ABSTRACT

The SPC control charts discussed in the previous several chapters, for monitoring

univariate or multivariate continuous numerical quality characteristics, are all based

on the assumption that the related quality characteristics follow normal distributions

when the production process in question is IC and after it becomes OC. As pointed

out in Subsection 2.3.1, normal distributions play an important role in statistics, be-

cause many continuous numerical variables in practice roughly follow normal dis-

tributions and much statistical theory is developed for normally distributed random

variables. An intuitive explanation about the reason many continuous numerical vari-

ables in our daily life roughly follow normal distributions can be given using the

central limit theorem (CLT) discussed in Subsection 2.7.1. For instance, a quality

characteristic in question (e.g., the lifetime of a machine) is often affected by many

different factors, including the quality of the raw material, labor, manufacturing fa-

cilities, proper operation in the manufacturing process, and so forth (cf., Figure 1.1

in Section 1.2). So, by the CLT, its distribution would be roughly normal.