Joint monitoring of mean and variance using likelihood ratio test statistic with measurement error

Abstract

ABSTRACT This paper explores the effect of measurement errors on a joint monitoring control chart by using three different techniques (i) covariate method (ii) multiple measurements (iii) linear increasing variance. The joint monitoring control chart in the presence of measurement errors are discussed by using an exponentially weighted moving average statistic in the generalized likelihood ratio (GLR) test statistic under ranked set sampling and pair ranked set sampling (PRSS) procedures. For this purpose, different out-of-control scenarios including mean shifts, variance shifts, and simultaneous shifts are discussed under the considered sampling schemes. The performance of the joint monitoring control chart is evaluated in terms of average run length (ARL) and the standard deviation of run length (SDRL) by conducting an extensive simulation study. The results show that PRSS procedure can reduce the adverse effect of measurement errors on the detection ability of joint monitoring control chart. An example is provided with real data set for the implementation of the joint monitoring control chart in the presence of measurement errors.