A dynamic economic model for an x¯-control chart design

Abstract

Parkhideh and Case (IIE Transactions, 21, 313–323 (1989)) developed an economic model for a dynamic x¯-control chart. In developing the model they considered six decision variables in their design methodology. It therefore became very complicated to obtain the optimal combination that resulted in the minimum loss-cost. This note proposes an alternative and simplified design methodology that reduces the number of design variables from six to three. The optimal values are obtained by imposing the following constraints. The optimal sampling interval hi (i =1,2,...) is chosen such that the integrated hazard rate over each sampling interval is constant. The optimal sample size ni (i = 1,2,...) is chosen such that the relative sample size per unit time during each sampling interval is constant. Analogously, the optimal control limit coefficient ki (i =1,2,...) is chosen so that the power of the control charts remains constant over each sampling interval. The process failure mechanism is assumed to follow a Weibull shock model and the product quality characteristic is considered to be normal. Computational experience indicates that the proposed dynamic nonuniform control chart design is much simpler and provides a lower cost than that of Parkhideh and Case's dynamic model.