An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains

الملخص EN

In many applications, the failure rate function may present a bathtub shape curve.

In this paper, an expectation maximization algorithm is proposed to construct a suitable continuous-time Markov chain which models the failure time data by the first time reaching the absorbing state.

Assume that a system is described by methods of supplementary variables, the device of stage, and so on.

Given a data set, the maximum likelihood estimators of the initial distribution and the infinitesimal transition rates of the Markov chain can be obtained by our novel algorithm.

Suppose that there are m transient states in the system and that there are n failure time data.

The devised algorithm only needs to compute the exponential of m×m upper triangular matrices for O(nm2) times in each iteration.

Finally, the algorithm is applied to two real data sets, which indicates the practicality and efficiency of our algorithm.