Statistics for Maintenance Modelling: Continuous Lifetime Distributions 1

# Summary¤

Fitting a parametric model to reliability data summarises the data using just a few parameters but more importantly allows decisions to be made in regions where there are not huge amounts of data. Apart from the Poisson/exponential distribution which is normally used because the hazard rate is thought to be approximately constant, the emphasis for the other distributions introduced in this and the next session, is on choosing the most appropriate one based on the shape of their curves. If this selection is done by considering a set of failure data, then the curves are likely to be the probability density or cumulative distribution curves. However if the decision is made more on the basis of engineering modelling and experience, then it is likely that the hazard function curve will be used.

The main characteristics of the distributions are:

- Exponential - it has a constant hazard rate. The probability of an individual (surviving) item failing does not increase with time.
- Weibull - it can take on a wide variety of unimodal shapes depending on the parameter settings while having the advantage of analytical expressions for the reliability and hazard functions. Depending on the parameter values, the hazard rate is either decreasing, increasing or constant. The latter case corresponds to the exponential function.
- Extreme Value (Gumbel) - it has a probability density function shape similar to the normal distribution's bell shape but with a longer tail to the left and a shorter tail to the right.