RENO Solution:

Define a Probability called “SnowProbability” and a Constant called “SnowThreshold” to determine whether it will snow on a given day. If a random number uniformly distributed from 0 to 1 (generated by SnowProbability) is less than or equal to the fixed probability that it will snow on any given winter day (defined by SnowThreshold), this indicates that it snowed during the simulation.

Define a Random Variable called “Snowfall_inches” to describe the depth of the snow.

Define a Random Variable called “Area_to_clean_ft2” to describe the area of the driveways.

Define an Equation Variable to describe the number of hours that the snow blower will be used based on the amount of snowfall and the area of the driveways.

Construct the flowchart as follows:

Steps 1 and 2: Use a Block to generate a random number uniformly distributed from 0 to 1 (based on the Probability called “SnowProbability) and then use a Conditional Block to check whether it is less than or equal to the fixed probability of snow on any given winter day (based on the Constant called “SnowThreshold”). If true, this indicates that it snowed and the “Usage_Hours” are passed to the TRUE path. If false, this indicates that it did not snow and “0” is passed to the FALSE path.

Steps 3a and 3B: Use Flag constructs called “Snow” and “No Snow” to mark the TRUE and FALSE paths coming from the Conditional Block.

Step 4: Use a Summing Gate to accept the two incoming paths and perform a summation on the snow blower usage information that is passed to the construct. The result is one outgoing path.

Step 5: Use a Result Storage construct called “Usage” to store an average of the snow blower usage information that is passed to the construct.

Step 6: Use a Block called “Reliability” to calculate the snow blower reliability. This equation uses RENO’s intrinsic function, WEIBULL_REL, which returns the Weibull reliability at a given time. The inputs to this intrinsic function are (Time, Beta, Eta, Gamma). The use of the reserved keyword IN indicates that the daily usage time from the previous “Usage” construct will be inserted into the equation for Time. Note: The list separator (,) given here is appropriate for the USA regional settings. If your regional settings differ, you must adjust the input accordingly. For example, under German regional settings, the input would be (Time; Beta; Eta; Gamma).

Step 7: Use another Result Storage construct called “Result” to store the last value.

After running 1,000 simulations (with a seed of 1 to provide repeatability), the results are displayed in the Simulation Results Explorer and in the flowchart, as shown next.

The reliability is 98.5975%.

A RENO project with the solution for this example (called "Snow Blower.rnp") is shipped with the software and stored in the Examples\Reliability folder in the application directory (e.g. C:\Program Files\ReliaSoft\RENO\Examples\Reliability\Snow Blower.rnp).