Statistics for Maintenance Modelling: Continuous Lifetime Distributions 2

# Example of Fitting the Lognormal Distribution to Failure Times¤

PET film is used for electrical insulation inside SF6 gas insulated transformers. The failure times from 15 accelerated life-tests were 50.25, 87.75, 87.77, 92.90, 92.91, 95.96, 108.3, 108.3, 117.9, 123.9, 124.3, 129.7, 135.6, 135.6. Fitting a lognormal distribution with = 4.66 and = 0.23 to the cdf for the failure times, gives:

The benefit of fitting a parameterised distribution can be seen in the smoothing of the jagged observation data.

Note:

- This data comes from Wang (2000).
- The graph suggests that the lognormal is a reasonably fit to the data, but the high to ratio suggests that the normal distribution would also be suitable.