Overcoming some limitations of imprecise reliability models

The application of imprecise reliability models is often hindered by the rapid growth in imprecision that occurs when many components constitute a system and by the fact that time to failure is bounded from above. The latter results in the necessity to explicitly introduce an upper bound on time to failure which is in reality a rather arbitrary value.

The practical meaning of the models of this kind is brought to question. We suggest an approach that overcomes the issue of having to impose an upper bound on time to failure and makes the calculated lower and upper reliability measures more precise. The main assumption consists in that failure rate is bounded.

Langrage method is used to solve the non-linear program. Finally, an example is provided.