A wind farm operator wants to optimize maintenance for gearboxes, which are critical components prone to failure. Historical data on times between failures (TBF) for 100 gearboxes is collected, showing the time (in months) until each gearbox requires repair or replacement. The goal is to schedule preventive maintenance to minimize downtime and costs.
The data set for the TBF (Time Between Failures) is given below. Note that you can copy/paste this data directly into Python.
Full TBF dataset (in months) for 100 gearboxes:
[28.36, 18.42, 24.15, 26.82, 17.68, 22.91, 21.07, 29.73, 25.94, 23.56, 27.05, 14.29, 19.52, 25.36, 22.36, 23.34, 29.04, 23.72, 24.99, 20.46, 18.55, 22.33, 27.44, 24.64, 25.46, 26.16, 28.65, 16.77, 18.63, 25.09, 25.24, 26.62, 21.71, 19.37, 17.85, 24.85, 21.58, 22.03, 17.12, 25.34, 23.65, 22.75, 24.11, 25.29, 18.97, 22.74, 22.58, 24.73, 25.65, 21.45, 22.87, 24.53, 29.07, 21.29, 26.06, 23.62, 25.84, 20.72, 25.02, 27.01, 22.68, 25.31, 19.64, 23.11, 24.36, 24.73, 21.48, 25.92, 26.02, 22.08, 22.94, 24.49, 20.85, 25.87, 22.43, 22.59, 25.47, 20.83, 22.86, 21.75, 24.03, 22.76, 25.32, 23.87, 24.09, 25.56, 22.45, 25.27, 23.94, 25.19, 22.97, 23.33, 24.79, 21.88, 23.62, 25.22, 22.47, 24.87, 22.65, 23.85]
You need to determine which distribution will best represent this data. The goal is to report to management a maintenance cycle that will provide reliability at 80%, 90%, and 95%. (This means that only 100 - Reliability % of the gear systems will experience a failure).
You will not need to do this next part, but I provide important reasoning here. In most real-world scenarios, there is a cost (repair + downtime) of a failure. There is also a cost (maintenance + downtime) for scheduled maintenance. The idea of using these statistics is to optimize the total cost of operation of the system.
I fully expect you to use AI for code generation and visualization to solve this problem. The data will fit one of the continuous distributions that are presented in Module 5.
You may discuss your approach and reasoning on Assignment 5 Discussion
Report Format (Details at Submission Guidelines (Engineering Reports) )
Cover - Name/Date/Class/Assignment #
Problem Statement - Copy/Paste and then modify to state problem
Methodology - The approach to the problem, not code, equations and explanation here
Results -Be sure to answer the problem asked in the problem statement
Conclusion - This can be short, any additional notes you want to make here
Appendices - Code or any additional information here