Bayesian Control Charts for Attributes and the Large
Subgroup Size in p
Humberto Gutiérrez
Abstract
The problems of the control charts
for attributes are analyzed. In particular, it is seen that the traditional
procedure to obtain the control limits has several difficulties: it does not
incorporate the uncertainty in the estimate of the parameter of the
distribution, it does not include the variation of the process, and the
procedure requires a base period to obtain the control limits. Along this
period it does not have a control chart to analyze the process. It is seen that
these problems are solved applying Bayesian methods. It is described a
sequential procedure to obtain the Bayesian control limits for p, np,
c and u charts, from the first observation. This eliminates the necessity
of the base period. Lastly it is analyzed the problem of the p chart when it is
based on a large subgroup size and it is proposed a Bayesian solution for this
problem.
Key words:
Quality control, Bayesian methods, Beta-binomial distribution, Poisson-gamma
distribution.
PDF (Spanish)