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