Comput Stat
DOI 10.1007/s00180-015-0586-6
ORIGINAL PAPER
A stochastic expectation-maximization algorithm
for the analysis of system lifetime data with known
signature
Yandan Yang
1
· Hon Keung Tony Ng
1
·
Narayanaswamy Balakrishnan
2
Received: 28 August 2014 / Accepted: 8 May 2015
© Springer-Verlag Berlin Heidelberg 2015
Abstract Statistical estimation of the model parameters of component lifetime distri-
bution based on system lifetime data with known system structure is discussed here. We
propose the use of stochastic expectation-maximization (SEM) algorithm for obtain-
ing the maximum likelihood estimates of model parameters based on complete and
censored system lifetimes. Different ways of implementing the SEM algorithm are
also studied. We have shown that the proposed methods are feasible and are easy
to implement for various families of component lifetime distributions. The proposed
methodologies are then illustrated with two popular lifetime models—the Weibull
and Birnbaum-Saunders distributions. Monte Carlo simulation is then used to com-
pare the performance of the proposed methods with the corresponding estimation by
direct maximization. Finally, two illustrative examples are presented along with some
concluding remarks.
Keywords Expectation-maximization algorithm · Maximum likelihood estimation ·
Monte Carlo simulation · Reliability data · Type-II censoring
Electronic supplementary material The online version of this article (doi:10.1007/s00180-015-0586-6)
contains supplementary material, which is available to authorized users.
B Hon Keung Tony Ng
ngh@mail.smu.edu
1
Department of Statistical Science, Southern Methodist University,
Dallas, TX 75275-0332, USA
2
Department of Mathematics and Statistics, McMaster University,
Hamilton, Ontario L8S 4K1, Canada
123