A Failure Model for Equipments Undergoing Complex Operation

A simple failure model for equipment undergoing several cycles of operation is given by the expression, 1 − exp(−Λ∑_ı=1^ı=kτ_i), where Λ is the failure coefficient, τ_i is the length of the ıth cycle of operation, and k is the number of cycles. A consequence of this model is that the probability of failure for a given total operating time is independent of the number of cycles of operation. It is shown that, under certain assumptions, a failure model that takes account of the number of cycles of operation, as well as the operating time, is given by the expression, 1 − exp(Λ₀∑_ı=1^ı=kτ_ı + Λ₁k). Interpretations of the constants, Λ₀ and Λ₁, are given. Also discussed is a method for testing the plausibility of the model against failure data.