Statistics for Maintenance Modelling: Repairable Systems

# Extending the Laplace Test¤

Strictly speaking, the Laplace test is based on the null hypothesis that the process is a homogeneous Poisson process. However, the test may be used for the more general hypothesis that the process is a renewal process (see the next session), that is, the inter-event times are identically and independently distributed (IID). This can be done by the U statistic being divided by the coefficient of variation of the inter-event times, which is estimated by the sample standard deviation divided by the sample mean. The exponential distribution has a coefficient of variation equal to 1, so this modification embraces the U of the equation on screen 18.

The formulation of the Laplace test rests on the central limit theorem, which would imply that the test is only good when the value of n is large. However, the test proves to be fairly robust against departure from normality and may be applied even when n is modest.

U =