Hodges-Lehmann estimator and usage in quality control chart

Widely used Shewhart's control chart for monitoring process location parameter is based on mean of the process and constructed under the Normal distribution. Performance of these charts is affected negatively when the process distribution is different from Normal. Nonparametric or distribution-free control charts are useful in such a case because these charts do not require any assumption about process distribution. One of such nonparametric control charts is Hodges – Lehmann control chart which is based on Hodges – Lehmann estimator. In this study, Hodges – Lehmann control chart is introduced and evaluated the performance of chart for in control and out of control states with average run length (ARL) values by using observations randomly generated from some distributions. Also, Hodges – Lehmann control chart and Shewhart type control chart for mean are compared for Normal distribution with a simulation study. Finally, results are interpreted.