ABSTRACT
This chapter describes a condensed, and as elementary as possible, study of those statistical distributions and their properties which are essential for a deeper understanding of the distributions of the process capability indices. It addresses problems arising from non-normality, and in most cases the authors will not have exact formulas for distributions of estimators of Process capability indices, or even for the moments. To benefit from studying the chapter, some basic knowledge of statistical methodology and in particular of the theory of a number of basic statistical distributions is essential. Although many books on quality control provide excellent descriptions of the normal distribution, the distributional properties of the process capability indices involve several other important but much less familiar distributions. Capability indices give rise to new interesting statistical distributions which may be of importance and promise in other branches of engineering and sciences in general. Further analytical treatment may be found in books and articles cited in the bibliography.
