A GENERALIZED-MODEL FOR THE ECONOMIC DESIGN OF (X)OVER-BAR-CONTROL CHARTS FOR PRODUCTION SYSTEMS WITH INCREASING FAILURE RATE AND EARLY REPLACEMENT

This article generalizes the model for the economic design of xBAR-con trol charts of Duncan [4], starting from the more recent papers of Lor enzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in-control pe riods and provided uniform sampling schemes. Banerjee and Rahim [3], h owever, assumed a Weibull-distributed in-control period having an incr easing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in-control periods having an increasing failu re rate is assumed and the possibility of age-dependent repair before failure is considered. Several different truncated and nontruncated pr obability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncat ing a production cycle when it attains a certain age. Numerical exampl es are presented to support this proposition. Finally, the effect of m odel specification in the choice of failure mechanism is investigated. (C) 1993 John Wiley & Sons, Inc.