随机参数非共轭分布下的可靠性建模方法
2025,47(1):230-238
鲁相
中国空气动力研究与发展中心 设备设计与测试技术研究所, 四川 绵阳 621000
褚卫华
中国空气动力研究与发展中心 设备设计与测试技术研究所, 四川 绵阳 621000
盖文
中国空气动力研究与发展中心 设备设计与测试技术研究所, 四川 绵阳 621000
陈旦
中国空气动力研究与发展中心 设备设计与测试技术研究所, 四川 绵阳 621000
中国空气动力研究与发展中心 设备设计与测试技术研究所, 四川 绵阳 621000
褚卫华
中国空气动力研究与发展中心 设备设计与测试技术研究所, 四川 绵阳 621000
盖文
中国空气动力研究与发展中心 设备设计与测试技术研究所, 四川 绵阳 621000
陈旦
中国空气动力研究与发展中心 设备设计与测试技术研究所, 四川 绵阳 621000
摘要:
为获取精确的产品寿命预测结果,在可靠性模型中引入服从非共轭分布的随机参数以描述产品的个体差异。针对单调退化的长寿命产品,提出了采用非共轭分布随机参数Gamma过程的可靠性模型;将传统的随机参数共轭分布扩展到非共轭分布,得到不同参数分布下统一的寿命分布函数表达式,利用蒙特卡罗算法计算寿命预测值;利用马尔可夫链蒙特卡罗算法估计模型参数,提出不同分布下似然函数值计算方法及参数分布的选取准则,分析不同随机参数分布对产品可靠性的影响。仿真算例和应用实例表明,该方法能够选择合适的参数分布。同时,验证了该方法参数估计及寿命预测的精确性。
为获取精确的产品寿命预测结果,在可靠性模型中引入服从非共轭分布的随机参数以描述产品的个体差异。针对单调退化的长寿命产品,提出了采用非共轭分布随机参数Gamma过程的可靠性模型;将传统的随机参数共轭分布扩展到非共轭分布,得到不同参数分布下统一的寿命分布函数表达式,利用蒙特卡罗算法计算寿命预测值;利用马尔可夫链蒙特卡罗算法估计模型参数,提出不同分布下似然函数值计算方法及参数分布的选取准则,分析不同随机参数分布对产品可靠性的影响。仿真算例和应用实例表明,该方法能够选择合适的参数分布。同时,验证了该方法参数估计及寿命预测的精确性。
基金项目:
国家自然科学基金资助项目(51705526,51875570)
国家自然科学基金资助项目(51705526,51875570)
Reliability modeling method in presence of non-conjugate distributions of random parameters
LU Xiang
Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000 , China
CHU Weihua
Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000 , China
GAI Wen
Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000 , China
CHEN Dan
Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000 , China
Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000 , China
CHU Weihua
Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000 , China
GAI Wen
Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000 , China
CHEN Dan
Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000 , China
Abstract:
To obtain accurate product lifetime prediction results, random parameters which obey non-conjugate distributions were introduced to describe the unit-to-unit variation of products in the reliability model. For long-life products with monotonic degradation, the reliability model was proposed based on the Gamma process with non-conjugate distribution random parameters. Extending the traditional conjugate distribution of random parameters to non-conjugate distribution, unified expression of life distribution function under different parameter distributions was derived, and the lifetime prediction values were calculated by using the Monte Carlo method. Markov chain Monte Carlo method was adopted for parameter estimation. The calculation algorithm for the likelihood function under different distributions and the selection criterion for the parameter distribution were presented, and the effect of the distribution of random parameters on the product reliability was analyzed. The simulation test and the application example show that this modeling method can select an appropriate distribution. Simultaneously, the accuracy of parameter estimation and lifetime prediction of the method is validated.
To obtain accurate product lifetime prediction results, random parameters which obey non-conjugate distributions were introduced to describe the unit-to-unit variation of products in the reliability model. For long-life products with monotonic degradation, the reliability model was proposed based on the Gamma process with non-conjugate distribution random parameters. Extending the traditional conjugate distribution of random parameters to non-conjugate distribution, unified expression of life distribution function under different parameter distributions was derived, and the lifetime prediction values were calculated by using the Monte Carlo method. Markov chain Monte Carlo method was adopted for parameter estimation. The calculation algorithm for the likelihood function under different distributions and the selection criterion for the parameter distribution were presented, and the effect of the distribution of random parameters on the product reliability was analyzed. The simulation test and the application example show that this modeling method can select an appropriate distribution. Simultaneously, the accuracy of parameter estimation and lifetime prediction of the method is validated.
收稿日期:
2022-08-16
2022-08-16