Effects of non-normal quality data on the integrated model of imperfect maintenance, early replacement, and economic design of $${\bar{X}}$$-control charts

Abstract

The quality characteristic of a product for designing a control chart is commonly assumed to be normally distributed. However, this may not be reasonable in many practical applications. This study investigates the effects of non-normality data on the economic design of $${\bar{X}}$$ -control charts for systems under imperfect maintenance and the possibility of age-dependent repair before failure. These preventive maintenance policies increase the reliability of a system by reducing the shift rate to the out-of-control state of the process. A generalized economic model of the joint optimization problem is adopted for the Burr distributed quality data to derive the optimal design parameters of the integrated model under non-normality; i.e., the maintenance level, the replacement time, the sample size, the sampling intervals, and the control limits coefficient. Numerical examples reveal that the choice of quality characteristic distribution significantly affects the optimal design parameters of the integrated model. Furthermore, the higher maintenance levels reduce the quality control costs in non-normal cases similar to normal traditional approach.