Quality is a critical keyword in almost all industries. Quality improvement is always the pursuit of a successful business. To reduce variability is a basic standard to improve quality. Statistical process control (SPC) is a set of powerful methods that are widely applied for the reduction of variability.

With the innovation of technology, data collected from many applications are richer than ever to allow us to conduct more comprehensive analysis, and also bring us more challenges. For example, mixed-type data consisting of both continuous observations and categorical observations are popular for describing quality. While conventional SPC tools target either continuous data or categorical data, they seldom consider both simultaneously. Another example is profile data. A profil...[ Read more ]

Quality is a critical keyword in almost all industries. Quality improvement is always the pursuit of a successful business. To reduce variability is a basic standard to improve quality. Statistical process control (SPC) is a set of powerful methods that are widely applied for the reduction of variability.

With the innovation of technology, data collected from many applications are richer than ever to allow us to conduct more comprehensive analysis, and also bring us more challenges. For example, mixed-type data consisting of both continuous observations and categorical observations are popular for describing quality. While conventional SPC tools target either continuous data or categorical data, they seldom consider both simultaneously. Another example is profile data. A profile describes the relationship between the response variable and one or more explanatory variables. SPC has many methods that monitor profiles with continuous responses and some techniques that monitor profiles with binary responses. Nevertheless, an efficient approach for profiles with categorical responses having more than two attribute levels still remains elusive.

The aforementioned two examples have one thing in common, that is both mixed-type data and profile data involve categorical observations. In fact, categorical data are becoming increasingly prevailing and attractive in many industries, since compared to continuous data, categorical data are easier and less expensive to collect. Furthermore, there usually exists a natural order among the attribute levels of a categorical variable. Such categorical variables are called ordinal categorical ones. The majority of the SPC literature ignores the ordinal information, and regards all categorical variables as nominal. It is reasonable to believe that if such ordinal information is fully taken advantage of, we can develop even more powerful methods. In many statistical methods that focus on ordinal data, it is assumed that the attribute levels of an ordinal variable are determined by a latent continuous distribution. This latent variable assumption reflects the quantitative nature of ordinal data.

Based on the latent continuous variable assumption, this thesis proposes three strategies for different types of data. First, a rank-based control chart is proposed for monitoring mixed-type data. Second, directional control schemes are developed for the monitoring and diagnosis of mixed-type data. Third, a novel control chart is presented for profile data with ordinal categorical responses and random predictors. All the proposed methods are designed for Phase II SPC applications. Monte Carlo simulations have demonstrated the efficiency of these methods in detecting changes, as well as their robustness under various latent continuous distributions.