| ${{f}_{{{X}_{m}}}}\left( x \right)$ | Probability density function (pdf) of ${{X}_{m}}$ |
| ${{T}_{k}}$ | Interval from (k-1)thminor inspection to kth minor inspection |
| ${{N}_{n}}$ | There are ${{N}_{n}}$minor inspection intervals between (n-1)thmajor inspection and nthmajor inspection, ${{N}_{0}}=0$ |
| $T$ | Minor inspection intervals sequence $T=\left\{ {{T}_{1}},{{T}_{2}},\cdots ,{{T}_{k}},\cdots \right\}$ |
| $N$ | Major inspection intervals sequence $N=\left\{ {{N}_{1}},{{N}_{2}},\cdots ,{{N}_{n}},\cdots \right\}$ |
| ${{S}_{j}}$ | Minor inspection is implemented at successive time${{S}_{j}}$,${{S}_{j}}=\sum\limits_{k=0}^{j}{{{T}_{k}}}$,${{T}_{0}}=0$,${{S}_{0}}=0$ |
| ${{A}_{n}}$ | The nth major inspection happens at the time whenAnthminor inspection should be taken, ${{A}_{n}}=\sum\nolimits_{k=0}^{n}{{{N}_{k}}}$ |
| ${{T}_{OM}}$ | The OM interval |
| $\tau $ | Random time to the next OM |
| $t$ | The threshold deciding whether to wait for OM |
| $\alpha $ | Probability of minor inspection detecting minor defective stage |
| ${{T}_{cr}}$ | Random time when the corrective replacement happens for the failed system |
| ${{T}_{ir}}$ | Random time when the inspection replacement is taken for the defective system |
| ${{T}_{or}}$ | Random time when the opportunistic replacement is implemented for the defective system |
| ${{c}_{mi}}$ | Cost of a minor inspection |
| ${{c}_{ma}}$ | Cost of a major inspection |
| ${{c}_{cr}}$ | Cost of a corrective replacement |
| ${{c}_{ir}}$ | Cost of an inspection replacement |
| ${{c}_{or}}$ | Cost of an opportunistic replacement |