Abstract
The sampling scheme plays an important role in the performance of control charts. This study leads to the development of a new Shewhart-type mean control chart to monitor the process by employing cost-effective quartile pair ranked set sampling (QPRSS) method. This competes with known mean control charts based on simple random sampling (SRS) and the existing pair ranked set sampling methods. The average run length (ARL) and the standard deviation of run length (SDRL) are utilized as performance measures to assess the efficiency of proposed QPRSS mean control chart and other considered SRS, pair ranked set sampling (PRSS) and extreme pair ranked set sampling (EPRSS) mean charts by using Monte Carlo simulations. The simulation results of the QPRSS mean control chart are better than the results obtained using SRS, PRSS and EPRSS mean control charts. The application of the proposed control chart is demonstrated with real-life data that supported the findings of the simulation study.
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References
Montgomery DC (2009) Introduction to statistical quality control. Wiley, New York
Shewhart WA (1924) Some applications of statistical methods to the analysis of physical and engineering data. Bell Syst Tech J 3(1):43–87
McIntyre G (1952) A method for unbiased selective sampling, using ranked sets. Aust J Agric Res 3(4):385–390
Takahasi K, Wakimoto K (1968) On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann Inst Stat Math 20(1):1–31
Dell TR, Clutter JL (1972) Ranked set sampling theory with order statistics background. Biometrics 28(2):545–555
Muttlak HA (1996) Pair rank set sampling. Biom J 38(7):879–885
Samawi HM, Ahmed MS, Abu-Dayyeh W (1996) Estimating the population mean using extreme ranked set sampling. Biom J 38(5):577–586
Muttlak HA (2003) Investigating the use of quartile ranked set samples for estimating the population mean. Appl Math Comput 146:437–443
Balci S, Akkaya AD, Ulgen BE (2013) Modified maximum likelihood estimators using ranked set sampling. J Comput Appl Math 238:171–179
Tayyab M, Noor-ul-Amin M, Hanif M (2018) Quartile pair ranked set sampling: development and estimation. Proc Natl Acad Sci India A (submitted for publication)
Noor-ul-Amin M, Tayyab M, Hanif M (2019) Mean estimation using even order ranked set sampling. Punjab Univ J Math 51(1):91–99
Salazar R, Sinha A (1997) Control chart X-bar based on ranked set sampling. Comun Tecica 1:1–97
Muttlak H, Al-Sabah W (2003) Statistical quality control based on ranked set sampling. J Appl Stat 30(9):1055–1078
Al-Nasser AD, Al-Rawwash M (2007) A control chart based on ranked data. J Appl Sci 7(14):1936–1941
Al-Omari AI, Al-Nasser AD (2011) Statistical quality control limits for the sample mean chart using robust extreme ranked set sampling. Econ Qual Control 26(1):73–89
Koyuncu N, Karagöz D (2018) New mean charts for bivariate asymmetric distributions using different ranked set sampling designs. Qual Technol Quant Manag 15(5):602–621
Awais M, Haq A (2018) A new cumulative sum control chart for monitoring the process mean using varied L ranked set sampling. J Ind Prod Eng 35(2):74–90
Noor-ul-Amin M, Arif F, Hanif M (2019) Joint monitoring of mean and variance using likelihood ratio test statistic under pair ranked set sampling scheme. Iran J Sci Technol Trans A Sci 43(5):2449–2460
Muttlak H, Al-Sabah W (2003) Statistical quality control based on pair and selected ranked set sampling. Pak J Stat 19(1):107–128
Noor-ul-Amin M, Khan S, Aslam M (2018) An EWMA control chart using two parametric ratio estimator. J Ind Prod Eng 35(5):298–308
Abid M, Nazir HZ, Riaz M, Lin Z (2017) Investigating the impact of ranked set sampling in nonparametric CUSUM control charts. Qual Reliab Eng Int 33(1):203–214
Noor-ul-Amin M, Khan S, Sanaullah A (2019) HEWMA control chart using auxiliary information. Iran J Sci Technol Trans A Sci 43(3):891–903
Lee H, Aslam M, Shakeel QUA, Lee W, Jun CH (2015) A control chart using an auxiliary variable and repetitive sampling for monitoring process mean. J Stat Comput Simul 85(16):3289–3296
Haq A (2017) A new maximum EWMA control chart for simultaneously monitoring process mean and dispersion using auxiliary information. Qual Reliab Eng Int 33(7):1577–1587
Javaid A, Noor-ul-Amin M, Hanif M (2018) A new Max-HEWMA control chart using auxiliary information. Commun Stat Simul Comput. https://doi.org/10.1080/03610918.2018.1494282
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The authors are thankful to the anonymous reviewers for valuable comments which led to an improvement in the paper.
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Tayyab, M., Noor-ul-Amin, M. & Hanif, M. A Control Chart Using Quartile Pair Ranked Set Sampling for Monitoring the Process Mean. J Stat Theory Pract 14, 2 (2020). https://doi.org/10.1007/s42519-019-0069-0
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DOI: https://doi.org/10.1007/s42519-019-0069-0