Parameter estimators in phase I and performance of individuals chart

Atalay, Murat
In the literature, Phase I analysis is often ignored and in-control process parameters are assumed as known. However process parameters are generally unknown in real control chart applications and these must be estimated from the obtained process data. Since Phase I analysis may have considerable impacts on the process monitoring performance in Phase II, effects of Phase I analysis on the Phase II performance must be investigated in detail. In this thesis, Shewhart type control charts are used to detect outliers and estimate parameters for control chart design. As a model for the observations, normal distribution is considered. Outliers are generated in different forms through simulations and Phase I steps of a control chart operation are simulated to design a control chart for use in Phase II. In Phase I, an Individuals Chart is considered with various selection of design parameters. For Phase II operations, an Individuals Chart with 3-sigma control limits is considered. To estimate standard deviation, several estimators are discussed. The accuracy of parameter estimation is evaluated with the Mean Squared Error criterion for the estimates. Average run length performance of Phase II implementations, effects of standard deviation estimators and selection of the width of control limits in Phase I analysis are evaluated. Results are discussed and some suggestions for practitioners are provided. In addition, a decision tree for the selection of estimators is provided. Also, a real-world example is presented to illustrate the application and express the significance of suggestions.


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Citation Formats
M. Atalay, “Parameter estimators in phase I and performance of individuals chart,” M.S. - Master of Science, Middle East Technical University, 2016.