| Citation: |
CAI Jing, HE Jian, XU Kaili, HE Fei, HAN Rong. Reliability Analysis of Stress-Strength Model under Adaptive Progressive Hybrid Censoring Accelerated Life Test[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(5): 117-128. DOI: 10.6054/j.jscnun.2024070
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The reliability analysis of the stress-strength model under the step-stress partial accelerated life test based on the adaptive progressive type-II hybrid censored samples is studied, addressing the issue of long life test times and test data is difficult to collect. Firstly, the maximum likelihood estimation of the reliability of the stress-strength model is obtained according to the maximum likelihood theory, and the asymptotic confidence interval is provided. Then, two kinds of Bootstrap confidence intervals are constructed using the Bootstrap method. Secondly, Bayesian estimation of the reliability of the stress-strength model is obtained by the Lindley approximation method and the Markov chain Monte Carlo method, and the highest posterior density credible interval is derived. Finally, a comparative study is conducted using numerical simulations on the maximum likelihood method, the Lindley approximation method, and the Markov Chain Monte Carlo method, while also comparing the excellence of the highest posterior density credible interval, Bootstrap confidence interval, and asymptotic confidence interval. The simulation results show that Bayesian estimation outperforms maximum likelihood estimation for the reliability of the stress-strength model, and Bayesian estimation based on the Markov chain Monte Carlo method is superior to that based on the Lindley approximation method. As the sample size increases, the mean square error and mean absolute deviation of both Bayesian estimation and maximum likelihood estimation decrease. The highest posterior density credible interval is found to perform better than both the asymptotic confidence interval and the Bootstrap confidence interval. From these conclusions, it can be inferred that the proposed method is practical for estimating the reliability of the stress-strength model under accelerated life testing. Furthermore, the Markov Chain Monte Carlo method outperforms both the maximum likelihood method and the Lindley approximation method. Additionally, the highest posterior density credible interval derived from Bayesian estimation is superior to both the Bootstrap and asymptotic confidence intervals constructed using maximum likelihood estimation.
| [1] |
罗君念, 蔡静, 张峰源. 广义逆指数分布应力-强度模型的可靠性评估[J]. 湖北民族大学学报(自然科学版), 2023, 41(1): 102-108.
LUO J N, CAI J, ZHANG F Y. Reliability evaluation of stress-strength model with generalized inverted exponential distribution[J]. Journal of Hubei Minzu University (Natural Science Edition), 2023, 41(1): 102-108.
|
| [2] |
焦君君, 程维虎. 二项指数2分布的应力强度模型的可靠性估计(英文)[J]. 应用概率统计, 2023, 39(2): 178-196.
JIAO J J, CHENG W H. Reliability estimation of stress-strength model for binomial Exponential 2 distribution[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(2): 178-196.
|
| [3] |
李珺, 闫在在. 逐次Ⅰ型混合截尾下基于FGM copula的应力强度模型可靠性估计[J]. 数学的实践与认识, 2022, 52(4): 183-195.
LI J, YAN Z Z. The estimation of the reliability of stress-strength model based on FGM copula under progressive hybrid censoring scheme[J]. Mathematics in Practice and Theory, 2022, 52(4): 183-195.
|
| [4] |
龙芳, 蔡静, 朱艳. 逐步Ⅱ型混合截尾下Lomax分布多部件应力强度模型的可靠性分析[J]. 广西师范大学学报(自然科学版), 2024, 42(2): 120-130.
LONG F, CAI J, ZHU Y. Analysis of reliability in a multicomponent stress-strength model for Lomax distribution under progressive type-Ⅱ hybrid censoring[J]. Journal of Guangxi Normal University (Natural Science Edition), 2024, 42(2): 120-130.
|
| [5] |
SHANG L F, YAN Z Z. Reliability estimation stress-strength dependent model based on copula function using ranked set sampling[J]. Journal of Radiation Research and Applied Sciences, 2024, 17(1): 100811/1-9. doi: 10.1016/j.jrras.2023.100811
|
| [6] |
MA J G, WANG L, MANI Y T, et al. Reliability inference for stress-strength model based on inverted exponential Rayleigh distribution under progressive type-Ⅱ censored data[J]. Communications in Statistics-Simulation and Computation, 2023, 52(6): 2388-2407. doi: 10.1080/03610918.2021.1908552
|
| [7] |
BAI X C, ZHANG J Q, CHAI J. Statistical inference for multicomponent system stress-strength model with boun-ded strengths[J]. Journal of Systems Science and Complexity, 2023, 36(2): 755-770. doi: 10.1007/s11424-023-1137-9
|
| [8] |
LEVENBACH G J. Accelerated life testing of capacitors[J]. Institute of Radio Engineers Transactions on Reliability and Quality Control, 1957, 10(1): 9-20.
|
| [9] |
DEGROOT M H, GOEL P K. Bayesian estimation and optimal designs in partially accelerated life testing[J]. Naval Research Logistics Quarterly, 1979, 26(2): 223-235.
|
| [10] |
AKGUI G F, YU K, SENOGLU B. Classical and Bayesian inferences in step-stress partially accelerated life tests for inverse Weibull distribution under type-I censoring[J]. Strength of Materials, 2020, 52(3): 480-496.
|
| [11] |
ALOTAIBI R, ALMETWALLY E M, HAI Q, et al. Optimal test plan of step stress partially accelerated life testing for alpha power inverse Weibull distribution under adaptive progressive hybrid censored data and different loss functions[J]. Mathematics, 2022, 10(24): 4652/1-24.
|
| [12] |
GSRMM Y. Parametric inference on partially accelerated life testing for the inverted Kumaraswamy distribution based on type-Ⅱ progressive censoring data[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 1674-1694.
|
| [13] |
ÇETINKAYA Ç. The stress-strength reliability model with component strength under partially accelerated life test[J]. Communications in Statistics-Simulation and Computation, 2023, 52(10): 4665-4684.
|
| [14] |
EL-SAGHEER R M, TOLBA A H, JAWA T M, et al. Inferences for stress-strength reliability model in the pre-sence of partially accelerated life test to its strength variable[J]. Computational Intelligence and Neuroscience, 2022, 2022(1): 4710536/1-13.
|
| [15] |
YOUSEF M M, FAYOMI A, ALMETWALLY E M. Simu-lation techniques for strength component partially accelera- ted to analyze stress-strength model[J]. Symmetry, 2023, 15(6): 1183/1-23.
|
| [16] |
NG H K T, KUNDU D, CHAN P S. Statistical analysis of exponential lifetimes under an adaptive type-Ⅱ progre-ssive censoring scheme[J]. Naval Research Logistics, 2009, 56(8): 687-698.
|
| [17] |
BITHAS P S. Weibull-gamma composite distribution: alternative multipath/shadowing fading model[J]. Electro-nics Letters, 2009, 45(14): 749-751.
|
| [18] |
BHATTACHARYYA G K, SOEJOETI Z. A tampered fai-lure rate model for step-stress accelerated life test[J]. Communications in Statistics-Theory and Methods, 1989, 18(5): 1627-1643.
|
| [19] |
陈新海. 最佳估计理论[M]. 北京: 北京航空航天大学出版社, 1985.
|
| [20] |
DICICCIO T J, EFRON B. Bootstrap confidence intervals[J]. Statistical Science, 1996, 11(3): 189-228.
|
| [21] |
茆诗松, 汤银才. 贝叶斯统计[M]. 北京: 中国统计出版社, 2012.
|
| [22] |
EL-SAGHEERR M. Estimation of parameters of Weibull-gamma distribution based on progressively censored data[J]. Statistical Papers, 2018, 59(2): 725-757.
|
| [23] |
LINDLEY D V. Approximate Bayesian methods(with discussions)[J]. Trabjosde Estadisticay Deinvestigacion Ope-rativa, 1980, 31(1): 223-245.
|
| [24] |
RAQAB M Z, MADI M T. Bayesian inference for the gene-ralized exponential distribution[J]. Journal of Statistical Computation and Simulation, 2005, 75(10): 841-852.
|
| [25] |
HYNDMAN R J, KOEHLER A B. Another look at mea-sures of forecast accuracy[J]. International Journal of Forecasting, 2006, 22(4): 679-688.
|
| [26] |
LIO Y, TSAI T R, WANG L, et al. Inferences of the multicomponent stress-strength reliability for Burr XⅡ distributions[J]. Mathematics, 2022, 10(14): 2478/1-29.
|
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