Inspection Error Modelling and Economic Design of Sampling Plans Subject to Inspection Error.

Abstract

The purpose of this research was to develop methods of modelling inspection error problems in statistical quality control and to evaluate both the impact of these errors on statistical properties of single sampling plans and costs associated with an inspection process. An example data set was used throughout the research to demonstrate the methods developed. Theory of Signal Detection was used as a tool for evaluation of the performance of inspectors. It was shown that this theory can successfully be applied to estimate the two types of inspection error. These procedures are distribution-free and are based on fitting Y = f(X), the equation of Receiver Operating Characteristic (ROC) curve, in the form of a power function. A non-linear least squares routine was used to estimate the parameters of this curve. Using the example data, the relationship between the incoming fraction defective, p', and type I error probability was found to have the form of a power curve. A logarithmic function was shown to best describe the relationship between p' and type II error probability. Stepwise regression for the example data showed that a linear function describes the relationship between p' and the effective fraction defective, p(,e). The effect of r and om variations in p' on Outgoing Quality (OQ), as a measure of performance of single sampling plans, was investigated. It was shown that the mean and the variance of OQ are a function of the parameters of the distribution of p' and the choice of the sampling plan. It was also shown that if p' has a Beta distribution, then p(,e) will be a r and om variable with generalized Beta distribution. Inspection error was shown to have a deteriorating effect on the statistical properties of single sampling plans. The OC curve for inspection under error is flatter than that of error-free inspection, indicating a loss in sensitivity of the sampling plan. Economic consequences of committing inspection errors were evaluated for the case of p' treated as r and om variable with a Beta distribution. Software developed in this research enables practitioners to design optimal single sampling plans meeting desired statistical properties, and test the sensitivity of design parameters to the payoff matrix associated with an inspection process.