Statistics for Maintenance Modelling: Regression Modelling

# Case Study: Breaking Strengths of Carbon Fibres - Accelerated Life Model¤

The models and concepts discussed so far in this session are by no means easy to understand, so we'll now examine a case study. The data were collected from experiments done at The University of Surrey. This analysis closely follows that of Watson and Smith (1985) and Lindgren and Rootzen (1987), which was reproduced in Crowder et al. (2000).

We have four different lengths of carbon fibres, 1mm, 10mm, 20mm and 50mm. This is the plot of survival probability against the log strength for lengths. Click here for the data and calculations of failure stresses for each length of fibre.

The plot is constructed as follows:

1. Take the natural logarithm of the failure stresses for each fibre.
2. Calculate the empirical cumulative distribution function using:
   (t) = (a formula given by Leitch (1995)).
3. Then calculate the estimated survival probability from:
   (t) = 1 - (t).

If the accelerated life model is appropriate for the data, the lines in the chart should look like horizontally shifted copies of one another. At this point we may decide this is observed here, but experience will tell us to check the other plots, and indeed, that other models are a more appropriate fit to the data.

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