Statistics for Maintenance Modelling: Repairable Systems

# Examples of Testing for a Trend¤

## Example 1

Failures occur at times 15, 42, 74, 117, 168, 233, 410. Using the equation for the Laplace test:

U = ((15 + 42 + 74 + 117 + 168 + 233) - 6 410 / 2) / (410 ) = - 2.0

For testing H0: no trend, against H1: decreasing ROCOF, the critical value for 2.5% significance level is -1.96 (from the normal distribution table) which > U, so H0 is rejected at this level and it is concluded that the incidence of failure is tending to reduce.

## Example 2

Taking the data of software failures used earlier on screen 15, we will test whether there is a decreasing trend. Since
n = 34, t0 = 850, and ti = 6980, we have from the equation for the Laplace test that:

U = (7015 - 1/2 34 850) / (850 ) = -5.2209

Since H0: no trend, and H1: decreasing trend, if we choose 1% as the significance level, the critical value is -2.33, which is greater than -5.2209, and strongly suggests we can accept H1.

U =