State Enumeration Tool MIL-STD-756 Example

The Reliability Analytics Toolkit System States tool provides the equivalent functionality as the Method 1002 procedure described in MIL-STD-756, Reliability Modeling and Prediction. While the approach described in MIL-STD-756 is very tedious, the System States tool makes the analysis process far easier. The following example shows the equivalent calculation as that shown in MIL-STD-756, Method 1002, Boolean Truth Table. The end result is a system probability of success of 0.13572 for the reliability block diagram and unit probability of success values shown on the left in the picture below.  The right side to the picture shows the equivalent inputs entered into the System States tool. We enter zero in for input 4 to output all possible states.

The next step is to review the enumerated states and compare them to the reliability block diagram, asking the question “is this state successful?”.  If the state is not successful, make a note of the state number shown in the left hand column.  For example, state number seven is unsuccessful, because either unit C1 or C2 is required for an end-to-end functional path, as shown in the reliability block diagram. If both units C1 and C2 are in a failed state, then there is no end-to-end path from the left side to the right side of the reliability block diagram.

The next step is to go back to the input screen and enter the list of unsuccessful state numbers into box 6, as shown below.

Upon recalculating, the System States tool provides the same result as that shown in the MIL-STD-756 Method 1002 example, a system probability of success of 0.13572.

While this example took unit probability of success as an input, the tool also allows for input of other unit reliability metrics, such as unit failure rate, or, assuming a Weibull failure distribution, unit characteristic life and shape parameter.  The tool will also simply enumerate all possible states given just a list of unique names.  Each of these options is controlled by the input format in box 1 and the selection made for input #2:

If failure rates or Weibull parameters are entered then unit reliability becomes a function of time, which is entered in input #3 as “mission time.” The units are assumed to start the mission at t=0 in a state “as good as new” and have to complete a mission of some length “T hours.” Input b above assumes that unit reliability follows an exponential failure distribution while input c assumes it follows a Weibull distribution.

See these posts for other application examples of the  System States tool:

Reliability Modeling: Parallel Configuration

Reliability Modeling: k out of n Configutations