Economic design of exponentially weighted moving average chart with variable sampling interval at fixed times scheme incorporating Taguchi loss function

Abstract

A control chart is a graph used to study how process changes over time. The exponentially weighted moving average (EWMA) chart is highly useful for not only detecting small changes in process parameters but also in inspecting individual unit observations. The objective of this paper is to develop an economic statistical design of the exponentially weighted moving average (EWMA) chart using variable sampling interval at fixed times (VSIFT) control scheme considering preventive maintenance and Taguchi loss function to determine the values of the seven test parameters (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, exponential weight constant and the time interval of preventive maintenance) such that the expected total cost per hour is minimised. A mathematical model is developed to analyse the cost of the integrated model. 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 Nelder-Mead downhill simplex performed better than genetic algorithm. A hypothetical example and its solution are provided to have a better understanding about the demonstration of the proposed model.