An EWMA signed ranks control chart with reliable run length performances

Theodoros Perdikis (1) , Stelios Psarakis (1) , Philippe Castagliola (2) , Petros Maravelakis (3)

1 AUEB - Athens University of Economics and Business
2 LS2N - équipe SLP - Systèmes Logistiques et de Production
3 University of Piraeus

During the design phase of a control chart, the determination of its exact run length properties plays a vital role for its optimal operation. Markov chain or integral equation methods have been extensively applied in the design phase of conventional control charts. However, for distribution-free schemes, due to the discrete nature of the statistics being used (such as the sign or the Wilcoxon signed rank statistics, for instance), it is impossible to accurately compute their run length properties. In this work, a modified distribution-free phase II exponentially weighted moving average (EWMA)-type chart based on the Wilcoxon signed rank statistic is considered and its exact run length properties are discussed. A continuous transformation of the Wilcoxon signed rank statistic, combined with the classical Markov chain method, is used for the determination of the average run length in the in- and out-of control cases. Moreover, its exact performance is derived without any knowledge of the distribution of sample observations. Finally, an illustrative example is provided showing the practical implementation of our proposed chart.

Mots clés: Nonparametric control chart; Wilcoxon signed rank statistic; Markov chain; EWMA control chart

Domaines: Autre; Statistiques [stat]

Theodoros Perdikis, Stelios Psarakis, Philippe Castagliola, Petros Maravelakis. An EWMA signed ranks control chart with reliable run length performances. Quality and Reliability Engineering International, 2021, 37 (3), pp.1266-1284. ⟨10.1002/qre.2795⟩. ⟨hal-03163631⟩