For the products with bathtub-shaped failure rate changing rule, the characteristics of bathtub-shaped failure rate curve is analyzed and the factors affecting the failure rate change in the different stages are also studied. According to the probability distribution characteristics reflected by the bathtub-shaped failure rate changing rule, the probability distribution model of products is developed, and the corresponding models of reliability, failure rate and mean time to failure are derived. Then, the effect of parameters including the ratio parameter, the first scale parameter, the first shape parameter, the second scale parameter and the second shape parameter on the probability distribution characteristics is studied. As an example, the life probability distribution characteristics of component with bathtub-shaped failure rate changing rule is fitted with the probability model proposed. The results show that the probability model developed can be used to describe the life probability distribution characteristics of products more correctively, and it can reflect the failure rate change rule of products in the different stages completely.
WANG Zheng
,
WANG Zengquan
,
XIE Liyang
. Life Probability Distribution Model of Products with the Bathtub-shaped Failure Rate Changing Rule[J]. Journal of Mechanical Engineering, 2015
, 51(24)
: 193
-212
.
DOI: 10.3901/JME.2015.24.193
[1] 王正, 谢里阳. 机械时变可靠性理论与方法[M]. 北京：科学出版社, 2012. WANG Zheng, XIE Liyang. Time-dependent reliability theory and method for mechanical products [M]. Beijing：Science Press, 2012.
[2] 谢里阳. 机械可靠性理论、方法及模型评述[J]. 机械工程学报，2014, 50(14)：27-35. XIE Liyang. Issues and commentary on mechanical reliability theories, methods and models[J]. Journal of Mechanical Engineering, 2014, 50(14)：27-35.
[3] 王正. 基于载荷-强度干涉的零件与系统失效率计算方法[D]. 北京：北京航空航天大学, 2010. WANG Zheng. Method for calculating failure rate of components and systems based on load-strength interference [D]. Beijing：Beihang University, 2010.
[4] 王正. 基于四要素的机械零部件失效率计算模型[J]. 中国机械工程, 2011, 22(12)：1472-1476. WANG Zheng. Failure rate model of mechanical components based on four elements[J]. China Mechanical Engineering, 2011, 22(12)：1472-1476.
[5] XIE M, TANG Y, GOH T N. A modified Weibull extension with bathtub-shaped failure rate function[J]. Reliability Engineering and System Safety, 2002, 76(3)：279-285.
[6] HJORTH U. A reliability distribution with increasing, decreasing, constant and bathtub-shaped failure rates[J]. Technometrics, 1980, 22(1)：99-107.
[7] ZHANG Xuemei, PHAM H. Software field failure rate prediction before software deployment[J]. The Journal of Systems and Software, 2006, 79(3)：291-300.
[8] XUE Xiaoling, FEI Heliang. Parameter estimation of the Weibull distribution tampered failure rate model under a normal stress[J]. Chinese Journal of Applied Probability and Statistics, 2004, 20(2)：126-132.
[9] ROSARIO T, PATRICK L. On-line reliability prediction via dynamic failure rate model[J]. IEEE Transactions on Reliability, 2008, 57(3)：452-457.
[10] ZAFIROPOULOS E P, DIALYNAS E N. Reliability and cost optimization of electronic devices considering the component failure rate uncertainty[J]. Reliability Engineering and System Safety, 2004, 84(3)：271- 284.
[11] AVINADAV T, RAZ T. A new inverted U-shape hazard function[J]. IEEE Transactions on Reliability, 2008, 57(1)：32-40.
[12] 陈殿生，王田苗，魏洪兴. 数控车床故障分布的两重威布尔分段模型[J]. 北京航空航天大学学报, 2005, 31(7)：766 -769. CHEN Diansheng, WANG Tianmiao, WEI Hongxing. Sectional model involving two Weibull distributions for CNC lathe failure probability[J]. Journal of Beijing University of Aeronautics and Astronautics, 2005, 31(7)：766-769.
[13] 陈文华, 崔杰, 潘骏, 等. 威布尔分布下失效率的Bayes 验证试验方法[J]. 机械工程学报, 2005, 41(12)：118-121.CHEN Wenhua, CUI Jie, PAN Jun, et al. Bayesian demonstration test method for failure rate under weibull distribution[J]. Chinese Journal of Mechanical Engingeering, 2005, 41(12)：118-121.
[14] 蒋仁言，左明健. 可靠性模型与应用[M]. 北京：机械工业出版社, 1999. JIANG Renyan, ZUO Mingjian. Reliability model and its application[M]. Beijing：China Machine Press, 1999.
[15] 王正，王增全. 基于失效行为的机械零部件寿命概率特征计算方法[J]. 机械工程学报, 2014, 50(12)：192-197. WANG Zheng, WANG Zengquan. Method for calculating the life probability distribution characteristic of mechanical components based on the failure behavior[J]. Journal of Mechanical Engineering, 2014, 50(12)：192-197.
