Short‐run statistical process control: Q‐chart enhancements and alternative methods

Enrique Del Castillo, Douglas C. Montgomery

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


In processes where the length of the production run is short, data to estimate the process parameters and control limits may not be available prior to the start of production, and because of the short run time, traditional methods for establishing control charts cannot be easily applied. Recently, Q charts have been proposed to address this problem. We study the average run length (ARL) of Q charts for a normally distributed variable assuming that a sustained shift occurs in the quality characteristic. It is shown that in some cases Q charts do not exhibit adequate ARL performance. Modifications that enhance the ARL properties of Q charts are presented. Some alternatives to Q charts are also discussed. For the case of a known process target two alternative methods are presented: an exponentially weighted moving average (EWMA) method and an adaptive Kalman filtering method. It is shown that both methods have better ARL performance than Q charts for that case. For the case of both process parameters unknown, an adaptive Kalman filtering method used with a tracking signal provides an ARL performance that improves as better estimates of the process mean and variance are given. A practical example illustrates the tracking signal method for the case when the process parameters are unknown.

Original languageEnglish (US)
Pages (from-to)87-97
Number of pages11
JournalQuality and Reliability Engineering International
Issue number2
StatePublished - 1994

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


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