||In the modern business environment, quality is one of the basic and critical factors for products or service, which influences the success and sustained development of an organization. The large variability caused by assignable causes results in the poor quality of products or service. Statistical process control (SPC) techniques including monitoring and diagnosis methods have been widely utilized in a variety of industries for the purpose of detecting and reducing the variability and identifying root causes. Even though most SPC schemes are developed for processes with a single stage and/or numerical data, due to practical constraints, only categorical data can be observed in many real industries. In addition, due the complexity of modern techniques, it is very rare to find a manufacturing or service process including only one single stage. Besides, the functional relationship between the response variable and explanatory variables needs to controlled in some practical processes. However, the application of conventional SPC schemes to such processes with categorical data usually has challenging problems and results in an unsatisfactory performance. Therefore, in this thesis, we try to introduce the new monitoring and diagnosing schemes to efficiently detecting the shift and identifying the root causes in manufacturing and service processes with binary outputs. In this thesis, we first proposes a binary state space model (BSSM) for modeling multistage processes with binomial (binary) data and develops corresponding monitoring and diagnosis schemes by utilizing a hierarchical likelihood approach and directional information based on the BSSM. The proposed schemes, the GHLR scheme and the Wald-type scheme, not only provide an SPC solution that incorporates both interstage and intrastage correlations, but they also resolve the confounding issue in monitoring and diagnosis due to the cumulative effects from stage to stage. Simulation results show that the proposed schemes consistently outperform the existing X2 scheme in monitoring and diagnosing for binomial multistage processes. An aluminum electrolytic capacitor example from the manufacturing industry is used to illustrate the implementation of the proposed approach. Apart from the monitoring multistage processes with binary outputs, diagnosing faulty stages after detecting the shift occurring in such a process is also studied in this thesis. Based on the univariate BSSM that describes the multistage process with binary data, a novel LASSO-based diagnostic procedure is proposed, which combines the model selection criterion, BIC, with the popular adaptive LASSO variable selection approach. With the help of the sparsity properties of the LASSO estimator and its algorithm, the faulty stages can be identified easily. Simulation results prove that the proposed LASSO-based scheme consistently and significantly outperforms the directional scheme in identifying the shifted stages correctly when more than one stages really shift. The purpose of profile monitoring is to check the stability over time of relationships between response variables and one or more explanatory variables. In many applications, categorical response variables are common and a generalized linear model is usually utilized to model this kind of profiles for quality improvement. In practice, different profiles often have random explanatory variables and these variables require careful monitoring as well. Statistical process control is important and challenging for monitoring profiles in such situations. A novel control chart is proposed by integrating an exponential weighted moving average (EWMA) scheme and a likelihood ratio test for the parameters of a logistic regression model. This new scheme not only monitors the functional relationship of the profile, but also the mean shift in explanatory variables. The proposed chart has reasonable computational and implementation complexity and is efficient in detecting shifts. The simulation results show that it performs better than the standard benchmarks in the literatures for the array of simulation examples that we consider. A real example from the electronic industries is used to illustrate the implementation of the proposed approach.