Statistics for Maintenance Modelling: Repairable Systems

# Exercise 1¤

This data set gives 13 observed intervals in operating hours between failures of the air-conditioning equipment in a Boeing 720 aircraft: 413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118.

1. Carry out a Laplace test at a 5% significance level to test the trend. With the null hypothesis H0: no trend and H1: decreasing 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 cannot be rejected. t0 = 1851, n = 13, and ti = 12641, which gives
U = (12641 - (13 1851) / 2) / (1851 (13 / 12)1/2 ) = 0.3163. At a 5% significance level, the critical value is -1.64 (we're looking for a decreasing trend). At less than 0.3163, it suggests that the null hypothesis cannot be rejected.

No, in fact the null hypothesis cannot be rejected. t0 = 1851, n = 13, and ti = 12641, which gives
U = (12641 - (13 1851) / 2) / (1851 (13 / 12)1/2 ) = 0.3163. At a 5% significance level, the critical value is -1.64 (we're looking for a decreasing trend). At less than 0.3163, it suggests that the null hypothesis cannot be rejected.

2. Plot ln MCNF against ln t (cumulative failure time). Is there a straightforward
   model for MCNF available? Select "Yes" or "No" and click the "Check Answer"
   button when you've finished.

Yes
No
Yes, there isn't a straightforward model available. As you can see from the plot, the linearity is not good and there is no straightforward model for the failure function. There is some suggestion of cycles in the data, but more observations would be needed to identify any firm pattern.
No, actually there isn't a straightforward model available. As you can see from the plot, the linearity is not good and there is no straightforward model for the failure function. There is some suggestion of cycles in the data, but more observations would be needed to identify any firm pattern.