Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty
1
Department of Mathematics and Information Technology, The Education University of Hong Kong, Tai Po, Hong Kong, China
2
Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
3
Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Academic Editor: Yuhlong Lio
Mathematics 2021, 9(23), 3032; https://doi.org/10.3390/math9233032
Received: 18 October 2021
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Revised: 23 November 2021
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Accepted: 24 November 2021
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Published: 26 November 2021
(This article belongs to the Special Issue Statistical Simulation and Computation II)
A device that performs its intended function only once is referred to as a one-shot device. Actual lifetimes of such kind of devices under test cannot be observed, and they are either left-censored or right-censored. In addition, one-shot devices often consist of multiple components that could cause the failure of the device. The components are coupled together in the manufacturing process or assembly, resulting in the failure modes possessing latent heterogeneity and dependence. In this paper, we develop an efficient expectation–maximization algorithm for determining the maximum likelihood estimates of model parameters, on the basis of one-shot device test data with multiple failure modes under a constant-stress accelerated life-test, with the dependent components having exponential lifetime distributions under gamma frailty that facilitates an easily understandable interpretation. The maximum likelihood estimate and confidence intervals for the mean lifetime of k-out-of-M structured one-shot device under normal operating conditions are also discussed. The performance of the proposed inferential methods is finally evaluated through Monte Carlo simulations. Three examples including Class-H failure modes data, mice data from ED01 experiment, and simulated data with four failure modes are used to illustrate the proposed inferential methods.
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Keywords:
gamma frailty; accelerated life-tests; one-shot devices; dependent failure modes; k-out-of-M system; expectation–maximization algorithm
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MDPI and ACS Style
Ling, M.-H.; Balakrishnan, N.; Yu, C.; So, H.Y. Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty. Mathematics 2021, 9, 3032. https://doi.org/10.3390/math9233032
AMA Style
Ling M-H, Balakrishnan N, Yu C, So HY. Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty. Mathematics. 2021; 9(23):3032. https://doi.org/10.3390/math9233032
Chicago/Turabian StyleLing, Man-Ho, Narayanaswamy Balakrishnan, Chenxi Yu, and Hon Y. So. 2021. "Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty" Mathematics 9, no. 23: 3032. https://doi.org/10.3390/math9233032
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