Notations

Definition

$M\left(t\right)$

Expected number of failures in the interval $\left(0,t\right)$

$F\left(t\right)$

Cumulative Distribution Function (CDF) of the time of first failure

$f\left(t\right)$

probability density function (pdf)

$\rho \left(t\right)$

Failure rate

T

Repair Time

$\alpha$

Quality of repair (shows partial repair)

d

Degradation rate when the item is idle during repair time

$S_1$

First time failure

h

Small grid point using in numerical integration-based algorithm

K, L

Positive integers using in numerical integration-based algorithm