Run length distributions and economic design of X̄ charts with unknown process variance

Research output: Contribution to journalArticle

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Abstract

The run length distribution of X̄ charts with unknown process variance is analized using numerical integration. Both traditional X̄ chart limits and a method due to Hillier are considered. It is shown that setting control limits based on the pooled standard deviation, as opposed to the average sample standard deviation, provides better run length performance due to its smaller mean square error. The effect of an unknown process variance is shown to increase the area under both tails of the run length distribution. If Hillier's method is used instead, only the right tail of the run length distribution is increased. Collani's model for the economic design of X̄ charts is extended to the case of unknown process variance by writing his standardized objective function in terms of average run lengths.

Original languageEnglish (US)
Pages (from-to)189-201
Number of pages13
JournalMetrika
Volume43
Issue number3
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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