A comparison of Phase I control charts

Abstract

A carefully done Phase I analysis is a vital part of an overall statistical process control and monitoring regime. Distribution-free control charts can play a useful role in this analysis, as a parametric model assumption often cannot be adequately verified. The performance of two distribution-free charts for the location – the mean-rank and the median chart – are compared in this paper. For benchmarking reasons, the parametric -chart is included in the comparisons. It is seen that the distribution-free charts are in-control robust, whereas the -chart is not, and they both perform similarly to the -chart for normally distributed data. However, for non-normal data, they both outperform the -chart. The results provide evidence in favour of using distribution-free Phase I charts in practice. Concluding remarks and suggestions for future research are given.

'n Versigtige analise van Fase I is 'n belangrike deel van 'n algehele statistiese proseskontrole en monitering skema. Verdelingsvrye kontrolekaarte kan 'n nuttige rol in hierdie fase speel, aangesien die model aannames nie voldoende geverifieer kan word nie. Die prestasie van twee verdelingsvrye kontrolekaarte - die gemiddelde-rank en die mediaan kontrolekaarte - word vergelyk in hierdie artikel. Vir vergelykingsredes, is die parametriese X-kontrolekaart ingeluit in die vergelykings. Dit is gevind dat die verdelingsvrye kontrolekaarte robuuste eienskappe het, terwyl die X-kontrolekaart dit nie het nie, en beide presteer op soortgelyke wyse as die X-kontrolekaart vir normaalverdeelde data. Egter, vir nie-normale data vaar albei beter as die X-kontrolekaart. Hierdie resultate bied bewyse ten gunste van die gebruik van verdelingsvrye Fase I kontrolekaarte in die praktyk. Slotopmerkings en voorstelle vir toekomstige navorsing word gegee.