Integrated economic design of quality control and maintenance management using CUSUM chart with VSIFT sampling policy

Abstract

Due to the close interrelation between statistical process control and maintenance management policy and the necessity of these two key tools in running a smooth production system, this paper presents an integrated economic model for joint optimization of quality control parameters and preventive maintenance policy with cumulative sum (CUSUM) control chart. In this model CUSUM chart is used to monitor both process mean and variance and joint average run length (ARL) is determined by combining mean and variance through absorbing Markov chain approach. Here the CUSUM chart is designed using variable sampling interval fixed time (VSIFT) sampling policy. In order to determine the in control and out of control chart for both mean and variance, Taguchi quadratic loss function and modified linear loss function are used respectively in this model. In this proposed model two types of maintenance policy i.e. imperfect preventive maintenance and minimal corrective maintenance have been considered. The proposed model determines the optimum values of eight test parameters (the sample size (n), the fixed sampling interval (h), the number of subintervals between two consecutive sampling times (ȵ), the control limit coefficient for CUSUM mean chart (k), the warning limit coefficient for CUSUM mean chart (w), the time interval of preventive maintenance (tpm), the control limit coefficient for CUSUM variance chart (k1) and the warning limit coefficient for CUSUM variance chart (w1)) so that expected total cost per unit time is minimized. A numerical example is presented to demonstrate the effectiveness of the test model in cost minimization. Nelder-Mead downhill simplex method and Genetic algorithm approaches are applied to search for the optimal values of the eight test parameters for the economic statistical design of VSIFT CUSUM charts. A sensitivity analysis has also been performed to observe the effect of different process parameters on total cost.