Whatever is the business, either manufacturing or service, quality is the most critical aspect, which affects the level of success of the business. The importance of quality cannot be overemphasized. According to its modern definition that quality is inversely proportional to variability, quality improvement is to reduce variability. Statistical process control (SPC) is such a methodology that has been widely used for detecting assignable causes and reducing variability....[ Read more ]

Whatever is the business, either manufacturing or service, quality is the most critical aspect, which affects the level of success of the business. The importance of quality cannot be overemphasized. According to its modern definition that quality is inversely proportional to variability, quality improvement is to reduce variability. Statistical process control (SPC) is such a methodology that has been widely used for detecting assignable causes and reducing variability.

Recently, in manufacturing and especially service industries, there have been more and more processes involving quality characteristics expressed as attribute levels such as conforming or nonconforming, which are not measured on a continuous scale. This follows partly because their accurate numerical values are expensive or even impossible to obtain and partly because such categorical values are sufficient for monitoring purpose. We consider monitoring processes that involve multiple categorical quality characteristics, namely multivariate categorical processes. Usually, these categorical characteristics correlate with each other, indicating a must of multivariate charting techniques.

Sufficient attention has been paid to monitoring multivariate continuous data, for example, data collected from a multivariate normal distribution. Such methods are easily found in the literature. However, there is a scarcity of research on monitoring multivariate categorical data, and most of the few existing methods lack robustness in two aspects. First, they apply to multiple characteristics that all have only two attribute levels. If at least one characteristic has three or more levels, they will fail. Second, they do not care the cross-classifications among characteristics. Instead, they focus on only the one-way marginal counts with respect to the attribute levels of each characteristic, neglecting the dependence among characteristics.

We employ log-linear models for describing the relationship among categorical characteristics, which can overcome the above-mentioned two difficulties. This thesis tries to make three major contributions to statistical process control for multivariate categorical processes. First, a general Phase II control chart is proposed for online monitoring, which is robust to detect various shifts efficiently, especially those in interaction effects representing the dependence among characteristics. Second, another Phase II control chart that exploits directional shift information is devised for online detection of some more practical shifts, namely one-coefficient shifts and high-order interaction shifts. Third, an off-line Phase I analysis method that considers directional shift information is proposed for change-point detection in a dataset collected from a multivariate categorical process.

The three approaches compose a systematic methodology of statistical process control for multivariate categorical processes. We have also performed numerical simulations to compare them with corresponding counterparts. In addition, real-data examples have demonstrated the effectiveness of these techniques. They can be implemented into practice with reliability.