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Optimum simple accelerated life tests based on progressively Type-I hybrid censoring

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Abstract

This paper presents the process of the optimum test design for simple constant-stress and step-stress accelerated life tests under the progressively Type-I hybrid censoring data. Considering the constant-stress and step-stress accelerated models, the explicit conditional density functions of order statistics under progressively Type-I hybrid censoring scheme are given to obtain the expected Fisher information matrix. By minimizing the asymptotic variance of the mean life under the use stress, the optimum test design is completed by determining the test units allocated to each stress in constant-stress accelerated life test and the changing time to severer accelerated stress in step-stress accelerated life test. Finally, an example is shown to illustrate the optimum test design. The numerical results show that the step-stress accelerated life test is a better choice.

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References

  • Balakrishnan N, Han D (2009) Optimal step-stress testing for progressively Type-I censored data from exponential distribution. J Stati Plan Inference 139(5):1782–1798

    Article  MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Xie Q (2007) Exact inference for a simple step-stress model with Type-I hybrid censored data from the exponential distribution. J Stat Plan Infer 137:3268–3290

    Article  MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Childs A, Chandrasekar B (2002) An efficient computational method for moments of order statistics under progressive censoring. Stat Probab Lett 60(4):359–365

    Article  MATH  MathSciNet  Google Scholar 

  • Childs A, Chandrasekar B, Balakrishnan N (2008) Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C (eds) Statistical models and methods for biomedical and technical systems. Birkhäuser, Boston, pp 319–330

    Chapter  Google Scholar 

  • Gouno E, Sen A, Balakrishnan N (2004) Optimal step-stress test under progressive Type-I censoring. IEEE Trans Reliab 53:383–393

    Article  Google Scholar 

  • 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):2486–2494

    Article  MathSciNet  Google Scholar 

  • 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 Comput Simul 79(10):3110–3121

    Article  MATH  MathSciNet  Google Scholar 

  • Ling L, Xu W, Li M (2011) Optimal bivariate step-stress accelerated life test for Type-I hybrid censored data. J Stat Comput Simul 81(9):1175–1186

    Article  MATH  MathSciNet  Google Scholar 

  • Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. Wiley, New York

    MATH  Google Scholar 

  • Miller R, Nelson W (1983) Optimum simple step-stress plans for accelerated life testing. IEEE Trans Reliab R-32:59–65

    Article  MATH  Google Scholar 

  • Nelson W (1990) Accelerated testing: statistical models, test plans, and data analyses. Wiley, New York

    Book  MATH  Google Scholar 

  • Tang Y, Guan Q, Xu P, Xu H (2012) Optimum design for type-I step-stress accelerated life tests of two-parameter Weibull distributions. Commun Stat Theory Methods 41(21):3863–3877

    Article  MATH  MathSciNet  Google Scholar 

  • Wang BX, Yu K (2009) Optimum plan for step-stress model with progressive type-II censoring. Test 18(1):115–135

    Article  MATH  MathSciNet  Google Scholar 

  • Wu M, Shi Y, Sun Y (2014) Inference for accelerated competing failure models from Weibull distribution under Type-I progressive hybrid censoring. J Comput Appl Math 263:423–431

    Article  MATH  MathSciNet  Google Scholar 

  • Yang GB (1994) Optimum constant-stress accelerated life-test plans. IEEE Trans Reliab 43(4):575–581

    Article  Google Scholar 

  • Zhang ZH (2001) Comparison of optimum design of accelerated life tests. Chin J Appl Probab Stat 7(3):303–307

    MATH  MathSciNet  Google Scholar 

  • Zhao J, Shi Y, Yan W (2014) Inference for constant-stress accelerated life test with Type-I progressively hybrid censored data from Burr-XII distribution. J Syst Eng Electron 25(2):340–348

    Article  Google Scholar 

  • Zhou K, Shi Y, Sun T (2012) Reliability analysis for accelerated life-test with progressive hybrid censored data using geometric process. J Phys Sci 16:133–143

    MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (71171164, 71401134, 71571144) and Natural Science Basic Research Program of Shaanxi Province (2015JM1003).

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi’an, China

    Chunfang Zhang & Yimin Shi

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  1. Chunfang Zhang
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  2. Yimin Shi
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Correspondence to Chunfang Zhang.

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Zhang, C., Shi, Y. Optimum simple accelerated life tests based on progressively Type-I hybrid censoring. Int J Syst Assur Eng Manag 8 (Suppl 2), 849–856 (2017). https://doi.org/10.1007/s13198-016-0532-1

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  • DOI: https://doi.org/10.1007/s13198-016-0532-1

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