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Abstract
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In system reliability engineering, systems are made up of
different components and these systems can be complex. For various purposes,
engineers and researchers are often interested in the lifetime distribution
of the system as well as the lifetime distribution of the components which
make up the system. In many cases, the lifetimes of an n-component coherent
system can be observed, but not the lifetimes of the components. In the
recent years, parametric and nonparametric inference for the lifetime
distribution of components based on system lifetime lifetimes has been
developed. We further investigate the estimation of the parameters in
component lifetime distributions based on censored system-level data.
Specially, we consider the maximum likelihood estimation and propose
alternative computational methods and approximations to the maximum
likelihood estimators (MLEs). Based on the special features of the system
lifetime data, we treat the system lifetime data as incomplete data and
apply the Expectation-Maximization (EM) algorithm to obtain the MLEs and
apply the stochastic EM (SEM) algorithm to approximate the MLEs. Different
implementations of the EM and SEM algorithms are proposed and their
performances are evaluated. We have shown that the proposed methods are
feasible and easy to implement for various families of component lifetime
distributions. Finally, some related statistical problems based on system
reliability data will also be discussed.
Collaborators: N. Balakrishnan (McMaster University, Canada), J. Navarro
(University of Murcia, Spain), Y. Yang (Javelin Marketing, Texas), J. Zhang
(SUNY Downstate Medical Center, Brooklyn, New York)
References:
Balakrishnan, N., Ng, H. K. T. and Navarro, J. (2011). Linear Inference for
Type-II Censored System Lifetime Data with Signatures Available, IEEE
Transactions on Reliability, 60, 426–440.
Balakrishnan, N., Ng, H. K. T. and Navarro, J. (2011). Exact Nonparametric
Inference for Component Lifetime Distribution based on Lifetime Data from
Systems with Known Signatures, Journal of Nonparametric Statistics, 23,
741-752.
Yang, Y., Ng, H. K. T. and Balakrishnan, N. (2016). A stochastic
expectation-maximization algorithm for the analysis of system lifetime data
with known signature, to appear in Computational Statistics, 31, 609 – 641.
Zhang, J., Ng, H. K. T. and Balakrishnan, N. (2015). Statistical Inference
of Component Lifetimes with Location-Scale Distributions from Censored
System Failure Data with Known Signature, IEEE Transactions on Reliability,
64, 613 – 626.
Zhang, J., Ng, H. K. T. and Balakrishnan, N. (2015). Tests for Homogeneity
of Distributions of Component Lifetimes from System Lifetime Data with Known
System Signatures, Naval Research Logistics, 62, 550 – 563.
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Affiliation
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Hon Keung Tony Ng received the M.Sc. and Ph.D. degrees in
statistics from McMaster University, Hamilton, ON, Canada, in 2000, and
2002, respectively. He is currently a Professor of Statistical Science with
Southern Methodist University, Dallas, TX, USA. He is an Associate Editor of
Communications in Statistics, Computational Statistics, Journal of
Statistical Computation and Simulation,
Journal of Statistical Distributions
and Applications and Statistics and Probability Letters. His research
interests include reliability, censoring methodology, ordered data analysis,
nonparametric methods, statistical methods in epidemiology and statistical
inference. Dr. Ng is a fellow of the American Statistical Association, an
elected senior member of IEEE and an elected member of the International
Statistical Institute.
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