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Software Used: Software Used: ALTA PRO
Download Example File for Version 10 (*.rsgz10) or Version 9 (*.rsr9)
Reliability analysis on a certain snow blower yielded a Weibull life distribution with a beta of 2 and an eta of 400 hrs.
The snow blower will be deployed in a part of the country where the probability that it will snow on any given winter day is 1 in 10.
If it snows, then the snow depth is normally distributed with a mean of 6 inches and a standard deviation of 2.
Furthermore, the area of the driveways in that region is also normally distributed with a mean of 300 square feet and a standard deviation of 40.
If the snow blower clears 30 cubic feet an hour, what would the reliability of the blower be assuming 100 winter days?
Define models that represent the depth of snowfall, the area of the driveways and the reliability of the snow blower, as shown below.
Note that even though the data are in varying units (inches, feet and cubic feet), the Model Unit has been set to Hours. This is because RENO flowchart results are always given in terms of the system base unit (SBU), and resources that require you to define a unit (i.e., Synthesis models) will have their values automatically converted to base units during simulation. Therefore, whenever you don’t want RENO to convert the value obtained from a model resource, simply make sure the model uses a unit that is defined as equal to 1 SBU. See the application help file for more information.
For this example, whenever the Depth model returns a value as “X hours,” it should be read as “X inches.” The values for the Area and Snowblower models can be read in a similar manner. If the model unit you are using is not equal to 1 SBU (choose File > Manage Repository > Manage Units to confirm), you will need to change the model units before resimulating the flowchart.
Define a RENO function to calculate the volume of snow, as shown below. For this example, divide the snow depth by 12 to convert inches to feet. The result of the function should be read as cubic feet. (Note that this equation uses the RENO internal function called “rvm” to draw random values based on the Depth model and the Area model.)
The picture shown next presents an overview of how the final flowchart will work.
To construct this flowchart, follow these steps:
Step 1: Use a standard block as a start block.
Step 2: Use a conditional block to check for the probability of snow, as shown next.
Here, the FP<=% condition configures the conditional block to draw a random number uniformly distributed from 0 to 100, and then evaluate whether that number is less than or equal to the condition value (the probability that it will snow on any given winter day).
If the condition is met, then it snowed. Calculate the number of hours the snow blower was used and pass the output to the “true” path. Here, SnowVolume is divided by the number of cubic feet the snow blower can clear in an hour (30). That figure is then multiplied by 100 days to determine the total number of hours of snow blower usage for winter.
If the condition is not met, then it did not snow. Pass the value 0 to the “false” path.
Step 3: Use two standard blocks and the RENO internal function called “in” to accept the values from the “true” and “false” paths.
Step 4: Use a result storage block to store the average value of the snow blower usage.
Step 5: Use a standard block to calculate the snow blower reliability. In this example, “in” indicates that the output of the previous block (which is usage hours) will be used to obtain the reliability based on the Snowblower model. The result is then subtracted from 1 to obtain the inverse of the reliability (probability of failure).
Step 6: Use another result storage block to store the last output value of the previous block.
Run 1,000 simulations, with a seed of 1 for repeatability. The result shows that the estimated reliability of the snow blower is 0.985555 or 98.5555%
