Appendix B: Laplace Trend Test

The Laplace Trend Test tests the hypothesis that a trend does not exist within the data. The Laplace Trend test is applicable to the following data types: Multiple Systems-Concurrent Operating Times, Repairable and Fleet. The Laplace Trend Test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, U, using the following equation:

MATH (8)

where:

Τ = total operating time (termination time)
Χi = age of the system at the ith successive failure
N = total number of failures

The test statistic U is approximately a standard normal random variable. The critical value is read from the Standard Normal tables with a given significance level, α.

Laplace Trend Test Example

Consider once again the data in Table B.1. Check for a trend within System 1 assuming a significance level of 0.10. Calculate the test statistic U for System 1 using Eqn. (8).

From the Standard Normal tables with a significance level of 0.10, the critical value is equal to 1.645. If -1.645 < U < 1.645 then we would fail to reject the hypothesis of no trend. However, since U < -1.645 then an improving trend exists within System 1. If U > 1.645 then a deteriorating trend would exist.