Research Papers: Design Automation

A Sequential Accelerated Life Testing Framework for System Reliability Assessment With Untestable Components

[+] Author and Article Information
Zhen Hu

Department of Industrial and
Manufacturing Systems Engineering,
University of Michigan-Dearborn,
2340 Heinz Prechter Engineering Complex
Dearborn, MI 48128
e-mail: zhennhu@umich.edu

Zissimos P. Mourelatos

Mechanical Engineering Department,
Oakland University,
Room 402D, 115 Library Drive,
Rochester, MI 48309
e-mail: mourelat@oakland.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 10, 2018; final manuscript received June 16, 2018; published online July 24, 2018. Assoc. Editor: Mian Li.

J. Mech. Des 140(10), 101401 (Jul 24, 2018) (13 pages) Paper No: MD-18-1119; doi: 10.1115/1.4040626 History: Received February 10, 2018; Revised June 16, 2018

Testing of components at higher-than-nominal stress level provides an effective way of reducing the required testing effort for system reliability assessment. Due to various reasons, not all components are directly testable in practice. The missing information of untestable components poses significant challenges to the accurate evaluation of system reliability. This paper proposes a sequential accelerated life testing (SALT) design framework for system reliability assessment of systems with untestable components. In the proposed framework, system-level tests are employed in conjunction with component-level tests to effectively reduce the uncertainty in the system reliability evaluation. To minimize the number of system-level tests, which are much more expensive than the component-level tests, the accelerated life testing (ALT) design is performed sequentially. In each design cycle, testing resources are allocated to component-level or system-level tests according to the uncertainty analysis from system reliability evaluation. The component-level or system-level testing information obtained from the optimized testing plans is then aggregated to obtain the overall system reliability estimate using Bayesian methods. The aggregation of component-level and system-level testing information allows for an effective uncertainty reduction in the system reliability evaluation. Results of two numerical examples demonstrate the effectiveness of the proposed method.

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Nelson, W. , 1980, “ Accelerated Life Testing-Step-Stress Models and Data Analyses,” IEEE Trans. Reliability, 29(2), pp. 103–108. [CrossRef]
Miller, R. , and Nelson, W. , 1983, “ Optimum Simple Step-Stress Plans for Accelerated Life Testing,” IEEE Trans. Reliab., 32(1), pp. 59–65. [CrossRef]
Candler, R. N. , Hopcroft, M. A. , Kim, B. , Park, W.-T. , Melamud, R. , Agarwal, M. , Yama, G. , Partridge, A. , Lutz, M. , and Kenny, T. W. , 2006, “ Long-Term and Accelerated Life Testing of a Novel Single-Wafer Vacuum Encapsulation for MEMS Resonators,” J. Microelectromech. Syst., 15(6), pp. 1446–1456. [CrossRef]
Van Dorp, J. R. , Mazzuchi, T. A. , Fornell, G. E. , and Pollock, L. R. , 1996, “ A Bayes Approach to Step-Stress Accelerated Life Testing,” IEEE Trans. Reliab., 45(3), pp. 491–498. [CrossRef]
Zhang, Y. , and Meeker, W. Q. , 2006, “ Bayesian Methods for Planning Accelerated Life Tests,” Technometrics, 48(1), pp. 49–60. [CrossRef]
Lee, J. , and Pan, R. , 2010, “ Analyzing Step-Stress Accelerated Life Testing Data Using Generalized Linear Models,” IIE Trans., 42(8), pp. 589–598. [CrossRef]
Hu, Z. , and Mahadevan, S. , 2016, “ Accelerated Life Testing (ALT) Design Based on Computational Reliability Analysis,” Qual. Reliab. Eng. Int., 32(7), pp. 2217–2232. [CrossRef]
Li, X. , Hu, Y. , Zhou, J. , Li, X. , and Kang, R. , 2018, “ Bayesian Step Stress Accelerated Degradation Testing Design: A Multi-Objective Pareto-Optimal Approach,” Reliab. Eng. Syst. Saf., 171, pp. 9–17. [CrossRef]
Zhu, Y. , and Elsayed, E. A. , 2013, “ Design of Accelerated Life Testing Plans Under Multiple Stresses,” Nav. Res. Logistics (NRL), 60(6), pp. 468–478. [CrossRef]
Zhu, Y. , and Elsayed, E. A. , 2013, “ Optimal Design of Accelerated Life Testing Plans Under Progressive Censoring,” IIE Trans., 45(11), pp. 1176–1187. [CrossRef]
Zhu, Y. , and Elsayed, E. A. , 2011, “ Design of Equivalent Accelerated Life Testing Plans Under Different Stress Applications,” Qual. Technol. Quant. Manage., 8(4), pp. 463–478. [CrossRef]
Xu, A. , and Tang, Y. , 2015, “ A Bayesian Method for Planning Accelerated Life Testing,” IEEE Trans. Reliab., 64(4), pp. 1383–1392. [CrossRef]
Guo, H. , and Yang, X. , 2007, “ A Simple Reliability Block Diagram Method for Safety Integrity Verification,” Reliab. Eng. Syst. Saf., 92(9), pp. 1267–1273. [CrossRef]
Kim, M. C. , 2011, “ Reliability Block Diagram With General Gates and Its Application to System Reliability Analysis,” Ann. Nucl. Energy, 38(11), pp. 2456–2461. [CrossRef]
Hu, Z. , and Mahadevan, S. , 2015, “ Time-Dependent System Reliability Analysis Using Random Field Discretization,” ASME J. Mech. Des., 137(10), p. 101404. [CrossRef]
Hu, Z. , and Mahadevan, S. , 2016, “ Resilience Assessment Based on Time-Dependent System Reliability Analysis,” ASME J. Mech. Des., 138(11), p. 111404. [CrossRef]
Pandey, V. , and Mourelatos, Z. P. , 2015, “ A New Method for Making Design Decisions: Decision Topologies,” ASME J. Mech. Des., 137(3), p. 031401. [CrossRef]
González, A. , Piel, E. , and Gross, H.-G. , 2009, “ A Model for the Measurement of the Runtime Testability of Component-Based Systems,” International Conference on Software Testing, Verification and Validation Workshops ICSTW'09, Denver, CO, Apr. 1–4, pp. 19–28.
Chen, G. , Reddy, S. M. , and Pomeranz, I. , 2003, “ Procedures for Identifying Untestable and Redundant Transition Faults in Synchronous Sequential Circuits,” IEEE 21st International Conference on Computer Design, San Jose, CA, Oct. 13–15, pp. 36–41.
Ichalal, D. , Marx, B. , Ragot, J. , and Maquin, D. , 2010, “ State Estimation of Takagi–Sugeno Systems With Unmeasurable Premise Variables,” IET Control Theory Appl., 4(5), pp. 897–908. [CrossRef]
Ao, D. , Hu, Z. , and Mahadevan, S. , 2017, “ Design of Validation Experiments for Life Prediction Models,” Reliab. Eng. Syst. Saf., 165, pp. 22–33. [CrossRef]
Ullah, K. , Alam, I. , and Lone, S. A. , 2017, “ Accelerated Life Testing Design Using Geometric Process for Generalized Rayleigh Distribution With Complete Data,” Reliab.: Theory Appl., 12(4), pp. 76–83. http://gnedenko-forum.org/Journal/2017/042017/RTA_4_2017-08.pdf
Gu, W. , Sun, Z. , Wei, X. , and Dai, H. , 2014, “ A New Method of Accelerated Life Testing Based on the Grey System Theory for a Model-Based Lithium-Ion Battery Life Evaluation System,” J. Power Sources, 267, pp. 366–379. [CrossRef]
Fard, N. , and Li, C. , 2009, “ Optimal Simple Step Stress Accelerated Life Test Design for Reliability Prediction,” J. Stat. Plann. Inference, 139(5), pp. 1799–1808. [CrossRef]
Shen, K.-F. , Shen, Y.-J. , and Leu, L.-Y. , 2011, “ Design of Optimal Step–Stress Accelerated Life Tests Under Progressive Type I Censoring With Random Removals,” Qual. Quantity, 45(3), pp. 587–597. [CrossRef]
Guo, H. , and Mettas, A. , 2007, “ Improved Reliability Using Accelerated Degradation & Design of Experiments,” IEEE Annual Reliability and Maintainability Symposium, Orlando, FL, Jan. 22–25, pp. 446–450.
Escobar, L. A. , and Meeker, W. Q. , 2006, “ A Review of Accelerated Test Models,” Stat. Sci., 21(4), pp. 552–577. [CrossRef]
Van Dorp, J. R. , and Mazzuchi, T. A. , 2005, “ A General Bayes Weibull Inference Model for Accelerated Life Testing,” Reliab. Eng. Syst. Saf., 90(2–3), pp. 140–147. [CrossRef]
Meeker, W. Q. , Escobar, L. A. , and Hong, Y. , 2009, “ Using Accelerated Life Tests Results to Predict Product Field Reliability,” Technometrics, 51(2), pp. 146–161. [CrossRef]
Pascual, F. , 2010, “ Accelerated Life Test Planning With Independent Lognormal Competing Risks,” J. Stat. Plann. Inference, 140(4), pp. 1089–1100. [CrossRef]
Wu, S. J. , Lin, Y. P. , and Chen, Y. J. , 2006, “ Planning Step-Stress Life Test With Progressively Type I Group-Censored Exponential Data,” Statistica Neerlandica, 60(1), pp. 46–56. [CrossRef]
Zhao, W. , and Elsayed, E. , 2004, “ An Accelerated Life Testing Model Involving Performance Degradation,” Annual Symposium Reliability and Maintainability (RAMS), Los Angeles, CA, Jan. 26–29, pp. 324–329.
Pascual, F. , 2008, “ Accelerated Life Test Planning With Independent Weibull Competing Risks,” IEEE Trans. Reliab., 57(3), pp. 435–444. [CrossRef]
Pascual, F. , 2007, “ Accelerated Life Test Planning With Independent Weibull Competing Risks With Known Shape Parameter,” IEEE Trans. Reliab., 56(1), pp. 85–93. [CrossRef]
Zhao, W. , and Elsayed, E. A. , 2005, “ A General Accelerated Life Model for Step-Stress Testing,” IIE Trans., 37(11), pp. 1059–1069. [CrossRef]
Teng, S.-L. , and Yeo, K.-P. , 2002, “ A Least-Squares Approach to Analyzing Life-Stress Relationship in Step-Stress Accelerated Life Tests,” IEEE Trans. Reliab., 51(2), pp. 177–182. [CrossRef]
Huan, X. , and Marzouk, Y. M. , 2013, “ Simulation-Based Optimal Bayesian Experimental Design for Nonlinear Systems,” J. Comput. Phys., 232(1), pp. 288–317. [CrossRef]
Hu, Z. , Ao, D. , and Mahadevan, S. , 2017, “ Calibration Experimental Design Considering Field Response and Model Uncertainty,” Comput. Methods Appl. Mech. Eng., 318, pp. 92–119. [CrossRef]
Sudret, B. , 2008, “ Global Sensitivity Analysis Using Polynomial Chaos Expansions,” Reliab. Eng. Syst. Saf., 93(7), pp. 964–979. [CrossRef]
Hu, Z. , and Mahadevan, S. , 2016, “ Global Sensitivity Analysis-Enhanced Surrogate (GSAS) Modeling for Reliability Analysis,” Struct. Multidiscip. Optim., 53(3), pp. 501–521. [CrossRef]
Hu, Z. , Zhu, Z. , and Du, X. , 2018, “ Time-Dependent System Reliability Analysis for Bivariate Responses,” ASME J. Risk Uncertainty Eng. Syst., Part B: Mech. Eng., 4(3), p. 031002.
Yu, S. , and Wang, Z. , 2018, “ A Novel Time-Variant Reliability Analysis Method Based on Failure Processes Decomposition for Dynamic Uncertain Structures,” ASME J. Mech. Des., 140(5), p. 051401. [CrossRef]
Sobol, I. M. , 2001, “ Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates,” Math. Comput. Simul., 55(1–3), pp. 271–280. [CrossRef]
Vrugt, J. A. , Ter Braak, C. , Diks, C. , Robinson, B. A. , Hyman, J. M. , and Higdon, D. , 2009, “ Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution With Self-Adaptive Randomized Subspace Sampling,” Int. J. Nonlinear Sci. Numer. Simul., 10(3), pp. 273–290. http://dare.uva.nl/search?identifier=4db85bf2-71b0-4536-8746-0c7f86e6084e
Nummiaro, K. , Koller-Meier, E. , and Van Gool, L. , 2003, “ An Adaptive Color-Based Particle Filter,” Image Vision Comput., 21(1), pp. 99–110. [CrossRef]
Hu, Z. , Mahadevan, S. , and Ao, D. , 2018, “ Uncertainty Aggregation and Reduction in Structure–Material Performance Prediction,” Comput. Mech., 61(1-2), pp. 237–257. [CrossRef]
Huang, D. , Allen, T. T. , Notz, W. I. , and Zeng, N. , 2006, “ Global Optimization of Stochastic Black-Box Systems Via Sequential Kriging Meta-Models,” J. Global Optim., 34(3), pp. 441–466. [CrossRef]
Zhu, Z. , and Du, X. , 2016, “ Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions,” ASME J. Mech. Des., 138(12), p. 121403. [CrossRef]
Giannakoglou, K. , 2002, “ Design of Optimal Aerodynamic Shapes Using Stochastic Optimization Methods and Computational Intelligence,” Prog. Aerosp. Sci., 38(1), pp. 43–76. [CrossRef]
Mockus, J. , 1994, “ Application of Bayesian Approach to Numerical Methods of Global and Stochastic Optimization,” J. Global Optim., 4(4), pp. 347–365. [CrossRef]
Pandey, V. , Mourelatos, Z. , Nikolaidis, E. , Castanier, M. , and Lamb, D. , 2012, “ System Failure Identification Using Linear Algebra: Application to Cost-Reliability Tradeoffs Under Uncertain Preferences,” SAE Paper No. 0148-7191.


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Fig. 1

Illustration of system with untestable component: (a) a mechanical system and (b) a system with untestable component

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Fig. 2

Overview of the proposed SALT framework

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Fig. 3

Flowchart for the evaluation of f(t|ssys, nsys, a0sys, θ, θu)

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Fig. 4

Implementation procedure of the proposed SALT framework

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Fig. 5

System configuration of a mixed system

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Fig. 6

Comparison of SALT and DS methods (best case)

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Fig. 7

Comparison of SALT and DS methods (worst case)

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Fig. 8

Posterior distribution updating history of untestable component (component 2) over iterations

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Fig. 9

Comparison of testing cost distributions to reach to the stopping criterion

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Fig. 10

A four-joint robot system: (a) kinematic diagram and (b) reliability block diagram

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Fig. 11

Comparison of SALT and DS methods (25 executions)

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Fig. 12

Comparison of testing cost distribution to reach the stopping criterion



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