Single Sampling Schemes

When a MIL..STD-lOSD sampling scheme is used for a long period, some lots will be subjected to normal, some to reduced, and some to tightened inspection. This paper provides for several single sampling plans and various quality levels,tthe expected fraction oflots rejected,the expected sample size per lot, and the expected number oflots to be processed before sampling inspection must be discontinued. Equations are given to calculate the long term c6st of sampling inspection using these expected values and appropriate cost parameters. • Many private and government purchasers of manufactured products require that each lot submitted be subjected to sampling inspection by attributes. Lots which contain too many defectives may be returned to the manufacturer, purchased with a price concession, subjected to 1 ()(J}& screening, or scrapped. Clearly, there are substantial costs involved for inspection, disposal of rejected lots, and for the occurrence of defectives in accepted lots. Dodge and Romig {2) have devised a set of attributes sampling plans based upon minimum cost, assuming a desired incoming quality. Hald (5) has greatly enlarged this idea, and developed plans which minimize cost for any prior distribution. However, neither the Dodge-Rornig nor the Hald approach have achieved widespread popularity. Attributes sampling in the western world is dominated by the set of plans designated MIL-STD-105D {6) first published by the Department of Defense in 1963. The MIL-STD-1050 plans are not based upon cost concepts. Instead, the plans are indexed by lot size and by a_nurnber designated "acceptable quality level." The AQL is specified by the consumer, and is defined as the percent defective which will lead to a high probability of acceptance. This probability of acceptance is not a constant, but varies with lot size and AQL. The domain for probability Received February 1973; revised April 1974. June 1974, AilE TRANSACTIONS of accep'tance in the MIL-STD-105D plans is about 0.890.99. Each plan in MILSTD-105D provides a sample size, n, and an acceptance number, c, to be used for "normal" inspection of a lot. If c, or fewer defectives are found in the sample, the lot is accepted. The user is required to keep a historical r~cord of lot-by-lot experience. Criteria are presented for an alteration of the values of nand/or c when the experience over several lots shows either unusually good or unusually bad quality. The®les are as follows (6): 1. A switch from the normal values of nand c to "reduced"' inspection is permissible when a. Ten consecutive lots have been accepted. b. The total number of defectives in the ten lots does not exceed a critical value supplied in Table VIII of MIL-STD-105D. c. Production is continuous. d. Reduced inspection is considered desirable by the responsible authority. Under reduced inspection, n is substantially decreased to a value, nR. Two numbers, c and r(>c) are supplied. Lots are accepted if the number of defectives is less than r. However, if a lot has more than c defectives, normal inspection must be resumed on the next lot.