A new distribution-free Phase-I procedure for bi-aspect monitoring based on the multi-sample Cucconi statistic

Abstract

The Phase-I analysis is necessary for verification of process stability based on the collected data and for establishing a reference sample for Phase-II monitoring. A large number of schemes designed for this purpose assume normality. In various practical applications, however, process distributions do not always meet the assumption of normality. Therefore, distribution-free schemes are appealing in practice for Phase-I analysis. Only a few distribution-free procedures, to our knowledge, can determine the stability of process location or scale parameters simultaneously via Phase-I analysis. The present research focuses on a new distribution-free Phase-I procedure for dual monitoring of two aspects of a process, namely, location and scale, using a single chart. To this end, we propose a distribution-free Phase-I scheme for bi-aspect monitoring using the multi-sample Cucconi statistic. In-control and out-of-control properties of the new Phase-I Cucconi scheme are studied. The proposed scheme appears to be as good or better than its competitors in terms of various performance metrics in a large number of situations. We demonstrate the design and implementation of the proposed scheme with a practical example.