Acceptance sampling by exponential smoothing

Abstract

Acceptance sampling by exponential smoothing presents a concept whereby each lot is accepted or rejected through interrogation of the current lot and all prior lots submitted. The number of defectives of a lot, in conjunction with historical results, is transformed to a quality index by simple exponential smoothing, utilizing larger values of the smoothing constant to lend more weight to the quality of current lots inspected. This quality index is compared with a predetermined threshold index to determine if the lot is to be accepted or rejected. This quality index is then retained to be used as the historical quality information to be applied to the quality index of the next lot.

An important feature of the exponential smoothing technique is that an attribute quality can be transformed easily into a measurement quality. This allows the user to select an acceptance quality level at any producer's risk. Further, the OC curve can be forced through any other point by selecting the proper smoothing constant.

The obvious limitation in the use of this technique is that the transformed variable—quality index—does not follow a known statistical distribution. This necessitates that simulation methods be used on the digital computer to derive OC curves for specified values of n and α. However, for the conditions of large n and large α, the transformed random variable is approximately normally distributed, giving an approximate normal solution for a plan of interest.

It is anticipated that attribute acceptance sampling utilizing any quality index other than proportion defective will be viewed with suspicion by the average user. In this sense the exponential smoothing concept violates a basic precept of Dodge (1955) in that an effective plan must be a simple plan that the non-theoretician can understand and apply with reasonable confidence. However, the flexibility in the selection of OC curves, the utilization of prior lot information, and the ease of application dictate that the concept be given serious consideration as a cost reduction tool in acceptance sampling.