Distribution-free control chart
Distribution-free (Nonparametric) control charts are one of the most important tool 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.
History and Background
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.
Most Popular Distribution-Free Control Charts for Univariate Continuous Processes
- Sign charts based on the Sign statistic[2]
- Wilcoxon Ranksum Charts based on the Wilcoxon Ranksum statistic[3]
- Shewhart Lepage Chart based on the Lepage Statistic[4]
- Shewhart Cucconi Chart based on the Cucconi Statistic[5]
- ^ Bhattacharya, P. K.; Frierson, Dargan (1981-05). "A Nonparametric Control Chart for Detecting Small Disorders". The Annals of Statistics. 9 (3): 544–554. doi:10.1214/aos/1176345458. ISSN 0090-5364.
{{cite journal}}: Check date values in:|date=(help) - ^ Amin, Raid W.; Reynolds, Marion R.; Saad, Bakir (1995-01). "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.
{{cite journal}}: Check date values in:|date=(help) - ^ Balakrishnan, N.; Triantafyllou, I.S.; Koutras, M.V. (2009-09). "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.
{{cite journal}}: Check date values in:|date=(help) - ^ 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.