A New Distribution-free Control Chart for Joint Monitoring of Unknown Location and Scale Parameters of Continuous Distributions

While the assumption of normality is required for the validity of most of the available control charts for joint monitoring of unknown location and scale parameters, we propose and study a distribution-free Shewhart-type chart based on the Cucconi statistic, called the Shewhart-Cucconi (SC) chart. We also propose a follow-up diagnostic procedure useful to determine the type of shift the process may have undergone when the chart signals an out-of-control process. Control limits for the SC chart are tabulated for some typical nominal in-control (IC) average run length (ARL) values; a large sample approximation to the control limit is provided which can be useful in practice. Performance of the SC chart is examined in a simulation study on the basis of the ARL, the standard deviation, the median and some percentiles of the run length distribution. Detailed comparisons with a competing distribution-free chart, known as the Shewhart-Lepage chart (see Mukherjee and Chakraborti) show that the SC chart performs just as well or better. The effect of estimation of parameters on the IC performance of the SC chart is studied by examining the influence of the size of the reference (Phase-I) sample. A numerical example is given for illustration. Summary and conclusions are offered.