Robust Optimization of an Imperfect Process when the Mean and Variance are Jointly Monitored under Dependent Multiple Assignable Causes

Imperfect processes experience fault productions over time due to specific causes. Integrating the statistical process control, maintenance policy, and economic production quantity has led to more favorable results for the imperfect processes in literature. When monitoring a process, multiple assignable causes (ACs) may shift it to an out-of-control state. As indicated recently, if the interdependency of ACs is neglected, the total cost will be underestimated. Moreover, the mean and variance can simultaneously be affected by the occurrence of ACs. A non-central chi-square (NCS) chart was suggested for its decent performance against X-R chart in detecting the process disturbances and lowering quality loss cost. Besides, the increased occurrence rate of ACs over time leads to higher quality and maintenance costs. Employing a non-uniform sampling (NUS) scheme can significantly reduce costs. In the literature of modeling for imperfect processes under multiple ACs, all input parameters have always been fixed. The effectiveness of the models depends somewhat on the accurate estimates of these parameters. In reality, the estimation of parameters may be associated with uncertainty. For the first time, a robust design approach is proposed for designing NCS chart by considering the interval estimation of uncertain parameters. A particle swarm optimization (PSO) algorithm is used to present solutions. The proposed model is investigated through a real numerical example.