A new nonparametric adaptive EWMA procedures for monitoring location and scale shifts via weighted Cucconi statistic

In the context of distribution-free process monitoring and control, the Cucconi statistic has attracted more and more attention in recent years. The original Cucconi statistic was introduced for the two-sample location-scale problems. It is computationally more straightforward and is highly efficient. The Cucconi statistic is recently adopted for jointly monitoring the location and scale parameters of univariate continuous quality and service processes. It is distribution-free and does not require any stringent assumption on the underlying process distribution. Some recent development further revealed that the Cucconi statistic is the average of the squared standardised Wilcoxon statistic for monitoring location and the squared standardised Mood statistic for scale parameters — a fact unnoticed by the practitioners over five decades. The Cucconi statistic gives equal weight to shifts in location and scale. Therefore, this paper proposes a new adaptive nonparametric process monitoring scheme based on the weighted Cucconi statistic. The proposed monitoring scheme is designed to adapt the weight factor according to the estimated relative magnitude of mean and scale shift combined with an EWMA-type set-up. The numerical results based on the Monte-Carlo simulation study and a real data analysis reveal that the proposed monitoring scheme performs well across a wide range of shifts and compares favourably with prevailing distribution-free process monitoring schemes.