Research Papers: Design Automation

A Simulation Method to Estimate Two Types of Time-Varying Failure Rate of Dynamic Systems

[+] Author and Article Information
Zhonglai Wang

School of Mechatronics Engineering,
University of Electronic Science and
Technology of China,
Chengdu, Sichuan 611731, China;
The State Key Laboratory of Advanced Design
Manufacturing for Vehicle Body,
Changsha 410082, China
e-mail: wzhonglai@uestc.edu.cn

Xiaoqiang Zhang

School of Mechatronics Engineering,
University of Electronic Science and
Technology of China,
Chengdu, Sichuan 611731, China
e-mail: xqzhanguestc@163.com

Hong-Zhong Huang

School of Mechatronics Engineering,
University of Electronic Science and
Technology of China,
Chengdu, Sichuan 611731, China
e-mail: hzhuang@uestc.edu.cn

Zissimos P. Mourelatos

Mechanical Engineering Department,
Oakland University,
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 January 22, 2016; final manuscript received July 5, 2016; published online September 14, 2016. Assoc. Editor: Xiaoping Du.

J. Mech. Des 138(12), 121404 (Sep 14, 2016) (10 pages) Paper No: MD-16-1067; doi: 10.1115/1.4034300 History: Received January 22, 2016; Revised July 05, 2016

The failure rate of dynamic systems with random parameters is time-varying even for linear systems excited by a stationary random input. In this paper, we propose a simulation-based method to estimate two types (type I and type II) of time-varying failure rate of dynamic systems. The input stochastic processes are discretized in time and the trajectories of the output stochastic process are calculated. The time of interest is partitioned into a series of time intervals and the saddlepoint approximation (SPA) is employed to estimate the probability of failure in each interval. Type I follows the commonly used definition of failure rate. It is estimated at discrete time intervals using SPA and the correlation information from a properly selected time-dependent copula function. Type II is a proposed new concept of time-varying failure rate. It provides a way to predict the failure rate considering a virtual “good-as-old” repair action of repairable dynamic systems. The effectiveness of the proposed method is illustrated with a vehicle vibration example.

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Fig. 2

Flowchart of the proposed method

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Fig. 1

Schematic of the time-varying failure rate estimation process

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Fig. 3

Vehicle vibration model

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Fig. 10

RE of cumulative probability of failure. RE means relative error.

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Fig. 11

Estimated type I failure rate λ(t)

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Fig. 12

RE of type I failure rate λ(t). RE means relative error.

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Fig. 14

RE of type II failure rate λr(t)

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Fig. 4

Estimated cumulative probability of failure from MCS with/without considering correlation

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Fig. 5

Scatter diagram for first (rΣ1 and r2) (a) and last (rΣ149 and r150) (b) data pairs

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Fig. 7

Parameters of time-dependent Clayton copula functions

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Fig. 9

Kolmogorov–Smirnov goodness of fit

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Fig. 8

Estimated cumulative probability of failure

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Fig. 6

Copula weights results for first (r∑1 and r2) (a) and last (rΣ149 and rΣ150) (b) data pairs

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Fig. 13

Estimated type II failure rate λr(t)



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