A single X chart outperforming the joint X & R and X & S charts for monitoring mean and variance. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Haridy, Salah; Ou, Yanjing; Wu, Zhang; Khoo, Michael B. C.
• Is Part Of: Quality technology & quantitative management. Volume 13:Issue 3(2016)
• Page Start: 289
• Page End: 308
• Publication Date: 2016-07-02
• Subjects: Quality control -- statistical process control -- control chart -- Shewhart chart -- Average extra quadratic loss; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2016.1189181
• Languages: English
• ISSNs: 1684-3703

Abstract

Abstract: The Shewhart X & R and X & S control charts have traditionally been used for detecting mean shift δμ and standard deviation shift δσ . This article studies and compares the overall performance of the X chart with that of the X & R and X & S charts, as well as the X&MR chart. The comparative study led to surprising results that contradict the conventional wisdom in Statistical Process Control (SPC) niche. It is found that the simplest single X chart (i.e., the X chart with a sample size n = 1) is always the optimal version of the X chart for detecting δμ and δσ . Moreover, the single X chart even outperforms the joint X & R and X & S charts in overall detection effectiveness. On average, the X chart is more effective than the X & R and X & S charts by around 5% under different circumstances. Most importantly, the X chart is very simple to understand, implement and design. As a result, it may be highly preferred for many SPC applications, in which both the mean and variance of a variable need to be monitored.