Inference for the Component and System Lifetime Distribution of a k-unit Parallel System Based on System Data

Abstract

In this paper, we consider the inference for the component and system lifetime distribution of a k-unit parallel system with independent components based on system data. The components are assumed to have identical Weibull distribution. We obtain the maximum likelihood estimates of the unknown parameters based on system data. The Fisher information matrix has been derived. We propose β-expectation tolerance interval and β-content γ-level tolerance interval for the life distribution of the system. Performance of the estimators and tolerance intervals is investigated via simulation study. A simulated dataset is analyzed for illustration.

Keywords:

• β-content γ-level tolerance interval
• β-expectation tolerance interval
• Fisher information matrix
• Maximum likelihood estimator

Mathematics Subject Classification:

• Primary 62N05
• Secondary 62F25

Acknowledgments

The authors would like to thank an Associate Editor and two anonymous reviewers for helpful comments and suggestions which led to a much improved presentation.