The Exact Run Length Distribution and Design of the Shewhart ¯X Chart with Estimated Parameters Based on Median Run Length

Wei Lin Teoh, Michael Boon Chong Khoo, Philippe Castagliola, Ming Ha Lee

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

This paper investigates the Shewhart (Formula presented.) chart with estimated parameters. When parameters are unknown, we show that the average run length is a confusing performance measure and that the median run length, which is a better representation of the central tendency associated with different shapes of the run length distribution, is more intuitive. A new design model for the Shewhart (Formula presented.) chart with estimated parameters is developed. With this proposed design model, the Shewhart (Formula presented.) chart for both known and estimated parameters, even with a small number of Phase-I samples, will have an almost similar sensitivity for a specified shift.

Original languageEnglish
Pages (from-to)2081-2103
Number of pages23
JournalCommunications in Statistics: Simulation and Computation
Volume45
Issue number6
DOIs
Publication statusPublished - 2016

Keywords

  • Average run length
  • Estimated parameters
  • Median run length
  • Run length distribution
  • Shewhart chart
  • Statistical process control

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation

Fingerprint Dive into the research topics of 'The Exact Run Length Distribution and Design of the Shewhart ¯X Chart with Estimated Parameters Based on Median Run Length'. Together they form a unique fingerprint.

Cite this