Probabilistic and membership approaches in the construction of control charts for linguistic data

Abstract

Two approaches for constructing control charts for quality assurance when the observations are in the form of linguistic data are presented. Both approaches are based on fuzzy set theory and use fuzzy subsets to model the linguistic terms used to describe product quality. They differ in the interpretation of the control limits and in the procedure used to reduce the fuzzy subsets to scalars for determining the chart parameters. The results obtained with simulated data suggest that, on the basis of sensitivity to process shifts, the control charts for linguistic data perform better than conventional p control charts. The number of linguistic terms used in classifying the observations was found to influence the sensitivity of these control charts. The transformation method used to obtain the representative values and the amount of fuzziness do not seem to affect the performance of either type of control charts.     

Optimal policy for imperfect inspection in discrete time

Abstract

The problem of finding the optimal inspection interval for a fallible system that operates in discrete time when inspection is subject to errors was addressed. A Markov chain model of the system state was developed to formulate the objective function, which is the minimum expected total cost per lime unit. A numerical search procedure was used to find local minima for a representative range of parameter values. The objective function turned out to be quite insensitive to deviations in the inspection interval in the neighbourhood of the minimum, so an approximate method based on curve fitting was developed and tested, yielding good results in the representative range.