Abstract
In this paper, we will present a control chart for exponentially distributed quality characteristics using multiple dependent state sampling. The proposed control chart has double control limits with two control coefficients, which is based on a normal approximation through transformation. The control coefficients are determined by considering the average run length (ARL) when the process is in control. The ARL for the shifted process is reported according to various shift ratios. The efficiency of the proposed control chart over the existing t-chart is compared in terms of the ARL.
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Aslam, M., Azam, M., Jun, C.-H.: Multiple dependent state sampling plan based on process capability index. J. Test. Eval. 41(2), 340–346 (2013a)
Aslam, M., Yen, C.-H., Chang, Chia-Hao, Jun, C.-H.: Multiple dependent state variables sampling plans with process loss consideration. Int. J. Adv. Manuf. Technol. doi:10.1007/s00170-013-5574-9
Balamurali, S., Jun, C.-H.: Multiple dependent state sampling plans for lot acceptance based on measurement data. Eur. J. Oper. Res. 180, 1221–1230 (2007)
Johnson, N.L., Kotz, S.-I.: Continuous Univariate Distributions. Wiley, New York (1970)
Kaminsky, F.C., Benneyan, J.C., Davis, R.D., Burke, R.J.: Statistical control charts based on a geometric distribution. J. Qual.Technol. 24, 63–69 (1992)
Majeed, M.Y., Aslam, M., Riaz, M.: Mixture cumulative count control chart for mixture geometric process characteristics. Qual. Quant. 47, 2289–2307 (2013)
Mohammed, M.A.: Using statistical process control to improve the quality of health care. Qual. Saf. Health Care. 13, 243–245 (2004)
Mohammed, M.A., Laney, D.: Overdispersion in health care performance data: Laney’s approach. Qual. Saf. Health Care. 15, 383–384 (2006)
Montgomery, D.C.: Introduction to Statistical Quality Control. Wiley, New York (2009)
Nelson, L.S.: A control chart for parts-per-million nonconforming items. J. Qual. Technol. 26, 239–240 (1994)
Santiago, E., Smith, J.: Control charts based on the exponential distribution: Adapting runs rules for the t chart. Qual. Eng. 25, 85–96 (2013)
Schilling, E.G., Nelson, R.R.: The effect of non-normality on the control limits of X charts. J. Qual. Technol. 8, 183–188 (1976)
Soundararajan, V., Vijayaraghavan, R.: Construction and selection of multiple dependent (deferred) state sampling plan. J. Appl. Stat. 17, 397–409 (1990)
Stoumbos, Z.G., Reynolds Jr, M.R.: Robustness to non-normality and autocorrelation of individuals control charts. J. Stat. Comput. Simul. 66, 145–187 (2000)
Szarka, J.L., Woodall, W.H.: A review and perspective on surveillance of Bernoulli processes. Qual. Reliab. Eng. Int. 27, 735–752 (2011)
Vaerst, R.: A procedure to construct multiple deferred state sampling plan. Method. Oper. Res. 37, 477–485 (1982)
Woodall, W.H.: The use of control charts in health-care and public health surveillance. J. Qual. Technol. 38, 89–104 (2006)
Wortham, A.W., Baker, R.C.: Multiple deferred state sampling inspection. Int. J. Prod. Res. 14, 719–731 (1976)
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The authors are deeply thankful to the Editor and anonymous reviewers for their valuable suggestions to improve the quality of this manuscript.
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Aslam, M., Azam, M., Khan, N. et al. A control chart for an exponential distribution using multiple dependent state sampling. Qual Quant 49, 455–462 (2015). https://doi.org/10.1007/s11135-014-0002-2
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DOI: https://doi.org/10.1007/s11135-014-0002-2