Constrained optimal design of X̅ control chart with multiple assignable causes under Burr XII failure mechanism

Purpose The purpose of this paper is to develop a cost model by the variable sampling interval and optimization of the average cost per unit of time. The paper considers an economic–statistical design of the X control charts under the Burr shock model and multiple assignable causes were considered and compared with three types of prior distribution for the mean shift parameter. Design/methodology/approach The design of the modified X chart is based on the two new concepts of adjusted average time to signal and average number of false alarms for X control chart under Burr XII shock model with multiple assignable causes. Findings The cost model was examined through a numerical example, with the same cost and time parameters, so the optimal of design parameters were obtained under uniform and non-uniform sampling schemes. Furthermore, a sensitivity analysis was conducted in a way that the variability of loss cost and design parameters was evaluated supporting the changes of cost, time and Burr XII distribution parameters. Research limitations/implications The economic–statistical model scheme of X chart was developed for the Burr XII distributed with multiple assignable causes. The correlated data are among the assumptions to be examined. Moreover, the optimal schemes for the economic-statistic chart can be expanded for correlated observation and continuous process. Practical implications The economic–statistical design of control charts depends on the process shock model distribution and due to difficulties from both theoretical and practical aspects; one of the proper alternatives may be the Burr XII distribution which is quite flexible. Yet, in Burr distribution context, only one assignable cause model was considered where more realistic approach may be to consider multiple assignable causes. Originality/value This study presents an advanced theoretical model for cost model that improved the shock model that presented in the literature. The study obviously indicates important evidence to justify the implementation of cost models in a real-life industry.