Читать книгу Introduction to Statistical Process Control - Muhammad Amir Aslam - Страница 28

When articles or units are studied on the basis of qualitative measures as go/no go, yes/no, satisfied/not satisfied, positive/negative, etc., then an attribute control chart is suitable to monitor the unusual changes. These are the charts commonly known as p‐chart used for monitoring proportion of nonconforming items in a sample or proportion of defective items in a sample, and np‐chart is used to monitor the number of nonconforming items in a sample of size n.

The control limits of these control charts are similar particularly when the sample size is fixed. The limits of p‐chart charts may be constructed by using the binomial probability distribution with parameter p. As we know that the mean of the binomial distribution is np and its standard deviation is . Thus

And the control limits for the np‐chart can be constructed as

Another attribute control chart that is commonly used in the control chart literature is the c‐chart used for monitoring the number of nonconformities in each sample or the number of defects in each sample. The limits of c‐chart charts may be constructed by using the Poisson probability distribution with parameter c. As we know that the mean of the Poisson distribution is c and its standard deviation is . Thus

Yet another attribute control chart commonly used in the literature of the SPC is the μ‐chart. It is used to monitor the nonconformity items per unit or the nonconforming items per unit. The distribution of the c‐chart and the μ‐chart is the same except the scale of the units, which is changed by n in the μ‐chart. The control limits of μ‐chart can be established as