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There are often many reasons for equipment failure. When the performance of a certain aspect drops to a certain threshold, the equipment will fail. Affected by other factors, the threshold is uncertain. A reliability model of uncertain thresholds where degradation and external shocks compete with each other is established, and the reliability of the model are evaluated according to uncertainty theory. Under three different shock types, the reliability of the equipment is obtained. The reliability with uncertain thresholds and the reliability with constants thresholds are compared. The results show that in different periods of equipment operation, the reliability of the uncertain thresholds is different with the reliability of the constants thresholds. If the threshold is simply regarded as a known constant, it will cause inaccuracies in the reliability assessment of the system, and miss the best maintenance time, causing unnecessary losses. Taking the microelectronic mechanical system as an example, the superiority of the proposed model is illustrated.

In this paper, we investigate a wear and mixed shock model in which the system can fail due to internal aging or external shocks. The lifetime of the system, due to internal wear, follows continuous phase-type (PH) distributions. The external random shocks arrive at the system according to a PH renewal process. The system will fail when the internal failure occurs or k1 consecutive external shocks, the size of at least d1 or k2 consecutive external shocks the size of at least d2 occur, where d1<d2, k1>k2. The failed system can be repaired immediately, and the repair times of the system are governed by continuous PH distributions. The system can be replaced by a new and identical one based on a bivariate replacement policy (L,N). The long-run average profit rate for the system is obtained by employing the closure property of the PH distribution. Finally, a numerical example is also given to determine the optimal replacement policy.