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Accelerated Life Testing

  • N. Balakrishnan
  • Erhard Cramer
Chapter
Part of the Statistics for Industry and Technology book series (SIT)

Abstract

Methods of accelerated life testing are applied to several kinds of progressively censored data. This includes step-stress testing as well as progressive stress models.

Keywords

Fisher Information Matrix Accelerate Life Testing Generalize Order Statistic Progressive Censoring Censoring Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 3.
    Abdel-Hamid AH (2009) Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring. Comput Stat Data Anal 53:2511–2523CrossRefMATHMathSciNetGoogle Scholar
  2. 4.
    Abdel-Hamid AH, AL-Hussaini EK (2011) Inference for a progressive stress model from Weibull distribution under progressive type-II censoring. J Comput Appl Math 235: 5259–5271Google Scholar
  3. 5.
    Abdel-Hamid AH, AL-Hussaini EK (2014) Bayesian prediction for Type-II progressive censored data from the Rayleigh distribution under progressive-stress model. J Stat Comput Simul 84:1297–1312Google Scholar
  4. 10.
    Abushal TA, Soliman AA (2013) Estimating the Pareto parameters under progressive censoring data for constant-partially accelerated life tests. J Stat Comput Simul (to appear)Google Scholar
  5. 67.
    Bagdonavičius V (1978) Testing the hypothesis of additive accumulation of damages. Probab Theory Appl 23:403–408Google Scholar
  6. 68.
    Bagdonavičius V, Nikulin M (2002) Accelerated life models: modeling and statistical analysis. Chapman & Hall/CRC Press, Boca Raton/FloridaGoogle Scholar
  7. 69.
    Bagdonavičius V, Cheminade O, Nikulin M (2004) Statistical planning and inference in accelerated life testing using the CHSS model. J Stat Plan Infer 126:535–551CrossRefMATHGoogle Scholar
  8. 71.
    Bai DS, Kim MS, Lee SH (1989) Optimum simple step-stress accelerated life tests with censoring. IEEE Trans Reliab 38:528–532CrossRefMATHGoogle Scholar
  9. 85.
    Balakrishnan N (2009) A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests. Metrika 69:351–396CrossRefMathSciNetGoogle Scholar
  10. 99.
    Balakrishnan N, Han D (2009) Optimal step-stress testing for progressively Type-I censored data from exponential distribution. J Stat Plan Infer 139:1782–1798CrossRefMATHMathSciNetGoogle Scholar
  11. 102.
    Balakrishnan N, Iliopoulos G (2010) Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring. Metrika 72: 89–109CrossRefMATHMathSciNetGoogle Scholar
  12. 130.
    Balakrishnan N, Cramer E, Kamps U, Schenk N (2001b) Progressive type II censored order statistics from exponential distributions. Statistics 35:537–556CrossRefMATHMathSciNetGoogle Scholar
  13. 152.
    Balakrishnan N, Kamps U, Kateri M (2012b) A sequential order statistics approach to step-stress testing. Ann Inst Stat Math 64:303–318CrossRefMATHMathSciNetGoogle Scholar
  14. 156.
    Balakrishnan N, Cramer E, Iliopoulos G (2014) On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints. Stat Probab Lett 89:124–130CrossRefMATHMathSciNetGoogle Scholar
  15. 182.
    Basu AP (1995) Accelerated life testing with applications. In: Balakrishnan N, Basu AP (eds) The exponential distribution: theory, methods and applications. Gordon and Breach, Newark, pp 377–383Google Scholar
  16. 192.
    Beutner E (2007) Progressive type-II censoring and transition kernels. Comm Dependability Qual Manag 10:25–32Google Scholar
  17. 200.
    Bhattacharyya GK, Soejoeti Z (1989) A tampered failure rate model for step-stress accelerated life test. Comm Stat Theory Meth 18:1627–1643CrossRefMathSciNetGoogle Scholar
  18. 298.
    Cramer E, Kamps U (1998) Sequential k-out-of-n systems with Weibull components. Econ Qual Control 13:227–239MATHGoogle Scholar
  19. 301.
    Cramer E, Kamps U (2003) Marginal distributions of sequential and generalized order statistics. Metrika 58:293–310CrossRefMATHMathSciNetGoogle Scholar
  20. 329.
    Davis DJ (1952) An analysis of some failure data. J Am Stat Assoc 47:113–150CrossRefGoogle Scholar
  21. 340.
    Ding C, Tse SK (2013) Design of accelerated life test plans under progressive Type II interval censoring with random removals. J Stat Comput Simul 83:1330–1343CrossRefMathSciNetGoogle Scholar
  22. 341.
    Ding C, Yang C, Tse SK (2010) Accelerated life test sampling plans for the Weibull distribution under Type I progressive interval censoring with random removals. J Stat Comput Simul 80:903–914CrossRefMATHMathSciNetGoogle Scholar
  23. 360.
    Fan TH, Wang WL, Balakrishnan N (2008) Exponential progressive step-stress life-testing with link function based on Box-Cox transformation. J Stat Plan Infer 138:2340–2354CrossRefMATHMathSciNetGoogle Scholar
  24. 407.
    Gouno E, Balakrishnan N (2001) Step-stress accelerated life test. In: Balakrishnan N, Rao CR (eds) Handbook of statistics. Advances in reliability, vol 20. North Holland, Amsterdam, pp 623–639Google Scholar
  25. 408.
    Gouno E, Sen A, Balakrishnan N (2004) Optimal step-stress test under progressive Type-I censoring. IEEE Trans Reliab 53:388–393CrossRefGoogle Scholar
  26. 430.
    Han D, Balakrishnan N, Sen A, Gouno E (2006) Corrections on ‘Optimal step-stress test under progressive Type-I censoring’. IEEE Trans Reliab 55:613–614CrossRefGoogle Scholar
  27. 498.
    Kamps U (1995a) A concept of generalized order statistics. Teubner, StuttgartCrossRefMATHGoogle Scholar
  28. 499.
    Kamps U (1995b) A concept of generalized order statistics. J Stat Plan Infer 48:1–23CrossRefMATHMathSciNetGoogle Scholar
  29. 511.
    Kateri M, Balakrishnan N (2008) Inference for a simple step-stress model with Type-II censoring, and Weibull distributed lifetimes. IEEE Trans Reliab 57:616–626CrossRefGoogle Scholar
  30. 524.
    Khamis I, Higgins J (1998) A new model for step-stress testing. IEEE Trans Reliab 47: 131–134CrossRefGoogle Scholar
  31. 558.
    Kundu D, Balakrishnan N (2009) Point and interval estimation for a simple step-stress model with random stress-change time. J Probab Stat Sci 7:113–126MathSciNetGoogle Scholar
  32. 567.
    Lai CD, Xie M, Murthy DNP (2003) A modified Weibull distribution. IEEE Trans Reliab 52:33–37CrossRefGoogle Scholar
  33. 619.
    Lu Y, Storer B (2001) A tampered Brownian motion process model for partial step-stress accelerated life testing. J Stat Plan Infer 94:15–24CrossRefMATHMathSciNetGoogle Scholar
  34. 625.
    Madi MT (1993) Multiple step-stress accelerated life test: the tampered failure rate model. Comm Stat Theory Meth 22:295–306CrossRefMathSciNetGoogle Scholar
  35. 644.
    McNichols D, Padgett W (1988) Inference for step-stress accelerated life tests under arbitrary right-censorship. J Stat Plan Infer 20:169–179CrossRefMATHMathSciNetGoogle Scholar
  36. 645.
    Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. Wiley, New YorkMATHGoogle Scholar
  37. 646.
    Meeker WQ, Hahn GJ (1985) How to Plan accelerated life tests. ASQC basic references in quality control: statistical techniques, vol 10. The American Society for Quality Control, MilwaukeeGoogle Scholar
  38. 649.
    Miller R, Nelson W (1983) Optimum simple step-stress plans for accelerated life testing. IEEE Trans Reliab R-32:59–65CrossRefGoogle Scholar
  39. 675.
    Nelson W (1980) Accelerated life testing: step-stress models and data analyses. IEEE Trans Reliab R-29:103–108CrossRefGoogle Scholar
  40. 677.
    Nelson W (1990) Accelerated testing: statistical models, test plans, and data analyses. Wiley, HobokenCrossRefGoogle Scholar
  41. 678.
    Nelson W, Meeker WQ (1978) Theory for optimum accelerated censored life tests for Weibull and extreme value distributions. Technometrics 20:171–177CrossRefMATHGoogle Scholar
  42. 788.
    Sedyakin NM (1966) On one physical principle in reliability theory (in Russian). Tech Cybern 3:80–87Google Scholar
  43. 800.
    Shaked M, Singpurwalla ND (1983) Inference for step-stress accelerated life tests. J Stat Plan Infer 7:295–306CrossRefMATHMathSciNetGoogle Scholar
  44. 803.
    Shen KF, Shen YJ, Leu LY (2011) Design of optimal step-stress accelerated life tests under progressive type I censoring with random removals. Qual Quant 45:587–597CrossRefGoogle Scholar
  45. 828.
    Sun T, Shi Y, Dang S (2012) Inference for Burr-XII with progressive Type-II censoring with random removals in step-stress partially accelerated life test. In: 2012 international conference on quality, reliability, risk, maintenance, and safety engineering (ICQR2MSE), pp 889–894Google Scholar
  46. 837.
    Tang LC (2003) Multiple steps step-stress accelerated. In: Pham H (ed) Handbook of reliability engineering. Springer, New York, pp 441–455CrossRefGoogle Scholar
  47. 861.
    Tse SK, Ding C, Yang C (2008) Optimal accelerated life tests under interval censoring with random removals: the case of Weibull failure distribution. Statistics 42:435–451CrossRefMATHMathSciNetGoogle Scholar
  48. 866.
    Van Dorp JR, Mazzuchi TA (2004) A general Bayes exponential inference model for accelerated life testing. J Stat Plan Infer 119:55–74CrossRefMATHGoogle Scholar
  49. 884.
    Wang BX (2010) Interval estimation for exponential progressive Type-II censored step-stress accelerated life-testing. J Stat Plan Infer 140:2706–2718CrossRefMATHGoogle Scholar
  50. 889.
    Wang BX, Yu K (2009) Optimum plan for step-stress model with progressive Type-II censoring. TEST 18:115–135CrossRefMATHMathSciNetGoogle Scholar
  51. 891.
    Watkins AJ (2001) Commentary: inference in simple step-stress models. IEEE Trans Reliab 50:36–37CrossRefGoogle Scholar
  52. 917.
    Wu SJ, Lin YP, Chen YJ (2006c) Planning step-stress life test with progressively type I group-censored exponential data. Stat Neerl 60:46–56CrossRefMATHMathSciNetGoogle Scholar
  53. 920.
    Wu SJ, Lin YP, Chen ST (2008a) Optimal step-stress test under type I progressive group-censoring with random removals. J Stat Plan Infer 138:817–826CrossRefMATHMathSciNetGoogle Scholar
  54. 927.
    Xie Q, Balakrishnan N, Han D (2008) Exact inference and optimal censoring scheme for a simple step-stress model under progressive Type-II censoring. In: Balakrishnan N (ed) Advances in mathematical and statistical modeling. Birkhäuser, Boston, pp 107–137CrossRefGoogle Scholar
  55. 928.
    Xiong C (1998) Inferences on a simple step-stress model with type-II censored exponential data. IEEE Trans Reliab 47:142–146CrossRefGoogle Scholar
  56. 929.
    Xiong C, Ji M (2004) Analysis of grouped and censored data from step-stress life test. IEEE Trans Reliab 53:22–28CrossRefGoogle Scholar
  57. 930.
    Xiong C, Milliken G (1999) Step-stress life-testing with random stress-change times for exponential data. IEEE Trans Reliab 48:141–148CrossRefGoogle Scholar
  58. 933.
    Yang C, Tse SK (2005) Planning accelerated life tests under progressive Type I interval censoring with random removals. Comm Stat Simul Comput 34:1001–1025CrossRefMATHMathSciNetGoogle Scholar
  59. 935.
    Yue HB, Shi YM (2013) Optimal sample size allocation for multi-level stress testing under progressive hybrid interval censoring. Appl Mech Mater 423–426:2423–2426CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • N. Balakrishnan
    • 1
  • Erhard Cramer
    • 2
  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  2. 2.Institute of StatisticsRWTH Aachen UniversityAachenGermany

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