JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 122-129.doi: 10.6040/j.issn.1671-9352.0.2023.064

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Statistical inference of step-stress partially accelerated life test model under Type-Ⅱ censoring

LONG Bing, JIANG Zaifu   

  1. School of Mathematics and Physics, Jingchu University of Technology, Jingmen 448000, Hubei, China
  • Published:2024-12-12

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Abstract: Under the step-stress partially accelerated life test, based on the test data, the maximum likelihood estimation and Bayesian estimation of the distribution parameter, acceleration factor and reliability function are obtained by the classical method and Bayesian method, respectively. According to the asymptotic theory of maximum likelihood estimation, the approximate confidence intervals of the distribution parameter and the acceleration factor are constructed. The failure times of the censored units are predicted by using the observed data, including the best unbiased predictor and the conditional median predictor. The mean values and average relative errors of various estimators are calculated by Monte-Carlo method, and the influence of sample size on estimation accuracy is discussed. Finally, a numerical example is analyzed using the method presented in the paper.

Key words: exponential distribution, step-stress partially accelerated life test, maximum likelihood estimation, Bayesian estimation

CLC Number: 

  • O213.2
[1] 师义民,师小琳. 竞争失效产品部分加速寿命试验的统计分析[J]. 西北工业大学学报,2017,35(1):109-115. SHI Yimin, SHI Xiaolin. Statistical analysis for partially accelerated life tests with competing causes of failure[J]. Journal of Northwestern Polytechnical University, 2017, 35(1):109-115.
[2] 龙兵,张忠占.恒定应力部分加速寿命试验的统计分析[J]. 应用数学,2019,32(2):302-310. LONG Bing, ZHANG Zhongzhan. Statistical analysis for constant-stress partially accelerated life tests[J]. Mathematica Applicata, 2019, 32(2):302-310.
[3] ISMAIL A A, ABDEL-GHALY A A, EL-KHODARY E H. Optimum constant-stress life test plans for Pareto distribution under Type-Ⅰ censoring[J]. Journal of Statistical Computation and Simulation, 2011, 81(12):1835-1845.
[4] NASSAR M, ALAM F M A. Analysis of modified kies exponential distribution with constant stress partially accelerated life tests under Type-Ⅱ censoring[J]. Mathematics, 2022, 10(5):819.
[5] DEY S, WANG L, NASSAR M. Inference on Nadarajah-Haghighi distribution with constant stress partially accelerated life tests under progressive Type-Ⅱ censoring[J]. Journal of Applied Statistics, 2022, 49(11):2891-2912.
[6] ALMALKI S J, FARGHAL A W A, RASTOGI M K, et al. Partially constant-stress accelerated life tests model for parameters estimation of Kumaraswamy distribution under adaptive Type-Ⅱ progressive censoring[J]. Alexandria Engineering Journal, 2022, 61(7):5133-5143.
[7] ISMAIL A A. Likelihood inference for a step-stress partially accelerated life test model with Type-Ⅰ progressively hybrid censored data from Weibull distribution[J]. Journal of Statistical Computation and Simulation, 2014, 84(11):2486-2494.
[8] ISMAIL A A. Statistical inference for a step-stress partially-accelerated life test model with an adaptive Type-Ⅰ progressively hybrid censored data from Weibull distribution[J]. Statistical Papers, 2016, 57(2):271-301.
[9] ISMAIL A A. Inference for a step-stress partially accelerated life test model with an adaptive Type-Ⅱ progressively hybrid censored data from Weibull distribution[J]. Journal of Computational and Applied Mathematics, 2014, 260:533-542.
[10] ZHANG Chunfang, SHI Yimin, WU Min. Statistical inference for competing risks model in step-stress partially accelerated life tests with progressively Type-Ⅰ hybrid censored Weibull life data[J]. Journal of Computational and Applied Mathematics, 2016, 297:65-74.
[11] ALJOHANI H M, ALFAR N M. Estimations with step-stress partially accelerated life tests for competing risks Burr XII lifetime model under Type-Ⅱ censored data[J]. Alexandria Engineering Journal, 2020, 59(3):1171-1180.
[12] ALAM I, AHMED A. Inference on maintenance service policy under step-stress partially accelerated life tests using progressive censoring[J]. Journal of Statistical Computation and Simulation, 2022, 92(4):813-829.
[13] KAMAL M, SIDDIQUI S A, RAHMAN A, et al. Parameter estimation in step stress partially accelerated life testing under different types of censored data[J]. Computational Intelligence and Neuroscience, 2022:3491732.
[14] WANG Liang, SHI Yimin, YAN Weian. Inference for Gompertz distribution under records[J]. Journal of Systems Engineering and Electronics, 2016, 27(1):271-278.
[15] 龙沁怡,徐丽平. 基于上记录值Lomax分布的统计推断[J]. 江西师范大学学报(自然科学版), 2023, 47(2):216-220. LONG Qinyi, XU Liping. Statistical inference for Lomax distribution based on upper record values[J]. Journal of Jiangxi Normal University(Natural Sciences Edition), 2023, 47(2):216-220.
[16] 邓严林. 双边定数截尾下Topp-Leone分布的Bayes估计与预测[J].江西师范大学学报(自然科学版), 2021,45(3):272-277. DENG Yanlin. The Bayesian estimation and prediction for the Topp-Leone distribution under Type-Ⅱ doubly censored sample[J]. Journal of Jiangxi Normal University(Natural Sciences Edition), 2021, 45(3):272-277.
[17] 龙兵,张忠占. 双定数混合截尾下两参数Pareto分布的统计分析[J]. 数学物理学报, 2022, 42A(1):269-281. LONG Bing, ZHANG Zhongzhan. Statistical analysis of two-parameter Pareto distribution under double Type-Ⅱ hybrid censoring scheme[J]. Acta Mathematica Scientia, 2022, 42A(1):269-281.
[18] ASL M N, BELAGHI R A, BEVRANI H. Classical and Bayesian inferential approaches using Lomax model under progressively Type-Ⅰ hybrid censoring[J]. Journal of Computational and Applied Mathematics, 2018, 343:397-412.
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