Parameter Estimation for a k-out-of-n: F System

Abstract

We propose an expectation maximization algorithm to estimate the parameters of a k-out-of-n: F system. Components composing the system are independent and have exponential duration distributions. As an ideal model of a practical system, we cannot observe any component’s duration. The observation consists of lifetime data of the system. Based on a construction of a continuous time Markov chain (CTMC) for the system, we determine some probabilities and expectations conditional on the lifetime of the system. Then, we use an expectation maximization algorithm to estimate the system’s parameters. We carry out simulation studies to test the accuracy of the algorithm.

Keywords:

• Continuous time Markov chain
• Expectation maximization algorithm
• k-out-of-n: F system
• Parameter estimation

Mathematics Subject Classification:

• 62P30
• 60J28