Abstract
In this paper, we propose a new improved Shewhart control chart for monitoring the process mean based on partially ordered judgment subset sampling design. The performance of the suggested control chart is compared with some of the existing control charts based on simple random sampling and ranked set sampling methods. Average, standard deviation and percentiles of the run lengths are used to evaluate the performances of the control charts. It is observed that the proposed control chart is efficient in detecting random shifts in process mean as compared with the traditional quality control charts.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abujiya, M.R., Muttlak, H.A.: Quality control chart for the mean using double ranked set sampling. J. Appl. Statist. 31(10), 1185–1201 (2004)
Al-Omari, A.I., Raqab, M.Z. : Estimation of population mean and median using truncation-based ranked set samples. J. Statist. Comput. Simul. 1–19 (2012)
Al-Omari, A.I.: Estimation of mean based on modified robust extreme ranked set sampling. J. Statist. Comput. Simul. 81(8), 1055–1066 (2010)
Al-Omari, A.I., Al-Nasser, A.D.: Statistical quality control limits for the sample mean chart using robust extreme ranked set sampling. Econ. Qual. Control 26, 73–89 (2011)
Al-Omari, A.I., Haq, A.: Improved quality control charts for monitoring the process mean using double ranked set sampling methods. J. Appl. Statist. 39(4), 745–763 (2012)
Al-Sabah, W.S.: Cumulative sum statistical control charts using ranked set sampling data. Pak. J. Statist. 26(2), 365–378 (2010)
Al-Saleh, M.F., Al-Omari, A.I.: Multistage ranked set sampling. J. Statist. Plann. Inf. 102, 273–286 (2002)
Alwan, L.C.: Statist. Process Anal. Irwin McGraw-Hill, Boston (2000)
Frey, J.: A note on ranked-set sampling using a covariate. J. Statist. Plann. Inf. 141, 809–816 (2011)
Haq, A., Shabbir, J.: A family of ratio estimators for population mean in extreme ranked set sampling using two auxiliary variables. SORT 34(1), 45–64 (2010)
McIntyre, G.A.: A method of unbiased selective sampling using ranked sets. Aust. J. Agric. Res. 3, 385–390 (1952)
Montgomery, D.C.: Introduction to Statistical Quality Control. John Wiley, New York (2005)
Muttlak, H.A., Al-Sabah, W.: Statistical quality control based on ranked set sampling. J. Appl. Statist. 30(9), 1055–2078 (2003)
Ozturk, O.: Nonparametric maximum-likelihood estimation of within-set ranking errors in ranked set sampling. J. Nonparametr. Statist. 22(7), 823–840 (2010)
Ozturk, O.: Sampling from partially rank-ordered sets. Environ. Ecol. Stat. 18, 757–779 (2011a)
Ozturk, O.: Parametric estimation of location and scale parameters in ranked set sampling. J. Statist. Plann. Inf. 141, 1616–1622 (2011b)
Ozturk, O.: Quantile inference based on partially rank-ordered set samples. J. Statist. Plann. Inf. 142(7), 2116–2127 (2012)
Salazar, R.D., Sinha, A.K.: Control chart \(\bar{{X}}\) based on ranked set sampling. Comunicacion Tecica 1, 1–97 (1997)
Shewhart, W.A.: Some applications of statistical methods to the analysis of physical and engineering data. Bell Syst. Tech. J. 3, 43–87 (1924)
Takahasi, K., Wakimoto, K.: On the unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann. Inst. Statist. Math. 20, 1–31 (1968)
Torng, C., Lee, P., Tseng, C.: An economic design of Tukey’s control chart. J. Chinese Inst. Ind. Eng. 26(1), 53–59 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Haq, A., Al-Omari, A.I. A new Shewhart control chart for monitoring process mean based on partially ordered judgment subset sampling. Qual Quant 49, 1185–1202 (2015). https://doi.org/10.1007/s11135-014-0042-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11135-014-0042-7