| This study examines the performance of cumulative sum (CUSUM) chart under autocorrelation and process capability index (PCI) under non-normality. These tools of statistical quality control have become a key to quality improvement in manufacturing and service industries. The successful use of these statistical tools, as we have seen in large companies both in the States and abroad, has promoted research in the area of quality control. These research in turn have advanced the general understanding of these statistical tools and populated their proper and popular use.; The performance of CUSUM chart under correlation is evaluated using the statistic of average run-length (ARL) through an integral approach. The first part of the analysis focuses on the integral approach under independence. Once appropriate results for ARL under independence are received using the integral approach, as compared to simulation, we then formulate the integral approach for the first-order autoregressive AR(1) case. This autocorrelated integral formulation is verified by calculating the ARLs under independence as a special case. Positively correlated ARLs are calculated once the approach under independence is validated. Comparison for the calculated ARLs, under autocorrelation, from the integral and simulation approach are presented.; The evaluation of PCI under non-normality assumption is conducted under sample distribution of Chi-squared and Student's t at four and five degrees of freedom with small sample size. In estimating the sample PCIs, successful and accurate estimation of the sample's second and fourth moments are necessary due to their sensitivity of the departure of normality. We rely on the Box method of estimating the fourth moment and improve upon its result by incorporating other sample information, such as sample skewness. Various methods of estimating the sample PCIs under non-normality are compared by examining how often do the lower 95% confidence intervals of the sample PCIs actually cover the true population PCI per 1000 samples. |
