Statistical Models for Monitoring the High-Quality Processes

One important application of statistical models in the industry is statistical process control. Many control charts have been developed and used in the industry. They are easy to use but have been developed based on statistical principles. However, for today’s high-quality processes, traditional control-charting techniques are not applicable in many situations. Research has been going on in the last few decades, and new methods have been proposed. This chapter summarizes some of these techniques. High-quality processes are generally defined as those with very low defective rate or defect-occurrence rate, which is achieved in six sigma environment and in the advanced manufacturing environment. Control charts based on the cumulative count of conforming items are recommended for such processes. The use of such charts has opened up new frontiers in the research and applications of statistical control charts in general. In this chapter, several extended or modified statistical models are described. They are useful when the simple and basic geometric distribution is not appropriate or is insufficient. In particular, we present some extended Poisson distribution models that can be used for count data with large numbers of zero counts. We also extend the chart to the case of general time-between-events monitoring; such an extension can be useful in service or reliability monitoring. Traditionally, the exponential distribution is used for the modeling of time-between-events, although other distributions such as the Weibull or gamma distribution can also be used in this context. © 2023 Springer-Verlag London Ltd., part of Springer Nature.