Distribution-free control chart

Distribution-free (nonparametric) control charts are one of the most important tools of statistical process monitoring and control. Implementation techniques of distribution-free control charts do not require any knowledge about the underlying process distribution or its parameters. The main advantage of distribution-free control charts is its in-control robustness, in the sense that, irrespective of the nature of the underlying process distributions, the properties of these control charts remain same when the process is smoothly operating without presence of any assignable cause.

Early evidence of research on nonparametric control charts may be found in 1981[1] when P.K. Bhattacharya and D. Frierson introduced a nonparametric control chart for detecting small disorders. However, major growth of nonparametric control charting schemes has taken place only in the recent years.

There are distribution-free control charts for both Phase-I analysis and Phase-II monitoring.

One of the most notable distribution-free control chart for Phase-I analysis is RS/P chart proposed by G. Capizzi and G. Masaratto. RS/P chart separately monitor location and scale parameters of a univariate process using two separate charts. In 2019, Chenglong Li, Amitava Mukherjee and Qin Su proposed a single distribution-free control chart for Phase-I analysis using multisample Lepage statistic.


Some popular Phase-II distribution-free control charts for univariate continuous processes includes:

  • Sign charts based on the sign statistic[2] - used to monitor location parameter of a process
  • Wilcoxon rank-sum charts based on the Wilcoxon rank-sum test[3] - used to monitor location parameter of a process
  • Control charts based on precedence or exceedance statistic
  • Shewhart-Lepage chart based on the Lepage test[4] - used to monitor both location and scale parameters of a process simultaneously in a single chart
  • Shewhart-Cucconi chart based on the Cucconi test[5] - used to monitor both location and scale parameters of a process simultaneously in a single chart
gollark: This is problematic. Apparently small stars would basically just be red anyway, and larger ones would become red after being in the main sequence!
gollark: Not sure about their evolution, though.
gollark: There are intermediate classes between M (red dwarf) and G (our sun, roughly).
gollark: If you remove *some* amount, I don't know.
gollark: If you remove a lot it would cool down and become a red dwarf.

References
  1. Bhattacharya, P. K.; Frierson, Dargan (May 1981). "A Nonparametric Control Chart for Detecting Small Disorders". The Annals of Statistics. 9 (3): 544–554. doi:10.1214/aos/1176345458. ISSN 0090-5364.
  2. Amin, Raid W.; Reynolds, Marion R.; Saad, Bakir (January 1995). "Nonparametric quality control charts based on the sign statistic". Communications in Statistics - Theory and Methods. 24 (6): 1597–1623. doi:10.1080/03610929508831574. ISSN 0361-0926.
  3. Balakrishnan, N.; Triantafyllou, I.S.; Koutras, M.V. (September 2009). "Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics". Journal of Statistical Planning and Inference. 139 (9): 3177–3192. doi:10.1016/j.jspi.2009.02.013. ISSN 0378-3758.
  4. Mukherjee, A.; Chakraborti, S. (2011-09-26). "A Distribution-free Control Chart for the Joint Monitoring of Location and Scale". Quality and Reliability Engineering International. 28 (3): 335–352. doi:10.1002/qre.1249. ISSN 0748-8017.
  5. Chowdhury, S.; Mukherjee, A.; Chakraborti, S. (2013-02-19). "A New Distribution-free Control Chart for Joint Monitoring of Unknown Location and Scale Parameters of Continuous Distributions". Quality and Reliability Engineering International. 30 (2): 191–204. doi:10.1002/qre.1488. ISSN 0748-8017.
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