Distribution-free Lepage Type Circular-grid Charts for Joint Monitoring of Location and Scale Parameters of a Process

In the last 5 years, research works on distribution-free (nonparametric) process monitoring have registered a phenomenal \ngrowth. A Google Scholar database search on early September 2015 reveals 246 articles on distribution-free control charts \nduring 2000–2009 and 466 articles in the following years. These figures are about 1400 and 2860 respectively if the word \n‘nonparametric’ is used in place of ‘distribution-free’. Distribution-free charts do not require any prior knowledge about \nthe process parameters. Consequently, they are very effective in monitoring various non-normal and complex processes. \nTraditional process monitoring schemes use two separate charts, one for monitoring process location and the other for \nprocess scale. Recently, various schemes have been introduced to monitor the process location and process scale \nsimultaneously using a single chart. Performance advantages of such charts have been clearly established. In this \npaper, we introduce a new graphical device, namely, circular-grid charts, for simultaneous monitoring of process \nlocation and process scale based on Lepage-type statistics. We also discuss general form of Lepage statistics and show \nthat a new modified Lepage statistic is often better than the traditional of Lepage statistic. We offer a new and \nattractive post-signal follow-up analysis. A detailed numerical study based on Monte-Carlo simulations is performed, \nand some illustrations are provided. A clear guideline for practitioners is offered to facilitate the best selection of \ncharts among various alternatives for simultaneous monitoring of location-scale. The practical application of the charts \nis illustrated.