Abstract
The traditional shock model generally describes the magnitude of the cumulative damage caused by a random shock sequence and compares the magnitude with a predetermined threshold to obtain the failure time of a component. There are two limitations in this kind of models in practice: First, the statistical characteristics of the damage due to a single shock may be difficult to obtain, which means the magnitude of the damage may not be described by an appropriate distribution; Second, the cumulative shock magnitude may be difficult to measure, or it may be difficult for a failure mode to be described by a threshold, meaning that the magnitude of the damage and the threshold may not be compared with each other. Considering both failure and censored samples, a reliability modeling method is proposed in this work to address the above problems. The shock model is first established by using both continuous and discrete phase-type (PH) distributions. Then the parameter estimation method of the shock model is derived based on EM method and the identifiability of the parameters in PH distributions is also given. Finally, the adaptability of the model is analyzed using three different types of simulation cases.
Highlights
In reliability theory, the shock model is often used to describe the probability distribution of a component’s reliability under a random shock environment
Aiming at the issues mentioned above, this paper proposes a modeling method based on continuous and discrete PH distributions, considering both failure and censored samples with the data of failure time, censored time and number of shocks
2) PARAMETER ESTIMATION RESULTS The distribution of the inter-arrival time is fitted by a 4-th order Coxian distribution, and the number of shocks is fitted by a 5-th order discrete PH distribution
Summary
The shock model is often used to describe the probability distribution of a component’s reliability under a random shock environment. When the cumulative magnitude (blue line) of the damage caused by the shock sequence (green line) exceeds the certain threshold (red line), the component fails. This moment, the reliability of the shock model satisfies: R t P T t P N (t) X i 0 i S = n 0 P n i 0 Xi N t n (1). In the early literature [2,3], in order to obtain the analytical expression of the parameters, the exponential distribution was frequently used to describe the magnitude of the damage due to a single shock, and the arrival time sequence was characterized by a Poisson process. Some follow-up researchers developed the modeling method with more types of distributions [4,5], which greatly extended its adaptability
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