# Estimation of Batch Quality

Estimation of Batch Quality October, 1944 AIRCRAFT ENGINEERING Workshop and Production Section By T. J. Lunt thought that it will be high enough for practical upper and lower limits within which the true value CERTAIN number of defectives, c, is observed purposes. is likely to lie. in a sample of n articles drawn at random Suppose c defectives are found in a random sample As an example, suppose that we find 1 defective from a large batch. Nothing else is known of n pieces. In the alignment chart giving a central in a sample of 50 then the values obtained from the about the batch. What inferences can be drawn as alignment charts are: estimate of batch quality, join the points corre­ to the true but unknown proportion Q of defectives sponding to these values of n and c on the appro­ in the lot? In his book An Engineers' Manual of priate scales. This joining line will cut the third scale Statistical Methods, Col. L. E. Simon gives several charts which help to answer this question. The basic at a point which' gives the estimate Qm required. The estimate will be too high as often as it is too low. assumption made is that before sampling one The probability is therefore ·9 that the true value In other words, the probability of the true value "lot-fraction-defective" is as likely as another. The of fraction defective is greater than ·0105 but less being higher than this value, Qm, is 1/2. charts are based on the incomplete β-function ratio. than ·074. If these are too widely spaced, then They make no assumption of homogeneity. From Using the other chart, two other values are ob­ larger samples must be taken. It is clear that the these charts the accompanying alignment charts tained. If we denote these by Q , Q , the probablity only way in which good estimates can be obtained L u have been constructed. The degree of accuracy is that the true value is less than Q is ·1, and the when there is only the sample on which to base such probability that it is less tha n Q is ·9. Thus we get estimates is to take a larger sample. not, of course, as high as in Simon's charts, but it is http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aircraft Engineering and Aerospace Technology Emerald Publishing

# Estimation of Batch Quality

, Volume 16 (10): 1 – Oct 1, 1944
1 page      /lp/emerald-publishing/estimation-of-batch-quality-DiGkHdRNYI
Publisher
Emerald Publishing
ISSN
0002-2667
DOI
10.1108/eb031179
Publisher site
See Article on Publisher Site

### Abstract

October, 1944 AIRCRAFT ENGINEERING Workshop and Production Section By T. J. Lunt thought that it will be high enough for practical upper and lower limits within which the true value CERTAIN number of defectives, c, is observed purposes. is likely to lie. in a sample of n articles drawn at random Suppose c defectives are found in a random sample As an example, suppose that we find 1 defective from a large batch. Nothing else is known of n pieces. In the alignment chart giving a central in a sample of 50 then the values obtained from the about the batch. What inferences can be drawn as alignment charts are: estimate of batch quality, join the points corre­ to the true but unknown proportion Q of defectives sponding to these values of n and c on the appro­ in the lot? In his book An Engineers' Manual of priate scales. This joining line will cut the third scale Statistical Methods, Col. L. E. Simon gives several charts which help to answer this question. The basic at a point which' gives the estimate Qm required. The estimate will be too high as often as it is too low. assumption made is that before sampling one The probability is therefore ·9 that the true value In other words, the probability of the true value "lot-fraction-defective" is as likely as another. The of fraction defective is greater than ·0105 but less being higher than this value, Qm, is 1/2. charts are based on the incomplete β-function ratio. than ·074. If these are too widely spaced, then They make no assumption of homogeneity. From Using the other chart, two other values are ob­ larger samples must be taken. It is clear that the these charts the accompanying alignment charts tained. If we denote these by Q , Q , the probablity only way in which good estimates can be obtained L u have been constructed. The degree of accuracy is that the true value is less than Q is ·1, and the when there is only the sample on which to base such probability that it is less tha n Q is ·9. Thus we get estimates is to take a larger sample. not, of course, as high as in Simon's charts, but it is

### Journal

Aircraft Engineering and Aerospace TechnologyEmerald Publishing

Published: Oct 1, 1944

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