Statistics for Maintenance Modelling: Regression Modelling

# Assessing the Appropriateness of a Proportional Hazards Model¤

To identify whether a data set should be modelled using the proportional hazards model it is easiest to examine an appropriate plot of the data.

1. In a variation of how we assessed the appropriateness of the accelerated life model on screen 4, if the data are grouped, the jth group of nj observed failure times having x = j and nj being large, then the plots of -lnj(t) against t for the different groups should resemble multiples of the baseline curve -lnS0(t) against t. This is because:
   if Sj(t) = S0(t) then -lnSt(t) = -j lnS0(t).
2. Alternatively, the plots ln{-lnj(t)} of against t should resemble vertically shifted copies of ln{-lnS0(t)} against t. To yield a possibly neater plot, the t axis may be transformed by taking logs. This will not change the pattern of the vertically parallel curves.
   See the case study later in this session for an example of using this plot (screen 12).

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