Homogeneously Weighted Moving Average Control Chart for Rayleigh Distribution
DOI:
https://doi.org/10.61506/01.00043Keywords:
HWMA chart, Average Run Length, Rayleigh distribution, EWMA, ShiftsAbstract
In this paper, we have proposed Homogeneously Weighted Moving Average (HWMA) control chart for Rayleigh distribution. The Average Run Length (ARL1) is used to evaluate the performance of the proposed HWMA control charts. The ARL1 performance of HWMA control chart is compared to the Exponentially weighted moving average (EWMA) control charts with respect to the different shift size (i.e. 10%, 15%, 20%, 30%, 40% increase and decrease in shift). The results are calculated using sample size n=5. It is observed that with the increase in shift proposed HWMA chart shows more efficient results i.e. ARL1 values decrease with the increase in shifts. It is found that the proposed HWMA chart for Rayleigh distribution outperforms the existing EWMA control chart.
References
Aczel, A. D. (1989). Complete Business Statistics, Irwin, p. 1056. ISBN 0-256-05710-8.
Abbas, N., Riaz, M., and Does, R. J. M. M. (2012). CS-EWMA Chart for Monitoring Process Dispersion. Quality and Reliability Engineering International, 29(5), 653–663.
Ahmed, S., Abbassi, SA.,Riaz, M., andAbbass, N. (2014). On efficient use of auxiliary information for control charting in SPC. Computers and Industrial Engineering, 67:173–184.
Azam M, Aslam M, 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), 1927–1933.
Aslam, M., Khan, N., and Jun, Chi-Hyuck. (2016), A hybrid exponentially weighted moving average chart for COM-Poisson distribution, Transactions of Institute of Measurement and Control.
Abbasi, S. A., and M. Riaz. 2016. On dual use of auxiliary information for efficient monitoring. Quality and Reliability Engineering International, 32(2):705–14.
Abbas, N. (2018). Homogeneously weighted moving average control chart with an application in substrate manufacturing process. Compute. Ind. Eng., 120, 460–470.
Adegoke, N.A.; Smith, A.N.H.; Anderson, M.J.; Sanusi, R.A.; Pawley, M.D.M. (2019). Efficient homogeneously weighted moving average chart for monitoring process mean using an auxiliary variable. IEEE Access, 7, 94021–94032
Abid, M., Shabbir, A., Nazir, H. Z., Sherwani, R. A. K., & Riaz, M. (2020). A double homogeneously weighted moving average control chart for monitoring of the process mean. Quality and Reliability Engineering International, 36(5), 1513-1527..
Butt, M. M., and Raza, S. M. M. (2017). The Optimization of Design of EWMA Control Chart using Box-Behnken Method under Type I Censoring. Journal of Statistics, 24(1), pp.133-149.
Chen, G., S. W. Cheng, and H. Xie. 2004. A new EWMA control chart for monitoring both location and dispersion. Quality Technology Quantity Management 1(2), 217–31.
Capizzi, G., & Masarotto, G. (2010). Combined Shewhart–EWMA control charts with estimated parameters. Journal of Statistical Computation and Simulation, 80(7), 793-807.
Asif, F., Khan, S., & Noor-ul-Amin, M. (2020). Hybrid exponentially weighted moving average control chart with measurement error. Iranian Journal of Science and Technology, Transactions A: Science, 44, 801-811.
Gan, F. F. (1990). Monitoring observations generated from a binomial distribution using modified exponentially weighted moving average control chart. Journal of Statistical Computation and Simulation,37(1-2),pp.45-60.
Gupta, C. B., and Gupta, V. (2009). Introduction to Statistical Methods. Vikas Publishing House Pvt Ltd.
Haq, A. (2012). A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean. Quality and Reliability Engineering International, 29(7), 1015–1025.
Haq, A. (2013), A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean, Quality and Reliability Engineering International, 29, 1015-1025.
Haq, A. (2016). A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean: Discussion. Quality and Reliability Engineering International, 33(7), 1629–1631.
Haq, A., and Khoo, M. B. C. (2017). A new double sampling control chart for monitoring process mean using auxiliary information. Journal of Statistical Computation and Simulation, 88(5), 869–899.
Javaid, A., Noor-ul-Amin, M., and Hanif, M. (2018). A new Max-HEWMA control chart using auxiliary information. Communications in Statistics - Simulation and Computation, 1–21.
Kotz, S. and Johnson, N.L. (1988). Encyclopedia of statistical sciences: vol.8. New York: Wiley.
Keller, G. (2015). Statistics for Management and Economics, Abbreviated. Cengage Learning.
Leavenworth, R. S., & Grant, E. L. (2000). Statistical quality control. Tata McGraw-Hill Education
Lucas J.M., and Saccucci M.S. (1990). Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements. Technometrics, 32, 1–12.
Lucas, J. M. (1982). Combined Shewhart-CUSUM quality control schemes. Journal of Quality Technology, 14(2), 51-59.
Lucas J.M, Crosier RB. (1982). Fast initial response for CUSUM quality-control schemes: give your CUSUM a head start. Technometrics. 24(23),199-205.
L. Xiaohong and W. Zhaojun, (2009). The CUSUM control chart for the autocorrelated data with measurement error. Chinese Journal of Applied Probability, 25(5), 461–474.
Monte Carlo Simulation. (2021, July 16). Retrieved September 27, 2021, from https://www.ibm.com/sg-en/cloud/learn/monte-carlo-simulation
Montgomery, D. C. (2009). Introduction to statistical quality control. John Wiley and Sons.
Munir, W., and Haq, A. (2017). New cumulative sum control charts for monitoring process variability. Journal of Statistical Computation and Simulation, 87(15), 2882–2899.
Noor-ul-Amin, M., and Hanif, M. (2012). Some Exponential Estimators In Survey Sampling. Pakistan Journal of Statistics, 28(3), 367-374.
Maravelakis, P., Panaretos, J., & Psarakis, S. (2004). EWMA chart and measurement error. Journal of Applied Statistics, 31(4), 445-455.
Raza, S. M. M., and Butt, M. M. (2018). New Shewhart and EWMA Type Control Charts using Exponential Type Estimator with Two Auxiliary Variables under Two Phase Sampling. Pakistan Journal of Statistics and Operation Research, 14(2), 367-386.
Riaz M. (2008) Monitoring process mean level using auxiliary information. Statistical Neerlandica, 62(4):458–481.
Riaz M and Does RJMM. (2009). A process variability control chart. Computational Statistics,24(2), 345–368.
Riaz M. (2011). An improved control structure for process location parameter. Quality and Reliability Engineering International, 27(8):1033–1041.
Raji, I. A., Abbas, N., andRiaz, M. (2018). On designing a robust double exponentially weighted moving average control chart for process monitoring. Transactions of the Institute of Measurement and Control,
Shabbir, J., and Awan, W. H. (2015). An Efficient Shewhart-Type Control Chart to Monitor Moderate Size Shifts in the Process Mean in Phase II. Quality and Reliability Engineering International, 32(5), 1597–1619.
Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3, 43–87.
