A model for k-out-of-m load-sharing systems

ABSTRACT

In a load-sharing system, the failure of a component affects the residual lifetime of the surviving components. We propose a model for the load-sharing phenomenon in k-out-of-m systems. The model is based on exponentiated conditional distributions of the order statistics formed by the failure times of the components. For an illustration, we consider two component parallel systems with the initial lifetimes of the components having Weibull and linear failure rate distributions. We analyze one data set to show that the proposed model may be a better fit than the model based on sequential order statistics.

Keywords:

• Conditional distribution
• Order statistics
• Proportional reversed hazard rate
• Two-step estimation procedure.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62N05; Secondary 60E05

Acknowledgment

The authors are grateful to the referees for their valuable comments and constructive suggestions.

Funding

First author is grateful to the University Grants Commission (UGC), India, for the financial support in the form of Research Fellowship in Science for Meritorious Students (F.4 − 1/2006(BSR)/5 − 84/2007(BSR)).