New extended distribution-free homogenously weighted monitoring schemes for monitoring abrupt shifts in the location parameter

Abstract

A homogeneously weighted moving average (HWMA) monitoring scheme is a recently proposed memory-type scheme that gained its popularity because of its simplicity and superiority over the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) schemes in detecting small disturbances in the process. Most of the existing HWMA schemes are designed based on the assumption of normality. It is well-known that the performance of such monitoring schemes degrades significantly when this assumption is violated. Therefore, in this paper, three distribution-free monitoring schemes are developed based on the Wilcoxon rank-sum W statistic. First, the HWMA W scheme is introduced. Secondly, the double HWMA (DHWMA) W scheme is proposed to improve the ability of the HWMA W scheme in detecting very small disturbances in the location parameter and at last, the hybrid HWMA (HHWMA) W scheme is also proposed because of its flexibility and better performance in detecting shifts of different sizes. The zero-state performances of the proposed schemes are investigated using the characteristics of the run-length distribution. The proposed schemes outperform their existing competitors, i.e. EWMA, CUSUM and DEWMA W schemes, in many situations, and particularly the HHWMA W scheme is superior to these competitors regardless of the size of the shift in the location parameter. Real-life data are used to illustrate the implementation and application of the new monitoring schemes.