Competing failure modes modeling with limited wearout failures

This paper proposes a new modeling approach which can be applied to solve some practical reliability engineering problems when competing failure modes present, but only one or limited failures have occurred. This type of failure data cannot be modeled by traditional time-to-failure distributions. The new approach is derived from Weibayes method and provides a viable solution when reliability inference is needed during early product deployment phase. The most important value of the derivation is: it provides a distributional interpretation about the Weibayes result, and the assumptions that are made. The derivation not only reproduces the important result in the literature, but also gives insight into the sampling distribution of the parameter estimate. A parametric bootstrap method is used to illustrate how to incorporate the result in competing failure mode modeling.