Discrete Event Simulation, Example 3, Comparison to Redundancy Equation Approach

This article compares the results obtained using the Discrete Event Simulation (DES) tool to those obtained deterministically by integrating the reliability function using this tool. This example assumes two identical units, serial number (sn) 1 and 2 are operated in parallel, with only one of the two required for mission success. The units are maintained on a periodic basis every 2,190 hours. If a unit fails during this interval, it waits until the next scheduled maintenance time for repair, at which time both units are fully checked out and restored to “as good as new.” The picture below shows the appropriate inputs for each tool to ensure an “apples-to-apples” comparison of the results. The inputs for the “active redundancy integrate” tool are shown on the right along with comparable inputs for the discrete event simulation tool shown on the left. We assume that each sn has a 1,250 hour mean time between failure (MTBF) and fails in accordance with the exponential failure distribution; therefore, on the left we enter “1250,e” as the failure characteristic and enter comparable inputs for item 4 on the right.  For this problem, we only model the periodic maintenance time of 2,190 hours and do not take into account any specific time to make a repair, therefore, zeros are shown for the repair characteristic in the first box on the left and “2190, delayed” is shown for each sn in the third input box. Since one of two units are required, we define a critical failure watch list set of “sn1,sn2” for the second  DES input box. If both items fail then a critical failure is tallied.  The comparable inputs shown on the right is m=1 units required out of n=2 total units (items #1 and #2 on the right).

Simulating 100 trials of ten years for each trial (87600 hours), with a seed of 1 provides the results shown in the second picture below, a average simulated MTBCF of 2,245 hours. The graph shown in the third picture below shows the variability of individual trial results, with the light blue line showing the result for each trial and the dark blue line showing the cumulative average over all previous trials.  This 2,245 hour simulated estimate compares to the 2,137 hours MTBCF shown in the fourth picture below, which was calculated using a closed-form equation.

Simulation Results:

Result from closed-form equation:

The underlying discrete event simulation engine is SimPy (Simulation in Python), which runs on the Google App Engine. See the references listed below for additional details on SimPy.

References:

  1. SimPy Home Page
  2. Matloff, Norm, University of California at Davis, Dept. of Computer Science, Introduction to Discrete-Event Simulation and the SimPy Language
  3. Matloff, Norm, University of California at Davis, Dept. of Computer Science, A Discrete-Event Simulation Course Based on the SimPy Language
  4. Python pseudo-random number generator