Availability

Capacity

Conditional failure intensity

Conditional repair intensity

Cost per unit time

Failure density

Here, Pi(t) is calculated considering that all failed states are absorbing states.

Failure frequency

Failure rate

Frequency of departures

Frequency of departures from state i:

Frequency of transitions

Frequency of transitions from state i to state j:

Frequency of visits

Frequency of visits to state i:

Mean availability

Mean capacity

Mean cost

Mean state probability

Mean unavailability

MTBF

Mean time to failure, steady state OR Mean time to first failure

The actual calculations are not discussed.

Mean time to failure, steady state

MTTR

Number of departures

Number of departures from state i:

Number of failures

Number of failures from state i:

Number of repairs

Number of repairs from state i:

Number of transitions

Number of transitions from state i to state j:

Number of visits

Number of visits to state i:

Reliability

Here, Pi(t) is calculated considering that all failed states are absorbing states.

Repair frequency

State probability

Individual state probabilities are calculated using information given in the Markov diagram. The probability of state i at time t, Pi(t), is calculated using the transition matrix and the initial state vector by the Fourth-Order Runge-Kutta Method. The error tolerance, ∈, is used to obtain the desired accuracy and stop the iterations. If ∈ is very small, then the computational time will be high; however, providing that round-off errors are negligible, results will be more accurate. If the system is repairable, then steady state results of individual state probabilities are calculated by solving a set of linear equations that correspond to the steady state behavior of the system.

Time spent in state

Total capacity

Total cost

Total downtime

Total uptime

Unavailability

Unreliability