Variables
Description
What is this formula?
The Maintainability Function calculates the probability that a failed system, machine, or component will be repaired within a specified time.
It is commonly used in reliability engineering to evaluate how quickly equipment can be restored after failure.
When to use it
Use this formula when:
- Estimating repair completion probability.
- Evaluating maintenance performance.
- Comparing repairability of equipment.
- Planning maintenance resources.
- Analyzing downtime risk.
Example
A machine has:
μ = 0.25 h⁻¹
Find the probability that it will be repaired within:
t = 6 h
Formula:
M(t)=1-e^(-μt)
Substitution:
M=1-e^(-(0.25×6))
M=1-e^(-1.5)
M≈0.777
Result:
The probability of completing the repair within 6 hours is approximately 77.7%.
Applications
- Reliability engineering
- Maintenance planning
- Asset management
- Downtime analysis
- Industrial repair performance
Note
This formula assumes a constant repair rate and follows an exponential repair-time model. Real repair times may vary due to spare-part availability, technician skill, troubleshooting complexity, logistics delays, and equipment accessibility.