A non-linear fuzzy regression for estimating reliability in a degradation process

Since some assumptions such as the function ϕ(·) needs to be completely specified and the relationship between μ and ϕ(s) must have linear behavior in the model μ = a + bϕ(S) used in the accelerated life testing analysis, generally do not hold; the estimation of stress level contains uncertainty. In this paper, we propose to use a non-linear fuzzy regression model for performing the extrapolation process and adapting the fuzzy probability theory to the classical reliability including uncertainty and process experience for obtaining fuzzy reliability of a component. Results show, that the proposed model has the ability to estimate reliability when the mentioned assumptions are violated and uncertainty is implicit; so that the classical models are unreliable.