On the performance of auxiliary-based control charting under normality and nonnormality with estimation effects

Process monitoring through control charts is a quite popular practice in statistical process control. From a statistical point of view, a superior control chart is the one which has an efficient design structure, for the case of both known and unknown parameters. There are auxiliary information-based location charts for an improved monitoring of process mean level. These charting structures have some limitations like assuming normality, the parameters to be known and focusing mainly on phase I monitoring. In many practical situations, nonnormal process behaviors are more frequent. Information about process parameters is not available, and we have to rely on the limited data available from the process to establish the limits in phase I and then use them in phase II monitoring. To have a compromise between the statistical and the practical purposes, a natural desire is to have a control chart that can serve both the concerns efficiently. This study is planned for the same objective focusing the auxiliary-based Shewhart's control charts for location parameter. We have investigated the properties of the design structures of different location charts based on some already used and some new estimators with known and unknown parameters for normal and nonnormally distributed processes. By evaluating the performance of different charting structures in terms of power and run length properties in phase I and phase II, we have identified those more capable of making a good compromise between the abovementioned purposes in terms of statistical efficiency and practical desires.