Flexible And Robust Control Charts For Statistical Process Monitoring

In statistical quality control, there are two types of quality characteristics. The quality characteristics that can be measured numerically are known as vari-ables. Many quality characteristics cannot be measured numerically but can be classified into various categories. Quality characteristics of this type are called attributes. This thesis proposed flexible and robust control charts for efficient statistical process monitoring. Count data may be used to measure the number of defective items in industrial applications or the incidence of a certain disease at a health facility. The Poisson distribution is a popular distribution used to describe count information, from which control charts involving count data have been es-tablished. The Poisson distribution is based on the underlying equi-dispersion (mean and variance are equal) assumption. In the reality, this assumption is seldom fulfill and the control charts based on the Poisson distribution are very sensitive to over-dispersed (mean is less than variance) or under-dispersed (mean is greater than variance) data. Therefore, flexible control charts are needed that can be used for under-dispersed or over-dispersed count data. This thesis con-tributes some univariate and a multivariate flexible control charting structures to be used as add-in for Statistical Process Control (SPC) toolkit. Control charts for variables are generally based on the assumption that the underlying process follow normal parent distribution. However, this assumption is also seldom ful-fill in the reality. Therefore, a robust control chart is needed that can be used to monitor the process parameter more efficiently for normal as well as non-normal processes. The robustness study and designing of Gini-Chart (a process variability chart) for various non-normal distributions is proposed in this thesis. The proposed charting structures are designed to monitor dispersed count data sets more efficiently in attributes and to provide a robust process monitoring in variables.Sellers (2012) proposed a flexible and generalized COM-Poisson chart for monitoring count data. She developed the3-sigma limits only. In this thesis, we extended her work and developed the exact κ-sigma and the true probabil-ity limits of the COM-Poisson charts, and analyzed using different performance measures. A generalized and flexible Exponentially Weighted Moving Average (EWMA) control chart based on the COM-Poisson distribution has been pro-posed. Three kinds of cumulative sum (CUSUM) control charts have been also proposed to monitor small shifts in dispersed count data more efficiently. A flexible multivariate shewhart type control chart, for efficient monitoring of dis-persed count data is also designed and studied in this work. The robustness of the Gini-chart, a newly proposed variability chart, has been studied for various non-normal processes. Finally, the designing of the Gini-chart for non-normal distribution along the X chart is made and the necessary coefficients and quar-tile points are provided. The performance ability of the proposals is evaluated in terms of some useful measures including power function (1-β), False alarm rate, average run length (ARL), median run length (MDRL), standard deviation of run length (SDRL) distribution, average number of signals (ANOS). We have investigated and compared the performance of different proposed control charts using extensive Monte Carlo simulations and Markov chain approach. We have also included some real and simulated data sets in order to highlight, the practi-cal application of the proposals cover in this thesis. A comprehensive review and perspective of the control charts to monitor dispersed count data is also provided in this thesis.The results of flexible design structures indicate that all the proposed chart-ing structures are flexible to under-or over-dispersed count data and generalize to the existing attributes charts as special cases. The proposed flexible charting structures are more efficient than the Sellers (2012) chart in detecting shifts in the average number of defects. Also, these structures are easy to implement and provide the real pictures about the state of process control. The results of the robust designed chart show that the Gini chart is very robust to non-normal processes than other existing variability charts. The Gini chart is more powerful than R and S charts in detecting the shift in the process variability. The results of this thesis are very helpful to the researchers and practioners in designing the attributes control chart to monitor dispersed count data and a robust variability control chart to monitor variable data.