A new class of survival distribution for degradation processes subject to shocks

Journal of Statistical Distributions and Applications

Table 1 Approximations for the survival probability of an illustrative shock-degradation model for survival time s=30

Order k	Lower Bound	Taylor S. F. Estimate	Upper Bound	Euler S. F. Estimate
Lower Bound on Survival Probability
1	0.2867	0.2556	0.4449	0.2556
Higher-order Approximations for the Survival Probability
2	0.2364	0.3040	0.3005	0.2798
3	0.2908	0.2867	0.3407	0.2840
4	0.2627	0.3005	0.2989	0.2867
5	0.2913	0.2908	0.3223	0.2883

The Fréchet shock stream is generated with α=1 and β=1.2 and the degradation process is a Wiener diffusion process with μ=−0.02 and σ=0.1. The table shows the Taylor and Euler estimates for the survival probability as well as bounds on these estimates for orders of approximation ranging from k=1 to k=5. The first line is the lower bound approximation for the survival function. The bold entries are discussed in the text