Economic design of Exponentially Weighted Moving Average (EWMA) chart with variable Sampling Interval at Fixed Times (VSIFT) scheme incorporating taguchi loss function

Abstract

Control charting is a graphical expression and operation of statistical hypothesis testing. Among various types of control chart Exponentially Weighted Moving Average (EWMA) chart is an widely used one and highly useful for not only detecting small changes in process parameters, but also in individual observation The objective of this thesis is to develop an economic statistical design of the exponentially weighted moving average (EWMA) chart using variable sampling intervals with sampling at fixed times (VSIFT) control scheme considering preventive maintenance and Taguchi Loss function to determine the values of the seven test parameters of the chart (i.e., the sample size, the fixed sampling interval, the number of subintervals between two consecutive sampling times, the warning limit coefficient, the control limit coefficient, and exponential weight constant and the time interval of preventive maintenance) such that the expected total cost per hour is minimized. It is because the performance of a production system depends on the breakdown-free operation of equipment and processes. Maintenance and quality control play an important role in achieving this goal. In addition to deteriorating with time, equipment may experience a quality shift (process moves to out-of-control state), which is characterized by a higher rejection rate and a higher tendency to fail the target value. That’s why another prime concern of the thesis is to consider an integrated influence of joint optimization of preventive maintenance interval and control parameters incorporating the Taguchi Loss function in the design of EWMA control chart with VSIFT scheme. A mathematical model is given to analyze the cost of the integrated model before the optimization algorithm approach is used to find the optimal values of seven variables (n, h, w, k, η, L and tpm) that minimize the hourly cost. Nelder-Mead downhill simplex method and Genetic algorithm approaches are applied to search for the optimal values of the seven test parameters for the economic statistical design of VSIFT EWMA chart, and then a hypothetical example and its solution are provided to have a better understanding about the demonstration of the proposed model.