Abstract
Accelerated life testing has now become the primary method for rapidly assessing product reliability and designing efficient test plans is a vital step in ensuring that accelerated life tests can properly, quickly, and economically assess product reliability. These tests subject the sample to high levels of stress. Then, based on the stress-life relationship, the product life at a normal stress level can be calculated by extrapolating the life information from a sample at a high-stress level to the normal level. The purpose of the study is to investigate the estimation of failure time data for step-stress partially accelerated life testing using multiply censored data. The test components’ lifetime distribution is assumed to follow Fréchet’s distribution. The distribution parameter and tampering coefficient are estimated using maximum-likelihood point and interval estimations. A Monte Carlo simulation study is used to evaluate and compare the performance of model parameter estimators utilizing multiply censored data in terms of biases and root mean squared errors.
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The research is purely based upon simulated data using R software.
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References
Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. Wiley, Hoboken
Shi Y (2022) Advances in big data analytics: theory, algorithm and practice. Springer, Singapore
Bekalo DB, Kebede DT (2021) Zero-inflated models for count data: an application to number of antenatal care service visits. Ann Data Sci 8:683–708
Olson DL, Shi Y (2007) Introduction to business data mining. McGraw-Hill/Irwin, New York
Shi Y, Tian YJ, Kou G, Peng Y, Li JP (2011) Optimization based data mining: theory and applications. Springer, Berlin
Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4(2):149–178
Goel HPK (1971) Some estimation problems in the study of tampered random variables. PhD. Dissertation, Department of Statistics, Carnegie-Mellon University, Pittsburgh, PA
Degroot MH, Goel PK (1979) Bayesian and optimal design in partially accelerated life testing. Nav Res Logist Q 26(2):223–235
Bai DS, Chung SW (1992) Optimal design of partially accelerated life tests for the exponential distribution under type censored. IEEE Trans Reliab 41(3):400–406
Bai DS, Chung SW, Chun YR (1993) Optimal design of partially accelerated life tests for the lognormal distribution under type-I censoring. Reliab Eng Syst Saf 40(1):85–92
Abdel-Ghaly AA, Aboaoja AF, Abdel-Ghani MM (2002) The maximum likelihood estimates in step partially accelerated life tests for the Weibull distribution parameters in censored data. Commun Stat Theory Methods 31(4):551–573
Lone SA, Rahman A, Islam A (2017) Step stress partially accelerated life testing plan for competing risk using adaptive type-I progressive hybrid censoring. Pak J Stat 33(4):237–248
Rahman A, Lone SA, Islam A (2018) Likelihood estimation of exponentiated exponential distribution under step stress partially accelerated life testing plan using progressive type-II censoring. Investig Operacional 39(4):551–559
Lone SA, Ahmed A (2021) Design and analysis of accelerated life testing and its application under rebate warranty. Sankhya Ser A 83:393–407
Lone SA, Rahman A, Tarray TA (2021) Inference for step-stress partially accelerated life test model with an adaptive type-I progressively hybrid censored data. J Mod Appl Stat Methods 19(1):13. https://doi.org/10.22237/jmasm/1608552180
Alam I, Ahmed A (2020) Parametric and interval estimation under step-stress partially accelerated life tests using adaptive type-II progressive hybrid censoring. Ann Data Sci. https://doi.org/10.1007/s40745-020-00249-1
Rahman A, Sindhu TN, Lone SA, Kamal M (2020) statistical inference for burr type X distribution using geometric process in accelerated life testing design for time censored data. Pak J Stat Oper Res 16(3):577–586
Wang FK, Cheng YF, Lu WL (2012) Partially accelerated life tests for the Weibull distribution under multiply censored data. Commun Stat Simul Comput 41(9):1667–1678
Lone SA (2021) Multiply censored partially accelerated life testing for power function model. Appl Math Inf Sci 15(2):147–152
Krishna E, Kanichukattu J, Ristic MM (2013) Applications of Marshall-Olkin Fréchet distribution. Commun Stat Simul Comput 42(1):76–89
Arul AJ, Kumar CS, Marimuthu S, Singh OP (2003) The power law character of off-site power failures. Ann Nucl Energy 30(14):1401–1408
Kotz S, Nadarajah S (2000) Extreme value distributions: theory and applications. Imperial College Press, London
Hintze J (2004) NCSS and PASS. Number cruncher statistical systems. Kaysville, Utah. www.ncss.com
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Lone, S.A. Simulating Fréchet Distribution Under Multiply Censored Partially Accelerated Life Testing. Ann. Data. Sci. 10, 1447–1458 (2023). https://doi.org/10.1007/s40745-022-00399-4
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DOI: https://doi.org/10.1007/s40745-022-00399-4