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. Copyright © 2013 John Wiley & Sons, Ltd.

A single distribution-free (nonparametric) Shewhart-type chart on the basis of the Lepage statistic is well known in literature for simultaneously monitoring both the location and the scale parameters of a continuous distribution when both of these parameters are unknown. In the present work, we consider a single distribution-free cumulative sum chart, on the basis of the Lepage statistic, referred to as the cumulative sum-Lepage (CL) chart. The proposed chart is distribution-free (nonparametric), and therefore, the in-control properties of the chart remain invariant and known for all continuous distributions. Control limits are tabulated for implementation of the proposed chart in practice. The in-control and out-of-control performance properties of the cumulative sum-Lepage (CL) chart are investigated through simulation studies in terms of the average, the standard deviation, the median, and some percentiles of the run length distribution. Detailed comparison with a competing Shewhart-type chart is presented. Several existing cumulative sum charts are also considered in the performance comparison. The proposed CL chart is found to perform very well in the location-scale models. We also examine the effect of the choice of the reference value (k) on the performance of the CL chart. The proposed chart is illustrated with a real data set. Summary and conclusions are presented.

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