Distribution-free control chart
Distribution-free (nonparametric) control charts are one of the most important tools of statistical process monitoring and control in the twenty-first century. 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 nonparamertric 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[when?].
Their use as distribution-free control charts for univariate continuous processes includes:
- Sign charts based on the sign statistic[2]
- Wilcoxon rank-sum charts based on the Wilcoxon rank-sum test[3]
- Shewhart-Lepage chart based on the Lepage test[4]
- Shewhart-Cucconi chart based on the Cucconi test[5]
References
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.