Windchill Risk and Reliability Desktop Help > Windchill Markov > Markov Calculations > Markov Calculation Properties > Calculation Options Page
Calculation Options Page
In the Calculate window, the Markov > Calculation Options page specifies which calculations to perform. Results are computed for the calculations with selected checkboxes. Because you can run so many different calculations, they are listed in alphabetical order. To make the selection process easier, you can click the Select All button or Clear All button to select or clear all calculations and then customize your selections from there. Your selections are saved as the defaults for the next time you calculate Markov results.
The following table describes the calculation choices on the Calculation Options page. It also indicates whether the calculation is performed for the system, states, and/or transitions.
Calculation
Calculated For
Description
Availability
System
The probability that the system is operating properly at a specific time point. Availability is a time-based probability metric between 0 and 1. It is computed by summing the probabilities of all good states. In the steady state, availability is a function of both reliability (how quickly a system fails) and of maintainability (how quickly the system can be repaired.
Capacity
System and States
The average throughput, profit, or reward of the system per unit time at a specified point in time.
Conditional failure intensity
System
The rate of failures (failures per unit time) of the system at a specified point in time given that the system is in a good state (operational) at the beginning of that interval.
Conditional repair intensity
System
The rate of repairs (repairs per unit time) of the system at a specified point in time given that the system is in a failed state at the beginning of the interval.
Cost per unit time
System, States, and Transitions
Cost associated with the system per unit time at a specified point in time. This includes the cost associated when events occur (transitions) and the cost of remaining in a state. In the steady state, it is the asymptotic cost per unit time.
Failure density
System
The failure probability density function (pdf), which is the frequency of first failures (number of first failures per unit) at a specified point in time.
Failure frequency
System
The expected number of system failures per unit time at a specified point in time. In the steady state, it is the asymptotic failure frequency of the system.
Failure rate
System
The expected number of failures of the system per unit time at a specified point in time given that no failure has occurred up to the beginning of the interval. This value is also known as the hazard rate, conditional failure rate, or instantaneous failure rate.
Frequency of departures
States
The expected number of departures from a state per unit time at a specified point in time.
Frequency of transitions
Transitions
The expected number of times the transition between two specified states is fired per unit time at a specified point it time.
Frequency of visits
States
The expected number of visits to a state per unit time at a specified point in time.
Mean availability
System
The average availability in a specified interval. This is the ratio of the expected uptime during an interval and the length of the interval.
Mean capacity
System and States
The mean capacity of a state is equivalent to the expected capacity delivered to that state up to a specified point in time. This is the ratio of the product of the capacity of the state and the mean time spent in that state with respect to the length of the interval. The mean capacity of a system is the sum of the mean capacities of the individual states.
Mean cost
System, States, and Transitions
The average cost in a specified interval.
Mean state probability
States
The average probability of a state up to a specified point in time. This is the ratio of the man time spent in a state and the length of the interval.
Mean unavailability
System
The average unavailability up to a specified point in time. This is the ratio of the expected downtime during an interval and the length of the interval.
MTBF
System
The mean time between failures, which is the number of hours a repairable system operates between failures given a long run. This average duration between subsequent failures is the reciprocal of the steady state failure rate.
Mean time to failure, steady state
System
The asymptotic average duration of an uninterrupted uptime. Often referred to as MTTF (mean time to failure), it is the product of steady state availability and MTBF.
Mean time to first failure
System
The average time until the first failure of the system. Frequently, it is simply but incorrectly referred to as MTTF.
MTTR
System
The mean time to repair, which is applicable to repairable systems.
Number of departures
States
The expected number of departures from a state up to a specified point in time. It is the integral of departure frequency over the interval.
Number of failures
System
The expected number of system failures up to a specified point in time. It is the integral of failure frequency over the interval.
Number of repairs
System
The expected number of system repairs up to a specified point in time. It is the integral of repair frequency over the interval.
Number of transitions
Transitions
The expected number of firings of a transition up to a specified point in time.
Number of visits
States
The expected number of visits to a state up to a specified point in time.
Probability
States
The probability that the system is in a specified state at a point in time.
Reliability
System
The probability that the system will remain operational until a specified time. Reliability is a time-based probability value, which means it has a value between 0 and 1. A reliability of 0 means that the system always fails before the specified time or never functions until the specified time. A reliability value of 1 indicates that a system always operates until the specified time.
Repair frequency
System
The expected number of system repairs per unit time at a specified point in time.In the steady state, it is the asymptotic repair frequency of the system.
Time spent in state
States
The expected time spent in a state up to a specified point in time.
Total capacity
System and States
The expected total capacity up to a specified point in time.
Total cost
System, States, and Transitions
The expected total cost up to a specified point in time.
Total downtime
System
The expected downtime up to a specified point in time.
Total uptime
System
The expected uptime up to a specified point in time.
Unavailability
System
The probability that, at a given time, the system will not function, due to either a failure or a repair. This is the sum of the probabilities of all failed states.In the steady state, it is the ratio of the MTTR and MTBF
Unreliability
System
The probability that, during a given time period, a failed state will occur, which means that the system is no longer able to operate. The probability of at least one failure occurring during the period is the compliment of the reliability. It is also the integral of the failure density over the interval.
Calculation results for the system are viewed in the View Calculations Results window. For more information, see Markov System Level Calculation Results. Calculation results for a particular state or transition are viewed on the Results page in its Calculation Properties window. For more information, see:
Markov Calculation Properties