Statistical inference for a step-stress partially-accelerated life test model with an adaptive Type-I progressively hybrid censored data from Weibull distribution

详细信息    查看全文

• 作者：Ali A. Ismail
• 关键词：Quality and reliability ; Step ; stress partially accelerated life test ; Weibull distribution ; Adaptive Type ; I progressively hybrid censoring scheme ; Coverage probability ; Optimum test plans
• 刊名：Statistical Papers
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：57
• 期：2
• 页码：271-301
• 全文大小：494 KB
• 参考文献：Abdel-Ghaly AA, El-Khodary EH, Ismail AA (2002) Maximum likelihood estimation and optimal design in step partially accelerated life tests for the Pareto distribution with type-I censoring. Proceedings of the 14th annual conference on Statistics and Computer Modeling in Human and Social Sciences, Faculty of Economics and Political Science, Cairo University, Egypt, 26–27 March: 27–40
  Abdel-Ghaly AA, El-Khodary EH, Ismail AA (2003) Estimation and optimal design in step partially accelerated life tests for Pareto distribution using Type-II censoring. Proceedings of the 15th annual conference on statistics and computer modeling in human and social sciences, Faculty of Economics and Political Science, Cairo University, Egypt, 25–26 March: 16–29
  Abdel-Ghaly AA, El-Khodary EH, Ismail AA (2003) Estimation and optimum constant-stress partially accelerated life test plans for Pareto distribution with Type-I censoring. Proceedings of the 38th annual conference of statistics, computer sciences and operation research, ISSR, Cairo University, Egypt, 13–16 December: 49–65
  Abdel-Ghani MM (1998) Investigation of some lifetime models under partially accelerated life tests, PhD Thesis, Department of Statistics, Faculty of Economics & Political Science, Cairo University, Egypt
  Abdel-Ghani MM (2004) The estimation problem of the log-logistic parameters in step partially accelerated life tests using type-I censored data. Nat Rev Soc Sci 41(2):1–19
  Aly HM, Ismail AA (2008) Optimum simple time-step stress plans for partially accelerated life testing with censoring. Far East J Theor Stat 24:175–200MathSciNet MATH
  Bai DS, Chung SW (1992) Optimal design of partially accelerated life tests for the exponential distribution under type-I censoring. IEEE Trans Reliab 41(3):400–406CrossRef MATH
  Bai DS, Chung SW, Chun YR (1993a) Optimal design of partially accelerated life tests for the Lognormal distribution under type-I censoring. Reliab Eng Syst Saf 40:85–92CrossRef
  Bai DS, Kim JG, Chun YR (1993b) Design of failure-censored accelerated life test sampling plans for lognormal and Weibull distributions. Eng Optim 21:197–212CrossRef
  Bhattacharya GK, Soejoeti Z (1989) A tampered failure rate model for step stress accelerated life test. Commun Stat Theory Methods 18(5):1627–1643MathSciNet CrossRef MATH
  Childs A, Chandrasekar B, Balakrishnan N (2008) Exact likelihood inference for an exponential parameter under progressively hybrid schemes. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C (eds) Statistical models and methods for biomedical and technical systems. Birkhauser, Boston, pp 323–334
  DeGroot MH, Goel PK (1979) Bayesian estimation and optimal designs in partially accelerated life testing. Nav Res Logist Q 26(2):223–235MathSciNet CrossRef MATH
  Goel PK (1971) Some estimation problems in the study of tampered random variables, Technical Rep. No. 50, Department of statistics, Carnegie-mellon university, Pittsburgh, Pennsylvania
  Ismail AA (2004) The test design and parameter estimation of Pareto lifetime distribution under partially accelerated life tests, PhD Thesis, Department of Statistics, Faculty of Economics & Political Science, Cairo University, Egypt
  Ismail AA (2010) Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with Type I censoring. J Stat Comput Simul 80(11):1253–1264MathSciNet CrossRef MATH
  Ismail AA (2012) Estimating the parameters of Weibull distribution and the acceleration factor from hybrid partially accelerated life test. Appl Math Model 36(7):2920–2925MathSciNet CrossRef MATH
  Ismail AA (2012) Inference in the generalized exponential distribution under partially accelerated tests with progressive Type-II censoring. Theor Appl Fract Mech 59(1):49–56CrossRef
  Ismail AA (2013) On designing step-stress partially accelerated life tests under failure-censoring scheme. Proc IMechE Part O: J Risk Reliab 227(6): 662–670
  Ismail AA (2014) Likelihood inference for a step-stress partially accelerated life test model with Type-I progressively hybrid censored data from Weibull Distribution. J Stat Comput Simul 84(11):2486–2494MathSciNet CrossRef
  Ismail AA, Sarhan AM (2009) Optimal design of step-stress life test with progressively Type-II censored exponential data. Int Math Forum 4(40):1963–1976MathSciNet MATH
  Kundu D, Joarder A (2006) Analysis of Type-II progressively hybrid censored data. Comput Stat Data Anal 50:2509–2528MathSciNet CrossRef MATH
  Lin C-T, Chou C-C, Huang Y-L (2012) Inference for the Weibull distribution with progressive hybrid censoring. Comput Stat Data Anal 56:451–467MathSciNet CrossRef MATH
  Lin C-T, Huang Y-L (2012) On progressive hybrid censored exponential distribution. J Stat Comput Simul 82(5):689–709MathSciNet CrossRef MATH
  Lin CT, Ng HKT, Chan PS (2009) Statistical inference of Type-II progressively hybrid censored data with Weibull lifetimes. Commun Stat Theory Methods 38:1710–1729MathSciNet CrossRef MATH
  Ling L, Xu W, Li M (2009) Parametric inference for progressive Type-I hybrid censored data on a simple step-stress accelerated life test model. Math Com Simul 79:3110–3121MathSciNet CrossRef MATH
  Miller RC (1981) Survival analysis. John Wiley & Sons, New York
  Nelson WB (1990) Accelerated life testing: statistical models. Data analysis and test plans. John Wiley & Sons, New YorkCrossRef
  Ng HKT, Chan PS, Kundu D (2009) Statistical analysis of exponential lifetimes under an adaptive hybrid Type-II progressive censoring scheme. Nav Res Logist 56:687–698MathSciNet CrossRef MATH
  Wu S-J, Huang S-R (2010) Optimal progressive group-censoring plans for exponential distribution in presence of cost constraint. Stat Papers 51:431–443MathSciNet CrossRef MATH
  
• 作者单位：Ali A. Ismail (1) (2)
  
  1. Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia
  2. Department of Statistics, Faculty of Economics & Political Science, Cairo University, Orman, Giza, 12613, Egypt
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1613-9798

文摘

In this paper, a new censoring scheme, namely, adaptive Type-I progressively hybrid censoring scheme under a step-stress partially accelerated test model is introduced. It has some advantages over the progressively hybrid censoring schemes already discussed in the literature. Based on this censoring scheme, the maximum likelihood estimations of Weibull distribution parameters and the acceleration factor are considered. The biases and mean squared errors of the maximum likelihood estimators of the model parameters are computed to evaluate their performances in the presence of censoring scheme developed in this paper through a Monte Carlo simulation study. The results obtained under the adaptive Type-I progressively hybrid censoring scheme are compared with those produced under the non-adaptive Type-I progressively hybrid censoring scheme using three different progressive censoring schemes. Moreover, the confidence intervals lengths and their associated coverage probabilities are obtained for both adaptive and non-adaptive Type-I progressively hybrid censoring scheme. In addition, Optimum test plans are also developed to improve/guarantee the quality of the statistical inference.