An EWMA Quality Control Procedure for Jointly Monitoring the Mean and Variance

Abstract

Introduction Quality control charts have been used widely for the purpose of detecting changes in a process. Usually, we can represent a change in the process by a change in the parameter of the distribution of the quality characteristic being monitored. When random variables of interest follow approximately the normal distribution, interest centres on controlling the mean, μ, and/or the variance, σ. Shewhart type charts, cumulative sum (CUSUM) procedures, and exponentially weighted moving averages (EWMA and DEWMA) procedures [1-7] have been commonly used to monitor shifts in the process mean using sample means (or individual observations). Usually it is assumed that independent samples of the same size are obtained at fixed-length sampling intervals. Relatively, little has appeared about the design and use of procedures for jointly controlling the mean and process variability, the latest article being Domangue and Patch[8]. Procedures for controlling the process variability usually are based on Shewhart-type charts such as the R-chart, S-chart, or the S-chart for controlling the range, the standard deviation, and the variance respectively. There has also been numerical work on the properties of CUSUM procedures on the range or the moving range. It is well known that for larger sample sizes the sample variance, s is a more efficient control statistic for controlling the process variability than the sample range. Domangue and Patch studied the properties of omnibus EWMA schemes. They proposed an omnibus EWMA procedure based on the statistic