Abstract |
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. |
Affiliation |
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. |