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Run Length Distribution and Percentiles: The Shewhart X Chart with Unknown Parameters

Summary: [This abstract is based on the author’s abstract.]Important information concerning the performance of control charts may be missed by focusing too much on the average run length, since the run length distribution is usually highly right-skewed. Examination of the entire run length distribution for a complete understanding of performance can be aided by an examination of a number of representative percentiles. This study examines the run length distribution and the percentiles of the Shewhart X-bar chart when the process mean and variance are both unknown and therefore estimated. An alternate chart design criterion, based on the in-control median run length, is proposed.>QICID:Copyright: 2007, Taylor & Francis Group, LLCTitle: Two Sets of Runs Rules for the X-Bar ChartAuthor: Acosta-Mejia, C.A.;Organization: Instituto Tecnologico Autonomo de Mexico, MexicoSubject: Average run length (ARL); Control limits; Markov chains; Run rules; Warning limits;Date: April 2007Source: QESponsor:Journal: Quality EngineeringVolume: 19Number: 2Page: 129-136[This abstract is based on the author’s abstract.]Control charts are used with run rules to increase their ability to detect small shifts. The performances of two sets of run rules are reviewed. Run rules based on these sets are proposed that are intended to be used with a modified Shewhart X-bar chart. These proposed charts performed better than the Shewhart X-bar chart for detecting small shifts, and were comparable in performance for large shifts.

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  • Topics: Statistical Process Control (SPC)
  • Keywords: Average run length (ARL), Cumulative sum control chart (CUSUM), False alarm rate (FAR), Run length, Parameters, Statistical process control (SPC), Stochastic models
  • Author: Chakraborti, S.
  • Journal: Quality Engineering