Statistically constrained economic design of X ¯ control chart with Weibull in-control time for processes subject to multiple assignable causes

Purpose: The purpose of this paper is to develop an economic statistical design based on the concepts of adjusted average time to signal (AATS) andANFfor<m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mover accent="true"><m:mi>X</m:mi><m:mo>¯</m:mo></m:mover></m:math>control chart under a Weibull shock model with multiple assignable causes. Design/methodology/approach: The design used in this study is based on a multiple assignable causes cost model. The new proposed cost model is compared with the same cost and time parameters and optimal design parameters under uniform and non-uniform sampling schemes. Findings: Numerical results indicate that the cost model with non-uniform sampling cost has a lower cost than that with uniform sampling. By using sensitivity analysis, the effect of changing fixed and variable parameters of time, cost and Weibull distribution parameters on the optimum values of design parameters and loss cost is examined and discussed. Practical implications: This research adds to the body of knowledge relating to the quality control of process monitoring systems. This paper may be of particular interest to practitioners of quality systems in factories where multiple assignable causes affect the production process. Originality/value: The cost functions for uniform and non-uniform sampling schemes are presented based on multiple assignable causes withAATSandANFconcepts for the first time.