Het aantal noodzakelijke waarnemingen bij toepassing van voortschrijdende steekproeven

J. H. Enters

Statistica Neerlandica, 1949, vol. 3, issue 5‐6, 179-200

Abstract: The amount of inspection required in sequential sampling. Sequential sampling plans as developed by Barnard 3) 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 Smin= H/n = a positive integer, n = b+1 being the size of the successive samples. Sequential sampling plans of this type for which Smin> 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 Smin= 2, 3, 4 and 5 respectively. In table I the 0,05 producer's and consumer's risk points (pl and p2) of the operating characteristics of these sampling plans are given for n = 10, 15, 20, …. 100. It may be shown that the products np1and np2tend 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 p i (the percetage of defectives in the batch). But even when H, b, and pi 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 npi. 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 6n, 12n, 22n, and 35n 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 np1

Date: 1949
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