Economic design of x̄-control charts with Weibull in-control times when there are multiple assignable causes

Abstract In this article, we present an economic design of x-control charts with a Weibull distributed process-failure mechanism when there is an occurrence of possible multiple assignable causes and assume that once an assignable cause occurs, no further assignable causes will occur. A cost model based on the variable sampling intervals is formulated and analyzed. Optimal values of the design parameters including the sample size, the sampling intervals, and control limit coefficient are solved by minimizing the expected total cost per unit time, based on the varieties of combinations of Weibull parameters. Comparisons between a multiplicity-cause model and a single-cause model are performed under both having same time and cost parameter and numerical results show that the former provides a lower loss-cost than the latter when the process has an increasing hazard rate.