Statistics for Maintenance Modelling: Repairable Systems

# Exercise 2¤

Following on from question 1, the next 10 failures were observed after the equipment had a major overhaul after the 13th failure. The intervals were 34, 31, 18, 18, 67, 57, 62, 7, 22, 34.

1. Plot ln MCNF against ln t using the data before and after the overhaul. Does there seem to be a change in the failure behaviour after the overhaul? Select "Yes" or "No" and click the "Check Answer" button when you've finished.
Yes
No

Yes, the plot again hints at some cyclic behaviour but also clearly shows the effect of the overhaul - it may have had an adverse effect on the failure behaviour of the unit since there appears to be an increase in the rate of occurrence of failures. It may be of interest to know whether the ROCOF has moved to a new level but is still constant. This can be done by resetting the time origin to zero at the 13th failure and redoing the chart and Laplace test.

No, actually the plot hints at some cyclic behaviour but also clearly shows the effect of the overhaul - it may have had an adverse effect on the failure behaviour of the unit since there appears to be an increase in the rate of occurrence of failures. It may be of interest to know whether the ROCOF has moved to a new level but is still constant. This can be done by resetting the time origin to zero at the 13th failure and redoing the chart and Laplace test.

2. Carry out a Laplace test at a 5% significance level to test the trend using all the data. With the null hypothesis H0: no trend and H1: increasing trend, can we reject the null hypothesis? Select "Yes" or "No" and click the "Check Answer" button when you've finished. Click here for the normal distribution table.

Yes
No
Yes, that's right, the null hypothesis is rejected. t0 = 2201, n = 23, and ti = 33074, which gives
U = (33074 - (23 2201) / 2) / (2201 (23 / 12)1/2 ) = 2.5474. At a 5% significance level, the critical value is 1.64. At less than 2.5474, it suggests that H0 can be rejected (since we're looking for an increasing trend).
No, in fact the null hypothesis can be rejected. t0 = 2201, n = 23, and ti = 33074, which gives
U = (33074 - (23 2201) / 2) / (2201 (23 / 12)1/2 ) = 2.5474. At a 5% significance level, the critical value is 1.64. At less than 2.5474, it suggests that H0 can be rejected (since we're looking for an increasing trend).