A Class of Distribution-Free Exponentially Weighted Moving Average Schemes for Joint Monitoring of Location and Scale Parameters

Abstract

In this chapter, we investigate and compare six distribution-free exponentially weighted moving average (EWMA) schemes for simultaneously monitoring the location and scale parameters of a univariate continuous process. More precisely, we consider a well-known distribution-free EWMA scheme based on the Lepage statistic, and we propose five new EWMA schemes for the same purpose. One of the five new schemes is based on the maximum of EWMA of two individual components, one for the location parameter and the other for the scale parameter, of the Lepage statistic. Such a component-wise combined EWMA is referred to as the cEWMA. Further, we consider an EWMA scheme based on the Cucconi test statistic. We show that it is possible to express the Cucconi statistic as a quadratic combination of two orthogonal statistics, one of which is useful for monitoring the location parameter and the other for monitoring the scale parameter. Such decomposition of the Cucconi statistic is not unique, and one can split it into three different ways. Therefore, we design three more cEWMA schemes corresponding to the decompositions of the Cucconi statistic. We discuss the implementation steps along with an illustration. We perform a detailed comparative study based on Monte Carlo simulation. We observe that the three cEWMA-Cucconi schemes perform very well for various location–scale models.