Design of Improved EWMA Control Chart for Monitoring the Process Mean Using New Median Quartile Double Ranked Set Sampling
It is essential to monitor the mean of a process regarding quality characteristics for the ongoing production. For enhancement of mean monitoring power of the exponentially weighted moving average (EWMA) chart, a new median quartile double ranked set sampling (MQDRSS) based EWMA control chart is proposed and named as EWMA-MQDRSS chart. In order to study the performance of the developed EWMA-MQDRSS chart, performance measures; average run length, and the standard deviation of run length are used. The shift detection ability of the proposed chart has been compared with counterparts, under the simple random sampling and ranking based sampling techniques. The extensive simulation-based results indicate that the EWMA-MQDRSS chart performs better to trace all kinds of shifts than the existing charts. An illustrative application concerning monitoring the diameter of the piston ring of a machine is also provided to demonstrate the practical utilization of the suggested chart.
Abujiya, M. R. and Lee, M. H. (2013). The three statistical control charts using ranked set sampling. In: 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO). Hammamet Tunisia, 1–6.
Abujiya, M. R. and Muttlak, H. A. (2004). Quality control chart for the mean using double ranked set sampling, Journal of Applied Statistics, 31(10), pp. 1185–1201.
Abujiya, M. R. and Muttlak, H. A. (2007). Monitoring the process mean and variance using ranked set sampling and its modifications, J. Stat. Theory Appl., 6(4), pp. 408–422.
Ali, S., Abbas, Z., Nazir, H. Z., Riaz, M., Zhang, X. and Li, Y. (2020). On designing non-parametric EWMA sign chart under ranked set sampling scheme with application to industrial process, Mathematics, 8, 1497. doi.org/10.3390/math8091497.
Al-Omari, A. I. and Al-Saleh, M. F. (2009). Quartile double ranked set sampling for estimating the population mean, Econ. Qual. Control, 24(2), pp. 243–253.
Al-Omari, A. I. and Haq, A. (2012). Improved quality control charts for monitoring the process mean using double-ranked set sampling methods, Journal of Applied Statistics, 39(4), pp. 745–763.
Al-Saleh, M. F. and Al-Kadiri, M. A. (2000). Double ranked set sampling, Statistics and Probability Letters, 48(2), pp. 205–212.
Haq, A., Brown, J. and Moltchanova, E. (2015). A new exponentially weighted moving average control chart for monitoring the process mean, Quality and Reliability Engineering International, 31(8), pp. 1623–1640.
McIntyre, G. A. (1952). A method for unbiased selective sampling using ranked sets, Australian Journal of Agricultural Research, 3, pp. 385–390.
Montgomery, D. C. (2009). Introduction to Statistical Quality Control, John Wiley and Sons, New York.
Muttlak, H. A. (1997). Median ranked set sampling, Journal of Applied Statistical Sciences, 6(4), pp. 245–255.
Muttlak, H. A. (2003). Investigating the use of quartile ranked set samples for estimating the population mean, Applied Mathematics and Computation, 146, pp. 437–443.
Noor-ul-Amin, M. and Tayyab, M (2020). Enhancing the performance of exponential weighted moving average control chart using paired double ranked set sampling, Journal of Statistical Computation and Simulation, 90(6), pp. 1118–1130.
Noor-ul-Amin, M., Arif, F. and Hanif, M. (2019). Joint monitoring of mean and variance using likelihood ratio test statistic under pair ranked set sampling scheme, Iranian Journal of Science and Technology, Transections A: Science, 43(5), pp. 2449–2460.
Roberts, S. W. (1959). Control chart tests based on geometric moving averages, Technometrics, 1(3), pp. 239–250.
Shewhart, W. A. (1924). Some applications of statistical schemes to the analysis of physical and engineering data, Bell Technical Journal, 3, pp. 43–87.
Tayyab, M., Noor-ul-Amin, M. and Hanif, M. (2019). Exponential weighted moving average control charts for monitoring the process mean using pair Ranked Set Sampling schemes, Iranian Journal of Science and Technology, Transactions A: Science, 43(4), pp. 1941–1950.