANCE SS df Ms Estimate Between Stratum 19.628 1 20 0.9814 Vi-I2Vpd Within Stratum 17.9889 21 0.8566 Vi 10 Total 37.6170 41 0.1248 2Vpd 0.0624 V pdj 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. Tie 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.

MAY. 24. 19,99 3:15 0PM LADAS PARRY NY 1 212 246 8959 NO. 0519 P. 6 *4 4.

4* 4 *4 4 4 4 4. 4@ 4* 4 *4 4 4*4 4 4 4 *44* Replicate Observations Within Stratum Variances As Rc'd As Rec'd Ash Sul 1 0.8566 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 11 1.4831 0.0392 12 0.9257 0.0282 13 1.0058 0.0247 14 1.4279 0.0372 1s 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 0.025 1 23 0.5937 0.0285 24 0.7421 0.0199 0.9272 0.0233 26 0.6296 0,0420 t MY. 2 4. 19199 3:15OPM LADAS PARRY NY 1 212 246 8959 NO. 0519 P. 7 -6- Replicate Observations Within Stratum Variances As Rc'd As Rec'd Ash Sul 27 1.3545 0,0264 28 0.5717 0.0499 29 1.0281 0.0344 0.5880 0.0 194 Max 1.4831 0.0499 Min 0.3843 0.0111 Avg 0.8404 0.0252 4 *5 S *5 SS S *9

S.

S.

S. 50.5 4* S. S 4

S

*5 S. S 5* 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 expresed in terms of measurement precision. Applying the GIrubbs Estimators 15 Procedure to exactly the same data, the following results were obtained.

Grubbs Statified Estimators Replicate F Determination Observations Ratio As Rec'd Ash 0.311 0.142 4.80 As Rec'd. 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 (4)

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 Where Va variance of precision of a single member of a pair d difference between members of pairs n number of differences.

4. A method of estimating the precision of an apparatus substantially as hereinbefore described. C* Dated 25 May, 1999 ~Gregory Gould Patent Attorneys for the Applicant/Nominated Person SPRUSON FERGUSON