Monitoring observations generated from a binomial distribution using modified exponentially weighted moving average control chart

Abstract

In many production processes, measures of quality of a product cannot be conveniently represented numerically, it is necessary or more convenient to use counts of defective or nonconforming products out of a random sample of n products as indications whether a production process is in control or out of control. The count of nonconforming products is usually assumed to be a binomial random variable with parameters n and p, where p is the actual fraction of nonconforming products produced. The Shewhart fraction nonconforming or p control chart is perhaps the simplest type of control charts commonly used for monitoring binomial counts. A modified exponentially weighted moving average (EWMA) control chart is developed in this paper for monitoring binomial counts. The average run length (ARL) and the probability function of the run length of the modified EWMA control chart can be computed exactly using results from the Markov chain theory. The modified EWMA control chart is demonstrated to be generally superior than the Shewhart control chart based on ARL consideration. The use of the modified EWMA control chart is illustrated with an example.

Keywords:

• Average run length (ARL)
• Markov chain
• p control chart
• np control chart
• statistical process control (SPC)

^∗Dr. Gan is a Lecturer in the Department of Mathematics.

^∗Dr. Gan is a Lecturer in the Department of Mathematics.

Notes

^∗Dr. Gan is a Lecturer in the Department of Mathematics.