The Exact Run Length Distribution and Design of the Shewhart Chart with Estimated Parameters Based on Median Run Length. Issue 6 (2nd July 2016)

• Record Type: Journal Article
• Authors: Teoh, W. L.; Khoo, Michael B. C.; Castagliola, Philippe; Lee, M. H.
• Is Part Of: Communications in statistics. Volume 45:Issue 6(2016)
• Page Start: 2081
• Page End: 2103
• Publication Date: 2016-07-02
• Subjects: Average run length -- Estimated parameters -- Median run length -- Run length distribution -- Shewhart chart -- Statistical process control; 62P30; 62E15; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2014.889158
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract : This paper investigates the Shewhart 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 chart with estimated parameters is developed. With this proposed design model, the Shewhart 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.