Reliability and Maintenance Modeling for Dependent Competing Failure Processes With Shifting Failure Thresholds

We present reliability and maintenance models for systems subject to multiple
s
-dependent competing failure processes with a changing, dependent failure threshold. In our model, two failure processes are considered: soft failure caused by continuous degradation together with additional abrupt degradation due to a shock process, and hard failure caused by the instantaneous stress from the same shock process. These two failure processes are correlated or
s
-dependent in two respects: 1) the arrival of each shock load affects both failure processes, and 2) the shock process impacts the hard failure threshold level. In previous research, the failure thresholds are fixed constants, which is appropriate for most design and reliability problems. However, the nature of the failure threshold has become a critical issue for certain classes of complex devices. When withstanding shocks, the system is deteriorating, and its resistance to failure is weakening. In this case, it becomes more sensitive to hard failure. In this paper, three cases of dependency between the shock process and the hard failure threshold level are studied. The first case is that the hard failure threshold value changes to a lower level when the first shock is recorded above a critical value, or a generalized extreme shock model. The second case is that the hard failure threshold value decreases to a lower level when the time lag between two sequential shocks is less than a threshold δ, or a generalized δ-shock model. The third case is that the hard failure threshold value reduces to a lower level right after
m
shocks whose magnitudes are larger than a critical value, or a generalized
m
-shock model. Based on degradation and random shock modeling, reliability models are developed for these two
s
-dependent failure processes with a shifting failure threshold. Two preventive maintenance policies are also applied and compared to decide which one is more beneficial. Then a Micro-Electro-Mechanical System example is given to demonstrate the reliability models and maintenance polices.