Stochastic comparisons of linear degradation and failure time models with dependent failure modes

The paper considers a reliability model for system which fails due to degradation failure or catastrophic failure. The linear degradation path is adopted to model the degradation process, and catastrophic failure rate is dependent on the degradation rate. Firstly, we conduct some stochastic comparisons between two systems when their respective degradation rate variables are ordered in the sense of various stochastic orders. Secondly, we conduct some stochastic comparisons between two systems with different conditional catastrophic failure rates. Finally, we give some examples with respect to some well-know models to illustrate the validity of the results.

Automated summary

This paper considers a reliability model for systems that fail due to degradation failure or catastrophic failure. The degradation process is modeled using a linear degradation path, and the catastrophic failure rate is dependent on the degradation rate. Firstly, stochastic comparisons are conducted between two systems with different stochastic orders for their respective degradation rate variables. Secondly, stochastic comparisons are conducted between two systems with different conditional catastrophic failure rates. Finally, examples are given using well-known models to demonstrate the validity of the results.