DOI QR코드

DOI QR Code

A Control Chart for Gamma Distribution using Multiple Dependent State Sampling

  • Aslam, Muhammad (Department of Statistics, Faculty of Sciences, King Abdulaziz University) ;
  • Arif, Osama-H. (Department of Statistics, Faculty of Sciences, King Abdulaziz University) ;
  • Jun, Chi-Hyuck (Department of Industrial and Management Engineering, POSTECH)
  • Received : 2016.05.18
  • Accepted : 2016.09.27
  • Published : 2017.03.30

Abstract

In this article, a control chart based on multiple dependent (or deferred) state sampling for the gamma distributed quality characteristic is proposed using the gamma to normal transformation. The proposed control chart has two pairs of control limits, which can be determined by considering the in-control average run length (ARL). The shift in the scale parameter of a gamma distribution is considered and the out-of-control ARL is evaluated. The performance of the proposed chart has been shown for different levels of the parameters of the proposed control chart. It is also shown that the proposed chart is better than the Shewhart chart in terms of ARLs. A case study with a real data has been included for the practical usage of the proposed scheme.

Keywords

Multiple Dependent states;Control Chart;Gamma Distribution;Wilson-Hilferty Transformation;Average Run Length;Simulation

References

  1. Abbasi, S. A. and Miller, A. (2013), MDEWMA chart: An efficient and robust alternative to monitor process dispersion, Journal of Statistical Computation and Simulation, 83(2), 247-268. https://doi.org/10.1080/00949655.2011.601416
  2. Ahmad, L., Aslam, M., and Jun, C.-H. (2013), Designing of X-bar control charts based on process capability index using repetitive sampling, Transactions of the Institute of Measurement and Control, 0142331213502070. https://doi.org/10.1177/0142331213502070
  3. Ahmad, S., Riaz, M., Abbasi, S. A., and Lin, Z. (2013), On monitoring process variability under double sampling scheme, International Journal of Production Economics, 142(2), 388-400. https://doi.org/10.1016/j.ijpe.2012.12.015
  4. Aksoy, H. (2000), Use of gamma distribution in hydrological analysis, Turkish Journal of Engineering and Environmental Sciences, 24(6), 419-428.
  5. Al-Oraini, H. A. and Rahim, M. (2002), Economic statistical design of X control charts for systems with Gamma (${\lambda}$, 2) in-control times, Computers & industrial engineering, 43(3), 645-654. https://doi.org/10.1016/S0360-8352(02)00119-5
  6. Aslam, M. (2016), A Mixed EWMA-CUSUM Control Chart for Weibull-Distributed Quality Characteristics, Quality and Reliability Engineering International.
  7. Aslam, M., Azam, M., and Jun, C.-H. (2015), Multiple dependent state repetitive group sampling plan for Burr XII distribution, Quality Engineering, 1-7.
  8. Aslam, M., Azam, M., Khan, N., and Jun, C.-H. (2015), A control chart for an exponential distribution using multiple dependent state sampling, Quality & Quantity, 49(2), 455-462. https://doi.org/10.1007/s11135-014-0002-2
  9. Aslam, M., Mohsin, M., and Jun, C.-H. (2016), A New t-Chart Using Process Capability Index, Communications in Statistics-Simulation and Computation (just-accepted).
  10. Azam, M., Aslam, M., and Jun, C.-H. (2015), Designing of a hybrid exponentially weighted moving average control chart using repetitive sampling, The International Journal of Advanced Manufacturing Technology, 77(9-12), 1927-1933. https://doi.org/10.1007/s00170-014-6585-x
  11. Balamurali, S. and Jun, C.-H. (2007), Multiple dependent state sampling plans for lot acceptance based on measurement data, European Journal of Operational Research, 180(3), 1221-1230. https://doi.org/10.1016/j.ejor.2006.05.025
  12. Chananet, C., Sukparungsee, S., and Areepong, Y. (2014), The ARL of EWMA chart for monitoring ZINB model using Markov chain approach, International Journal of Applied Physics and Mathematics, 4(4), 236. https://doi.org/10.7763/IJAPM.2014.V4.290
  13. Hogg, R. V. and Craig, A. T. (1970), introduction to. Mathematical stati sties EDITION.
  14. Jearkpaporn, D., Montgomery, D. C., Runger, G. C., and Borror, C. M. (2003), Process monitoring for correlated gamma-distributed data using generalized-linear-modelbased control charts, Quality and Reliability Engineering International, 19(6), 477-491. https://doi.org/10.1002/qre.521
  15. Johnson, N. L. and Kotz, S. (1970), Distributions in Statistics: Continuous Univariate Distributions: Vol.2: Houghton Mifflin.
  16. Mohammed, M. (2004), Using statistical process control to improve the quality of health care, Quality and Safety in Health Care, 13(4), 243-245.
  17. Mohammed, M. and Laney, D. (2006), Overdispersion in health care performance data: Laney's approach, Quality and Safety in Health Care, 15(5), 383-384. https://doi.org/10.1136/qshc.2006.017830
  18. Montgomery, D. C. (2007), Introduction to Statistical Quality Control, John Wiley & Sons.
  19. Nelson, L. S. (1994), A control chart for parts-per-million nonconforming items, Journal of Quality Technology, 26(3), 239-240. https://doi.org/10.1080/00224065.1994.11979529
  20. Santiago, E. and Smith, J. (2013), Control charts based on the exponential distribution: Adapting runs rules for the t chart, Quality Engineering, 25(2), 85-96. https://doi.org/10.1080/08982112.2012.740646
  21. Santos, D. (2009), Beyond Six Sigma: A Control Chart for Tracking Defects per Billion Opportunities (dpbo), International Journal of Industrial Engineering: Theory, Applications and Practice, 16(3), 227-233.
  22. Schilling, E. G. and Nelson, P. R. (1976), The effect of non-normality on the control limits of X-bar charts, Journal of Quality Technology, 8(4).
  23. Sheu, S. H. and Lin, T. C. (2003), The generally weighted moving average control chart for detecting small shifts in the process mean, Quality Engineering, 16(2), 209-231. https://doi.org/10.1081/QEN-120024009
  24. Shu, L., Huang, W., and Jiang, W. (2014), A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts, Naval Research Logistics (NRL), 61(3), 223-237. https://doi.org/10.1002/nav.21579
  25. Soundararajan, V. and Vijayaraghavan, R. (1990), Construction and selection of multiple dependent (deferred) state sampling plan, Journal of Applied Statistics, 17(3), 397-409. https://doi.org/10.1080/02664769000000012
  26. Stoumbos, Z. G. B. and Reynolds Jr, M. R. (2000), Robustness to non-normality and autocorrelation of individuals control charts, Journal of Statistical Computation and Simulation, 66(2), 145-187. https://doi.org/10.1080/00949650008812019
  27. Wortham, A. and Baker, R. (1976), Multiple deferred state sampling inspection, The International Journal Of Production Research, 14(6), 719-731. https://doi.org/10.1080/00207547608956391
  28. Zhang, C., Xie, M., Liu, J., and Goh, T. (2007), A control chart for the Gamma distribution as a model of time between events, International Journal of Production Research, 45(23), 5649-5666. https://doi.org/10.1080/00207540701325082

Cited by

  1. A new variable control chart under generalized multiple dependent state sampling pp.1532-4141, 2018, https://doi.org/10.1080/03610918.2018.1517213