Process Monitoring Control Charts using Auxiliary Information

Abstract

The present research study proposes the auxiliary information based memory type CCs where the quality characteristic under investigation follows the normal distribution. An auxiliary information based hybrid exponentially weighted moving average chart for process mean has been developed. The extension of hybrid EWMA charts is made for the process variance named as Exponentially Weighted Moving Variance (EWMV) chart with and without auxiliary information. The study discusses the maximum exponentially weighted moving average chart for simultaneous observing and checking of process mean and process coefficient of variation (CV) with and without auxiliary information for the quality characteristic. Further, the study extends to the maximum hybrid exponentially weighted moving average chart for simultaneous observing and checking the process mean and process CV with and without auxiliary information for the quality characteristic under study following the normal distribution. The thesis is divided into six chapters. Chapter 1 discusses five different types of control charts (CCs) including Shewart type CCs, EWMA, HEWMA, joint observing and checking CCs, and CV CCs. Furthermore, normal standard normal distribution and use of auxiliary information in CCs is also illustrated in this chapter. Chapter 2 displays a detailed survey of the studies conducted on EWMA CCs, HEWMA CCs, auxiliary information based CCs, CV CCs, and joint monitoring CCs for process parameters. Chapter 3 contains exponentially weighted moving average CCs to observe and check the small and moderate shifts in the process mean. The regression estimator is utilized to estimate the population mean of the study variable. It is revealed from the results of simulation study that the recommended MxHEWMA CC efficiently detects smaller shifts in process mean as compared to the existing HEWMA CC. In Chapter 4, a new HEWMA CC for monitoring the process dispersion has been recommended. This chart is named as HEWMTn. The logarithmic transformation is used to normalize the distribution of sample variance. The recommended HEWMTn CC has been compared with the corresponding existing charts to detect the increase and the decrease in the process variability. The comparison shows that the recommended HEWMTn CC is uniformly better than its parallels for detecting shifts in the process variability. This chapter further deals with a CC to observe and check the process variance using auxiliary information in the setting of hybrid exponentially moving variance CC. A difference type estimator is utilized to estimate the population x variance of the study variable. The execution of the recommended CC is evaluated in accordance with the average run length, and standard deviation of run length is estimated with the help of monte carlo simulation. The results of the simulation study reveal that the recommended AIB-HEWMTn CC efficiently detects small and moderate shifts in process dispersion as compared to some of the existing competitor CCs. In Chapter 5, the study proposes a blended CC that monitors the process mean and process CV simultaneously. Furthermore, the sensitivity of the CC is enhanced by incorporating an auxiliary variable. The present study has utilized the concept of EWMA chart and the log transformation to transform the distribution of sample CV for normalization of the distribution with N (0, 1) for structuring a joint monitoring CC. The performance comparison among the recommended CCs is presented. Several advantages of the recommended CCs are diagnosed. The empirical evidence is also provided to support the recommended CC with a real-life data set. Chapter 6 proposes the blended CCs that observe and check the process mean and process CV simultaneously. The study has utilized the concept of HEWMA chart and the log transformation to transform the distribution of the sample CV for normalization of the distribution with N (0, 1) and structuring joint monitoring CC. The research proposes two types of CCs, one is joint monitoring of mean and CV, and the second is auxiliary information based joint monitoring of mean and CV. A comparison of the performance of the two recommended CCs is also given. Many advantages of the recommended CCs are traced. The empirical evidence is also provided to support the recommended CC with a real-life data set.