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Het aantal noodzakelijke waarnemingen bij toepassing van voortschrijdende steekproeven
Author(s) -
Enters J. H.
Publication year - 1949
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1949.tb00402.x
Subject(s) - mathematics , sampling (signal processing) , range (aeronautics) , statistics , table (database) , limit (mathematics) , quality (philosophy) , acceptance sampling , integer (computer science) , computer science , sample size determination , data mining , engineering , filter (signal processing) , computer vision , programming language , aerospace engineering , mathematical analysis , philosophy , epistemology
Summary The amount of inspection required in sequential sampling. Sequential sampling plans as developed by Barnard3)are most easy to apply in industrial quality inspection if (in Barnard's notation) the ‘hand cap’ H and the ‘penalty’ b are so adjusted that S min = H/n = a positive integer, n = b + 1 being the size of the successive samples. Sequential sampling plans of this type for which S min > 5 are not of great interest, because by their extreme severity they necessitate the inspection of too great a number of items. This paper presents the results of computations concerning the amount of inspection required by 4 Standard Sequential Sampling Plans, for which S min = 2, 3, 4 and 5 respectively.In table I the 0,05 producer's and consumer's risk points (p l and p 2 ) of the operating characteristics of these sampling plans are given for n = 10, 15, 20, …. 100. It may be shown that the products np 1 and np 2 tend to a limit as n →∞. When setting up a sequential inspection plan it is also necessary to be informed about the amount of inspection that will be involved. The average amount of inspection is a function of H, b, and pi ( the percetage of defectives in the batch ). But even when H, b, and p i are constant the actual amount of inspection in a particular case may differ considerably from the average and may vary within a wide range; hence it is of importance to know its probability distribution.Assuming a Poisson distribution for the number of defectives in a sample, the probability that a sequential sampling plan will necessitate a given amount of inspection will be a function of the product np i . For the four standard plans under consideration the 10, 20, 30, 40 and 50% points of these probability distributions are represented in figs 5–8. The sample sizes of single sampling plans possessing the same operating characteristics were found to be approximately 6 n , 12 n , 22 n, and 35 n respectively, and from figs 5–8 it will be seen that the actual amount of inspection in sequential sampling may considerably exceed the sample size of these equivalent single sampling plans, particularly in the region np 1 < np i < np 2.As these extreme values may occasionally lay a heavy load on the inspection department it is desirable to curtail sequential sampling by setting an upper limit to the number of items that are to be examined. The effect on the operating characteristics of truncating the standard sequential plans after S max samples of n items each have been drawn, is illustrated in figs 9–12. These show that if in the four cases under consideration S max is fixed at 6, 12, 22 and 35 respectively, the amount of information lost by truncating is relatively small. The resultant truncated standard sequential plans can be condensed into very simple precepts which are easily learnt by heart by the quality inspector and have proved of great practical convenience.