Exponential Weighted Moving Average Control Charts for Monitoring the Process Mean Using Pair Ranked Set Sampling Schemes

  • Muhammad Tayyab
  • Muhammad Noor-ul-AminEmail author
  • Muhammad Hanif
Research paper


An economical and efficient sampling scheme plays a vital role in the statistical process monitoring. In this paper, cost-efficient and precise pair ranked set sampling, extreme pair ranked set sampling (EPRSS) and recently suggested quartile pair ranked set sampling (QPRSS) schemes are exploited to propose new exponentially weighted moving average (EWMA) control charts, named EWMA-PRSS, EWMA-EPRSS and EWMA-QPRSS charts for efficiently monitoring the process mean. An extensive simulation study is carried out to compute run-length characteristics of the suggested control charts and compare with the simple random sampling (SRS)-based EWMA chart (EWMA-SRS). It is revealed that proposed EWMA-type charts, with either perfect or imperfect ranking, have better shift diagnostic abilities than the classical EWMA-SRS chart. This study also explored the in control robustness of the proposed charts under different non-normal distributions. An example of real data is also considered to demonstrate the working and implementation of the proposed EWMA-type control charts.


Average run length Control chart EWMA Process mean Pair ranked set sampling 


  1. Abbasi SA, Miller A (2013) MDEWMA chart: an efficient and robust alternative to monitor process dispersion. J Stat Comput Simul 83:247–268MathSciNetCrossRefGoogle Scholar
  2. Ahmad M, Hanif M, Muttlak HA (2010) Ranked set sampling. Cambridge Scholars Publishing, CambridgeGoogle Scholar
  3. Al-Nasser AD, Al-Rawwash M (2007) A control chart based on ranked data. J Appl Sci 7:1936–1941CrossRefGoogle Scholar
  4. Awais M, Haq A (2018) An EWMA chart for monitoring the process mean. J Stat Comput Simul 88(5):1003–1025MathSciNetCrossRefGoogle Scholar
  5. Balci S, Akkaya AD, Ulgen BE (2013) Modified maximum likelihood estimators using ranked set sampling. J Comput Appl Math 238:171–179MathSciNetCrossRefGoogle Scholar
  6. Borror CM, Montgomery DC, Runger GC (1999) Robustness of the EWMA control chart to non-normality. J Qual Technol 31(3):309–316CrossRefGoogle Scholar
  7. Chen Z, Bai Z, Sinha BK (2004) Ranked set sampling: theory and application. Springer, New YorkCrossRefGoogle Scholar
  8. Haq A (2014) An improved mean deviation exponentially weighted moving average control chart to monitor process dispersion under ranked set sampling. J Stat Comput Simul 84(9):2011–2024MathSciNetCrossRefGoogle Scholar
  9. Haq A, Brown J, Moltchanova E (2015) A new exponentially weighted moving average control chart for monitoring the process mean. Qual Reliab Eng Int 31(8):1623–1640CrossRefGoogle Scholar
  10. McIntyre GA (1952) A method for unbiased selective sampling using ranked sets. Aust J Agric Res 3:385–390CrossRefGoogle Scholar
  11. Montgomery DC (2009) Introduction to statistical quality control. Wiley, New YorkzbMATHGoogle Scholar
  12. Muttlak HA (1996) Pair rank set sampling. Biom J 38(7):879–885CrossRefGoogle Scholar
  13. Muttlak HA (1997) Median ranked set sampling. J Appl Stat Sci 6(4):245–255zbMATHGoogle Scholar
  14. Muttlak HA (2003) Investigating the use of quartile ranked set samples for estimating the population mean. Appl Math Comput 146:437–443MathSciNetzbMATHGoogle Scholar
  15. Muttlak HA, Al-Sabah W (2003) Statistical quality control based on ranked set sampling. J Appl Stat 39(9):1055–1078MathSciNetCrossRefGoogle Scholar
  16. Roberts SW (1959) Control chart tests based on geometric moving averages. Technometrics 1(3):239–250CrossRefGoogle Scholar
  17. Salazar RD, Sinha AK (1997) Control chart \(\bar{X}\) based on ranked set sampling. Comunicacion Tecica, no. 1-97-09 (PE/CIMAT)Google Scholar
  18. Samawi HM, Ahmed MS, Abu-Dayyeh W (1996) Estimating the population mean using extreme ranked set sampling. Biom J. 38(5):577–586CrossRefGoogle Scholar
  19. 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 20:1–31CrossRefGoogle Scholar
  20. Tayyab M, Noor-ul-Amin M, Hanif M (2017) Quartile pair ranked set sampling: development and estimation. In: Proceedings of the national academy of sciences, India section A: physical sciences (submitted for publication) Google Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  • Muhammad Tayyab
    • 1
  • Muhammad Noor-ul-Amin
    • 2
    Email author
  • Muhammad Hanif
    • 1
  1. 1.National College of Business Administration and EconomicsLahorePakistan
  2. 2.COMSATS Institute of Information TechnologyLahorePakistan

Personalised recommendations