加速退化试验广泛用于退化失效型产品的可靠性评估,为提高试验效费比,加速退化试验的优化设计理论与方法成为了研究热点。为进一步推动相关理论与方法发展,以Wiener退化模型及步进温度应力加速退化试验为具体背景,提出基于加速因子不变原则的加速退化试验优化设计方法。根据加速因子不变原则推导Wiener退化模型的各参数是否与加速应力相关,从而客观建立加速退化模型并得到加速因子的解析式;为使产品在加速应力下的失效机理与额定应力下的失效机理尽可能一致,推导出加速因子的渐进方差并将其作为优化目标函数构建试验方案优化的数学模型。提出包含3个连续步骤的组合算法解析数学模型,并将算法程序化以提高解析效率。通过某型电连接器加速退化试验优化的实例应用,验证了所提方法的有效性与可行性。
Accelerated degradation test has been extensively applied to reliability assessment for degrading-failure products. To improve the efficiency-cost ratio, the optimal design theory and method of accelerated degradation test becomes a research hot. In order to promote the development of relative theory and method, the optimal design of accelerated degradation test based on acceleration factor constant principle, in which Wiener degradation model and step-temperature accelerated degradation test are considered, is proposed. Whether the parameters of Wiener degradation model are dependent on accelerated stress or not is derived according to the acceleration factor constant principle. Thus the accelerated degradation model is objectively constructed and the expression of acceleration factor is got. Furthermore, in order to ensure that the failure mechanism under accelerated stresses is probably consistent with that under the normal use stresses, the asymptotic variance of acceleration factor, which is selected to be the objective function of optimization, is then derived to set up a mathematical model of test plan. A combined algorithm consisting of 3 sequent steps is developed to resolve the mathematical model, and the algorithm is actualized by programs to improve the solving efficient. Through a case application of optimal design for the accelerated degradation test of a certain type electrical connector, the effectiveness and feasibility of the proposed method is validated.
[1] NELSON W B. Accelerated testing:Statistical models,test plans and data analysis[M]. New Jersey:John Wiley & Sons,2004.
[2] 汪亚顺,张春华,陈循,等. 仿真基混合效应模型加速退化试验优化设计研究[J]. 机械工程学报,2009,45(12):108-113. WANG Yashun,ZHANG Chunhua,CHEN Xun,et al. Simulation-based optimal design for accelerated degradation tests with mixed-effects model[J]. Journal of Mechanical Engineering,2009,45(12):108-113.
[3] 潘骏,王小云,陈文华,等. 基于多元性能参数的加速退化试验方案优化设计研究[J]. 机械工程学报,2012,48(2):30-35. PAN Jun,WANG Xiaoyun,CHEN Wenhua,et al. Research on optimal design of accelerated degradation test plan based on multiple performance parameters[J]. Journal of Mechanical Engineering,2012,48(2):30-35.
[4] PADGETT W J,TOMLINSON M A. Inference from accelerated degradation and failure data based on Gaussian process models[J]. Lifetime Data Analysis,2004,10:191-206.
[5] PARK C,PADGETT W J. Accelerated degradation models for failure based on geometric Brownian motion and Gamma processes[J]. Lifetime Data Analysis,2005,11:511-527.
[6] PARK C,PADGETT W J. Stochastic degradation models with several accelerating variables[J]. IEEE Transactions on Reliability,2006,55(2):379-390.
[7] LIAO C M,TSENG S T. Optimal design for step-stress accelerated degradation tests[J]. IEEE Transactions on Reliability,2006,55(1):59-66.
[8] LIM H,YUM B J. Optimal design of accelerated degradation tests based on wiener process model[J]. Journal of Applied Statistics,2011,38(2):309-325.
[9] WANG L,PAN R,LI X,JIANG T. A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information[J]. Reliability Engineering & System Safety,2013,112:38-47.
[10] WHITMORE G A,SCHENKELBERG F. Modelling accelerated degradation data using wiener diffusion with a time scale transformation[J]. Lifetime data analysis,1996,3:27-45.
[11] LIAO H,ELSAYED E A. Reliability inference for field conditions from accelerated degradation testing[J]. Naval Research Logistics,2006,53(6):576-587.
[12] TSENG S T,BALAKRISHNAN N,TSAI C C. Optimal step-stress accelerated degradation test plan for Gamma degradation process[J]. IEEE Transactions on Reliability,2009,58(4):611-618.
[13] PAN Z Q,BALAKRISHNAN N. Multiple-steps step-stress accelerated degradation modeling based on Wiener and Gamma processes[J]. Communications in Statistics-Simulation and Computation,2010,39(7):1384-1402.
[14] LAWLESS J F,CROWDER M J. Covariates and random effects in a gamma process model with application to degradation and failure[J]. Lifetime data analysis,2004,10:213-227.
[15] WANG X. Nonparametric estimation of the shape function in a Gamma process for degradation data[J]. The Canadian Journal of Statistics,2009,37:102-118.
[16] LING M H,TSUI K L,BALAKRISHNAN N. Accelerated degradation analysis for the quality of a system based on the Gamma process[J]. IEEE Transactions on Reliability,2015,64(1):463-472.
[17] YE Z S,CHEN L P,TANG L C,et al. Accelerated degradation test planning using the inverse Gaussian process[J]. IEEE Transactions on Reliability,2014,63(3):750-763.
[18] HU C H,LEE M Y,TANG J. Optimum step-stress accelerated degradation test for Wiener degradation process under constraints[J]. European Journal of Operational Research,2015,241(2):412-421.
[19] WANG H,WANG G J,DUAN F J. Planning of step-stress accelerated degradation test based on the inverse Gaussian process[J]. Reliability Engineering & System Safety,2016,154:97-105.
[20] 周源泉,翁朝曦,叶喜涛. 论加速系数与失效机理不变的条件(Ⅰ)-寿命型随机变量的情况[J]. 系统工程与电子技术,1996,18(1):55-67. ZHOU Yuanquan,WENG Chaoxi,YE Xitao. Study on accelerated factor and condition for constant failure mechanism[J]. Systems Engineering and Electronics,1996,18(1):55-67.
[21] WANG H W,XI W J. Acceleration factor constant principle and the application under ADT[J]. Quality and Reliability Engineering International,2016,32(7):2591-2600.
[22] 王浩伟,徐廷学,赵建忠. 融合加速退化和现场实测退化数据的剩余寿命预测方法[J]. 航空学报,2014,35(12):3350-3357. WANG Haowei,XU Tingxue,ZHAO Jianzhong. Residual life prediction method fusing accelerated degradation and field degradation data[J]. Acta Aeronautica et Astronautica Sinica,2014,35(12):3350-3357.
[23] 潘正强. 加速应力下二元退化可靠性建模及其试验设计方法[D]. 长沙:国防科学技术大学,2011. PAN Z Q. Bivariate degradation reliability modeling and experimental design approaches under accelerating stress scenarios[D]. Changsha:National University of Defense Technology,2011.
[24] WANG X. Wiener processes with random effects for degradation data[J]. Journal of Multivariate Analysis,2010,101(2):340-351.