Integration of Production Planning, Maintenance Scheduling and Noncentral Chi-square Chart Parameters with Random Failures and Multiple Assignable Causes

This study presents an integrated model of three dependent concepts including production planning, maintenance scheduling, and statistical process monitoring (SPM) in order to improve both economic and statistical features of the production systems. To bring the proposed model closer to real applications, the possibility of occurring several types of assignable causes during the production cycle is taken into account. Besides, a noncentral chi-square chart is used for simultaneous monitoring of the process mean and variability parameters. Moreover, it is assumed that both time-to-failure and time-to-shift are Weibull distributed random variables. In other words, the system may suddenly fail and goes to an out-of-control condition with two different increasing rates including the failure rate function and the shift occurrence rate function. Hence, to improve the system reliability, a nonuniform sampling scheme is developed in which a same integrated shift occurrence rate is obtained for all intervals. The goal of the model is to minimize the expected total cost per time unit, subject to some statistical constraints. Ultimately, three comparative studies are given to demonstrate the efficiency of the proposed model. The first one indicates that a nonuniform sampling scheme reduces the expected total cost and the length of out-of-control period. The second one confirms that considering the system failure not only increases the length of in-control period but also improves the economic feature of the production system. The third one shows that using chi-square chart decreases the quality loss cost which in turn decreases the expected total cost.