Table 7 Optimal \({\hat{T}}\), \({\hat{N}}\), \({\hat{Z}}\) and the corresponding minimal expected cost rate \(C({\hat{T}}, {\hat{N}}, {\hat{Z}})\) for dependent damages. Means of the relevant distributions are given in parentheses
From: Optimal replacement policy under cumulative damage model and strength degradation with applications
K(t) | F | G | \(c_{K}\) | Method | \({\hat{T}}\) | \({\hat{N}}\) | \({\hat{Z}}\) | \(C({\hat{T}}, {\hat{N}}, {\hat{Z}})\) |
|---|---|---|---|---|---|---|---|---|
\(100\exp (-0.1t)\) | Exp(0.2) | MVGa(0.5, 10) | 2 | Approx: GS | 13.62 | 4 | 24.88 | 0.099 |
(5) | (10.5) | Approx: SA | 13.59 | 4 | 25.57 | 0.099 | ||
\(\max \left\{ 60 - t, 0 \right\} \) | Exp(0.2) | MVGa(10, 5) | 4 | Approx: GS | 25.40 | 3 | 22.49 | 0.088 |
(5) | (15) | Approx: SA | 25.10 | 3 | 23.11 | 0.088 | ||
\(100\exp (-0.03t)\) | LN(2, 1) | MVGa(0.5, 10) | 2 | Approx: GS | 40.19 | 4 | 29.71 | 0.035 |
(12.18) | (10.5) | Approx: SA | 41.61 | 4 | 28.46 | 0.035 | ||
\(\max \left\{ 50 - t, 0 \right\} \) | LN(2, 1) | MVGa(0.5, 5) | 2 | Approx: GS | 33.89 | 4 | 16.10 | 0.037 |
(12.18) | (5.5) | Approx: SA | 33.94 | 4 | 16.01 | 0.039 |