# Palmgren-Miner linear damage modelΒΆ

The function palmgren_miner_linear_damage uses the Palmgren-Miner linear damage hypothesis to find the outputs listed below.

Inputs:

- rated_life - an array or list of how long the component will last at a given stress level
- time_at_stress - an array or list of how long the component is subjected to the stress that gives the rated_life
- stress - what stress the component is subjected to. Not used in the calculation but is required for printing the output.
Note

- Ensure that the time_at_stress and rated_life are in the same units. The answer will also be in those units.
- The number of items in each input must be the same.

Outputs:

- Fraction of life consumed per load cycle
- Service life of the component
- Fraction of damage caused at each stress level

In the following example, we consider a scenario in which ball bearings fail after 50000 hrs, 6500 hrs, and 1000 hrs, after being subjected to a stress of 1kN, 2kN, and 4kN respectively. If each load cycle involves 40 mins at 1kN, 15 mins at 2kN, and 5 mins at 4kN, how long will the ball bearings last?

```
from reliability.PoF import palmgren_miner_linear_damage
palmgren_miner_linear_damage(rated_life=[50000,6500,1000], time_at_stress=[40/60, 15/60, 5/60], stress=[1, 2, 4])
'''
Palmgren-Miner Linear Damage Model results:
Each load cycle uses 0.01351 % of the components life.
The service life of the component is 7400.37951 load cycles.
The amount of damage caused at each stress level is:
Stress = 1 , Damage fraction = 9.86717 %.
Stress = 2 , Damage fraction = 28.463 %.
Stress = 4 , Damage fraction = 61.66983 %.
'''
```

**References:**

- Probabilistic Physics of Failure Approach to Reliability (2017), by M. Modarres, M. Amiri, and C. Jackson. pp. 33-37