Abstract Statistical process control (SPC) charts that originated in manufacturing have nowadays been implemented in a wide variety of settings for quality improvement. Monte Carlo simulations, Markov chain and integral equation approaches are often used to analyze performance of control charts. Compared to simulations, the Markov chain and integral equation approaches do not require a large number of simulation replicates and thus receive a great deal of attention in the SPC literature. The Gauss-based quadrature is often used to evaluate the integral equation. However, this quadrature method might not be able to provide satisfactory approximation under skewed distributions or other cases such when the integration kernel is not smooth. To meet the gap in part, this thesis suggests an accurate but fast algorithm based on the collocation method for analyzing the chart performance under these cases. In particular, we will analyze the evaluation accuracy under the following three specific cases: (i) CUSUM chart under gamma distributions; (ii) the AEWMA charts, and (iii) the EWMA chart under linear drifts in the process standard deviation. In additional to the evaluation accuracy issue, the optimal design of control charts is another important issue in SPC. The optimal design of traditional control charts is often carried out based on simulations, and there is lack of systemic approach. In this thesis, a gradient-based approach is proposed for efficient design and analysis of control charts as the gradients provide valuable information in search of the optimal values over the parameter space. Different from the conventional simulation-based ARL gradient estimators, this thesis derives the ARL gradients from the integral equation. As the proposed approach gets rid of running a large number of simulations, it is expected to be more accurate and efficient. Moreover, the proposed method can be applied to a wide range of settings as it only requires the charting statistic to poss the Markovian property, which represents an important family of control charts in SPC. In this case, the ARL of the underlying control chart can be formulated as an integral equation, and thus one can employ a similar procedure to estimate the ARL gradients. Keywords integral equation, average run length, run length distribution, optimal design