Economic Design of A Dynamic CCC – r Chart for High-Yield Processes

Abstract

Recently, Ohta et al. [Quality and Reliability Engineering International 17: 439-446, 2001] have studied the economic design of CCC(Cumulative Count of Conforming)-r charts for high-yield processes assuming a fixed hazard rate. Generally, however, the hazard rate is varying over time. With the ageing of a process, the hazard rate gets first gradually smaller, while during the last stage of the wear-out process, the hazard rate increases. For such processes, the Weibull distribution is used to model the circumstances. In this paper, we discuss an economic design of a dynamic CCC – r chart with time-varying parameters. Concretely, we propose a process control model for a Weibull distributed-shock model and determine the initial values and dynamic decision rules for the time-varying parameters of the CCC–r chart, that is, the required number of nonconforming observations r, the sampling interval h, and the lower control limit LCL maximizing the expected profit per unit time derived from the process. Finally, we compare the profits obtained applying a dynamic CCC – r chart with those obtained with a traditional static CCC – r chart.