The pharmaceutical products may develop impurities at different stages of their development, making the pharmaceutical risky to be administered, so they need to be detected and monitored. Thus, the application of statistics in pharmaceutical process production and research has advanced significantly, motivated by the maintenance of the regulatory standards associated with the quality manufacturing process. This project is based on analyzing and monitoring the pharmaceutical process using various statistical methods. The multivariate statistical analysis combined with univariate analysis is presented in this project to evaluate the batch quality consistency of pharmaceutical products. The variable reduction is one of the key factors in multivariate analysis when the variables are strongly correlated. Thus, techniques such as PCA, PLS, and phase-wise correlation helped in variable reduction. Also, correlation statistics have proved to be the key sample generating technique for batch-wise and phase-wise analysis to study the high impacting batches and phases. Similarly, an ANOVA test was performed to assess the variations between phases. The EWMA and CUSUM univariate control charts were constructed to study the variations in the individual variables and their impact on the pharmaceutical process. In this project, the Hotelling’s 𝑇2 and MEWMA statistics proved to be an effective statistical criterion for monitoring process variations. The control chart performance was evaluated, and model parameters were designed using Average Run Length (ARL). The simulation was carried out to select the optimum control chart parameters. Furthermore, nominal, PCA, and PLS based MEWMA and 𝑇2control charts were constructed and evaluated based on the Hotelling’s test of similarity. The M-Shapiro test of normality was performed that validates the normality of the two samples to confirm the Hotelling’s test assumption. The number of in-control and out-of-control samples were analyzed and monitored using a different combination of control chart construction. The PCA based MEWMA control chart samples gave the optimum performing batches. Multivariate statistical analysis has proven its usefulness and applicability in determining the process quality of industrial chemical products.
This project successfully studied and analyzed the pharmaceutical processing data. The study includes an analysis using multivariate and univariate statistical tools. This project provides promising applications of multivariate statistical analysis for pharmaceutical products in batch control and evaluation. Initially, exploratory data analysis was performed to check for the normality of the data; it was proved that no variable follows a normal distribution, and many variables contain most of the data value as zero. Based on this analysis, variable reduction techniques were performed considering statistical techniques using correlation, PCA, and PLS. The reduced variables were transformed to standard normal form to perform multivariate statistical analysis.
Further, batch-wise and phase-wise analysis were performed using multivariate control chart techniques to understand high impacting batches and phases. The independent phase-wise and batch-wise samples required to construct control charts were generated using the correlation technique. Specifically, ANOVA statistics were conducted to learn the variations between the phases. Univariate analysis was constructed using EWMA and CUSUM control charts on an individual variable to learn the variables with the greatest number of out-of-control samples. Multivariate MEWMA and Hotelling’s 𝑇2 control charts were constructed to monitor process variations. The ARL was used to design and assess the performance of the MEWMA control chart. Accordingly, a simulation was performed by considering different control chart parameters (𝜆, ℎ4, 𝑝). Further, The MEWMA and 𝑇2control charts were constructed based on weighted nominal, PCA, and PLS data. Furthermore, the Hotelling’s statistical test was performed on each control chart and was assessed based on the test of similarity between in-control and out-of-control samples. Additionally, the M-Shapiro test of normality was carried out to validate the Hotelling’s test assumption.
Finally, the MEWMA control chart constructed on the PCA sample gave the optimum batches. Although the batch development process control requires an elaborated statistical structure during the pilot and monitoring phase, the techniques used in this project facilitate the analysis and detection of possible out-of-control batches, impacting variables, and phases.