Comparison of estimators of standard deviation, mean moving range and median moving range to estimate process standard deviation using autocorrelated data

Kalantari, Mehdi; Fatemi Ghomi, S.M.T.

Comparison of estimators of standard deviation, mean moving range and median moving range to estimate process standard deviation using autocorrelated data

Authors

Mehdi Kalantari

S.M.T. Fatemi Ghomi

Abstract

Independence of observations is a fundamental assumption in designing an X chart for individual observations. But unfortunately, the assumption of existence of independent data is not even approximately satisfied. In fact, there is one kind of autocorrelation in the data. This paper demonstrates, through simulating an AR(1) process, that the autocorrelation in the data has deep effect on X chart. Moreover, estimators of standard deviation, mean moving range and median moving range to estimate process standard deviation are introduced. Among the cited estimators, the best of them is considered to estimate process standard deviation using autocorrelated data. Finally, two new estimators are presented to estimate process standard deviation using autocorrelated data.

Keywords

AR(1) Process

Autocorrelation

Complete minimal sufficient statistic

Independent data

Multivariate normal

Uniform minimum variance unbiased estimator (UMVUE)

X chart