Читать книгу Introduction to Statistical Process Control - Muhammad Amir Aslam - Страница 25

Let a process consists of a set of n independent trials. Here the term independent means that any outcome is not affected by the previous outcome whether it had occurred or not. Here we define any outcome as either success or failure. Suppose that the probability of success is denoted by p, p belongs to the interval (0,1), and the probability of failure is denoted by q = 1 − p, then the binomial probability distribution can be defined as

where n is the total number of independent trials and x is a binomial random variable ranging from 0 to n. This distribution has only two parameters n and p. The distribution is symmetric when , the distribution is positively skewed if , and it is negatively skewed if .

The binomial probability distribution is the most commonly used distribution in the control chart literature to model the number cases in a sample of n items when the proportion in the population is known. For example, if the proportion of defective item in any mass production unit is 0.12, then find the complete binomial probability distribution for n = 10 (Table 1.1).