Enhancements to Control Charts for Monitoring Process Dispersion and Location

Abstract

Control charts are widely used to monitor stability and performance of processes with an aim of detecting abnormal variations in process parameters. Control charts typically work in two phases: the retrospective phase (Phase I) and the monitoring phase (Phase II). Phase I involves estimating the in-control state of a process by using a historical dataset, whereas, in Phase II the focus mainly lies in the quick detection of process parameters from their in-control values. Chapter 2 of this thesis investigates a wide range of Shewhart type dispersion control charts in Phase II for normal and a variety of non-normal parent distributions. These charts are based on the sample range, the sample standard deviation, the inter-quartile range, Downton's estimator, the average absolute deviation from median, the median absolute deviation, Sn and Qn estimates. The Phase I analysis of these charts together with the charts based on the pooled sample standard deviation and the distribution-free scale rank statistic is investigated in Chapter 3. The performance of a variety of Phase II EWMA dispersion charts is evaluated and compared in Chapter 4, using different run length characteristics (the average run length, the median run length and the standard deviation of the run length distribution). The overall effectiveness of these EWMA charts is examined using the extra quadratic loss and the relative ARL measures. Chapter 5 investigates the effect of two component measurement error (model) on the performance of the EWMA location chart, for the monitoring of analytical measurements. The two component model proposed by Rocke and Lorenzato (1995) combines both additive and multiplicative errors in analytical measurements in a single model. It is shown that the two component measurement error can seriously effect the detection ability of the EWMA location chart and this effect can be reduced by the use of multiple measurements at each sample point. A cost function approach is used to determine appropriate choices of the sample size and the number of multiple measurements per sample to maximize the detection ability of the EWMA chart in presence of two component measurement error. Chapter 6 proposes two run rule schemes for the CUSUM dispersion chart. The run length characteristics of the proposed schemes are evaluated using the Markov chain approach and compared with the simple dispersion CUSUM and the relevant EWMA dispersion charts for individual observations. Finally, Chapter 7 proposes a nonparametric progressive mean control chart for the quick detection of out-of-control signals in the process target or location. This thesis, in general, will help quality practitioners to choose efficient control charts for the monitoring of process dispersion and location.