Approximate average run length and its eigenvalue problem on exponentially weighted moving average control chart: an economic application

Abstract

The average run length (ARL) is a criterion for measuring the efficiency of a control chart conventionally computed based on the assumption of type I errors for the in-control process and type II errors for the out-of-control process. Still, the eigenvalue approach for the ARL by controlling the direction on its eigenvector is a good alternative. Thus, the objectives of this research are to evaluate the ARL based on the eigenvalue approach on an exponentially weighted moving average (EWMA) control chart and to apply ARL computation to the inflation rate data of the Thai economy. The methods used for ARL evaluation in a comparative study are based on integral equations, a numerical method, the eigenvalue approach, parameter estimation, and fitting of the probability density function. The findings show that the distinct eigenvalues of the ARL on an EWMA control chart monitoring the Thai economy inflation rate with a symmetric kernel are all real and the maximum eigenvalue returns the maximum values of ARL0 (the in-control process) and ARL1 (the out-of-control process). Moreover, an eigenvalue close to zero returns ARL0 and ARL1 values close to one.