Signal detection for human error correction in quality control

Abstract

Acceptance sampling by attributes is now a universal and fundamental tool in statistical quality control. Among the various plans, single sampling has been recognized to offer significant cost savings and administrative simplicity. Single sampling by attributes is generally carried out or supervised by a human inspector. Unfortunately, human inspection error is another fact of life in industrial inspection. Two types of errors are possible. One is the Type 1 error, in which a good item is classified as defective (i.e., nonconforming); the other is the Type 2 error, in which a defective item is passed as good. Presently, little has been written on the effects of inspection errors on the outgoing quality and on how to compensate for these errors. The research objective of this paper is to show how a knowledge of the errors can be used to design compensating acceptance sampling plans for industrial quality control tasks. In contrast to the typical human inspection models in quality control, with fixed performance irrespective of incoming product quality, the model proposed here uses a form of signal detection theory (SDT) to predict inspector performance in order to improve system performance. The paper proposes the concept of lability, measured by a number ranging from 0 to 1, to characterize an inspector's ability to response to costs, rewards and probabilities involved in the inspection decision. This concept allows the modeling of both a constant-error inspector having a lability of 0, an SDT inspector having a lability of 1, and all those which fall within this range. Using this concept, the paper presents two models of the human inspector with considerations of: (a) constant Type 1 and Type 2 errors independent of the incoming fraction nonconforming, and (b) increasing Type 2 error and decreasing Type 1 error with increasing fraction nonconforming as specified by SDT. A general model covering these inspection errors is proposed. The paper shows that an imperfect inspector, who can detect the signal properly to adjust the decision criterion conservatively in the direction specified by the SDT, can compensate for the potential errors. A numerical example is proposed to illustrate the model application.