Economic and economic statistical designs of <span style="text-decoration: overline">X</span> control charts under Burr XII shock model

Abstract

The optimal values of economic and economic statistical designs of -X control charts are influenced by a model used for distribution of occurring time of assignable causes or shock model. So far, only a small number of failure time distributions such as exponential, gamma and Weibull with fixed or increasing hazard rates have been used as shock models. However, from both theoretical and practical aspects, processes under study may not have fixed or increasing hazard rates. A proper alternative is the Burr XII distribution which its hazard rate can be fixed, increasing, decreasing, single mode or even U-shaped. In this research paper, economic and economic statistical designs of -X control charts under the Burr XII shock models were proposed and constructed. The obtained design models have been implemented by a numerical example and a sensitivity analysis were conducted.