Nonparametric Control Chart for the Joint Monitoring of Location and Scale Using Ranked Set Sampling
Abstract
A single nonparametric Shewhart-type control chart based on Lepage test (SL chart) has recently been introduced in the literature for joint monitoring of the location and the scale parameters of a continuous process. The SL chart is based on simple random sampling (SRS) scheme. In the literature, ranked set sampling (RSS) technique is preferred over SRS scheme as it reduces the variability and improves the performance of the control chart. In this paper, RSS scheme is used in the construction of the existing SL chart to enhance the performance of the chart for joint monitoring of location and scale. The run length performance of the proposed SL chart under RSS scheme is compared with the chart using SRS scheme. The comparison revealed that the proposed SL chart based on RSS scheme outperforms the chart with SRS scheme.
References
1. A. Mukherjee and S. Chakraborti; A Distribution-Free Control Chart for the Joint Monitoring of Location and Scale. Quality and Reliability Engineering International, 28(3), 335-352 (2012).
2. D.M. Zombade and V.B. Ghute; Nonparametric CUSUM Charts for Process Variability. Journal of Academia and Industrial Research, 3(1), 53-57 (2014).
3. D.M. Zombade and V.B. Ghute; Shewhart-Type Nonparametric Control Chart for Process Location. Communications in Statistics-Theory and Methods, 48(7), 1621-1634 (2019).
4. D.T. Shirke and M.S. Barale; A Nonparametric CUSUM Chart for Process Dispersion. Quality and Reliability Engineering International, 34(5), 858-866 (2018).
5. G.A. McIntyre; A Method of Unbiased Selective Sampling using Ranked Sets. Australian Journal of Agricultural Research, 3(4), 385–390 (1952).
6. H. Muttlak and W. Al-Sabah; Statistical Quality Control based on Ranked Set Sampling. Journal of Applied Statistics, 30(9), 1055–1078 (2003).
7. I.M. Almanjahie; Z. Rasheed; M. Khan; S.M. Anwar and A.N. Cheema; Ranked Set Sampling based Distribution-Free Control Chart with Application in CSTR Process. Computer Modeling in Engineering and Sciences, 135(3), 2091-2118 (2023).
8. J.M. Boone and S. Chakraborti; Two Simple Shewhart-Type Multivariate Nonparametric Control Charts. Applied Stochastic Models in Business and Industry, 28(2), 130-140 (2012).
9. M. Abid; H. Nazir; M. Riaz and Z. Lin; Use of Ranked Set Sampling in Nonparametric Control Charts. Journal of the Chinese Institute of Engineers, 39(5), 627–636 (2016).
10. M. Abid; H. Nazir; M. Riaz and Z. Lin; An Efficient Nonparametric EWMA Wilcoxon Signed-Rank Chart for Monitoring Location. Quality and Reliability Engineering International, 33(3), 669–685 (2017a).
11. M. Abid; H. Nazir; M. Riaz and Z. Lin; Investing the Impact of Ranked Set Sampling in Nonparametric CUSUM Control Charts. Quality and Reliability Engineering International, 33(1), 203–214 (2017b).
12. M. Murakami and T. Matsuki; A Nonparametric Control Chart based on Mood Statistic for Dispersion. International Journal of Advanced Manufacturing Technology, 49(5), 757-763 (2010).
13. N. Das; Nonparametric Control Chart for Controlling Variability based on Rank Test. Economic Quality Control, 23(2), 227-242 (2008a).
14. N. Das; A Nonparametric Control Chart for Controlling Variability based on Squared Rank Test. Journal of Industrial and System Engineering, 2(2), 114-125 (2008b).
15. N. Das; A New Multivariate Nonparametric Control Chart based on Sign Test. Quality Technology and Quantitative Management, 5(2), 155-169 (2009).
16. R.D. Salazar and A.K. Sinha; Control Chart based on Ranked Set Sampling, Comunicacion Tecica, 1, 1–97 (1997).
17.R.W. Amin; M.R. Reynolds Jr. and S.T. Bakir; Nonparametric Quality Control Charts based on Sign Statistic. Communications in Statistics-Theory and Methods, 24(6), 1579-1623 (1995).
18.S. Asghari; B.S. Gildeh; J. Ahmadi and G.M. Borzadaran; Sign Control Chart based on Ranked Set Sampling. Quality Technology and Quantitative Management, 15(5), 568–588 (2018).
19. S. Chakraborti; P. Van-der-Laan and S.T. Bakir; Nonparametric Control Charts: An Overview and Some Results. Journal of Quality Technology, 33(3), 304-315 (2001).
20. S. Chakraborti and M.A. Graham; Nonparametric Control Charts. Encyclopaedia of Statistics in Quality and Reliability, John Wiley, New York (2007).
21.S. Chakraborti and S. Eryilmaz; A Nonparametric Shewhart-Type Signed-Rank Control Chart based on Runs. Communications in Statistics-Simulation and Computation, 36(2), 335-356 (2007).
22.S. Chakraborti and M.A. Graham; Nonparametric (Distribution-Free) Control Charts: An Updated Overview and Some Results. Quality Engineering, 31(4), 523-544 (2019).
23.S. Chowdhury; A. Mukherjee and S. Chakraborti; 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 (2013).
24.S.K. Khilare and D.T. Shirke; A Nonparametric Synthetic Control Chart using Sign Statistic. Communications in Statistics-Theory and Methods, 39(18), 3282-3293 (2010).
25. S.K. Khilare and D.T. Shirke; Nonparametric Synthetic Control Chart for Process Variation. Quality and Reliability Engineering International, 28, 193-202 (2012).
26.S.K. Khilare and D.T. Shirke; A Nonparametric Group Runs Control Chart for Location using Sign Statistic. Thailand Statistician, 21(1), 165-179 (2023).
27.S.T. Bakir; A Distribution-Free Shewhart Quality Control Chart based on Signed-Ranks. Quality Engineering, 16(4), 613-623 (2004).
28.S.T. Bakir; Distribution-Free Quality Control Charts based on Signed Rank like Statistics. Communications in Statistics-Theory and Methods, 35(4), 743-757 (2006).
29. S.W. Human; S. Chakraborti and C.F. Smit; Nonparametric Shewhart-Type Sign Control Chart based on Runs. Communications in Statistics-Theory and Methods, 39(11), 2046-2062 (2010).
30. V.B. Ghute and D.T. Shirke; Bivariate Nonparametric Synthetic Control Chart based on Sign Test. Journal of Industrial and System Engineering, 6(2), 108-121 (2012a).
31. V.B. Ghute and D.T. Shirke; A Nonparametric Signed-Rank Control Chart for Bivariate Process Location. Quality Technology and Quantitative Management, 9(4), 317-328 (2012b).
32.V.K. Ghadage and V.B. Ghute; A Nonparametric Control Chart for Joint Monitoring of Location and Scale. Reliability: Theory and Applications, 18(1), 553-563 (2023).
33. W. Tapang; A. Pongpullponsak and S. Sarikavanji; Three Nonparametric Control Charts based on Ranked Set Sampling. Chiang Mai J. Sci, 43(4), 914–929 (2016).
34.Y.A. Lepage; Combination of Wilcoxon’s and Ansari-Bradley’s Statistics. Biometrika, 58(1), 213-217 (1971).
35. Z. Abbas; H.Z. Nazir; M. Abid; N. Akhtar and M. Riaz; Enhanced Nonparametric Control Charts under Simple and Ranked Set Sampling Schemes. Transactions of the Institute of Measurement and Control, 42(14), 2744–2759 (2020).
36. Z. Rasheed; M. Khan; N.L. Abiodun; S.M. Anwar; G. Khalaf and S.A. Abbasi; Improved Nonparametric Control Chart based on Ranked Set Sampling. Mathematical Problems in Engineering, 2022, p. 7350204 (2022).
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