Statistics for Maintenance Modelling: Proportional Hazards and Accelerated Life Models

# Case Study 1 - Failure of Insulating Fluid Subject to Voltage Stress¤

Nelson (1972) describes the result of a life test experiment in which specimens of a type of electrical insulating fluid were subject to a constant voltage stress. The length of time until each specimen failed, or "broke down" was observed. These are the results for three groups of specimens, tested at voltages of 28, 30 and 32 kilovolts.

The chart shows the product-limit (Kaplan-Meier) estimates of the ln(-ln(i(t)) against time to failure. It can be seen that the curves are roughly parallel, which indicates a potential proportional hazards model.

M
i
n
u
t
e
s

28 kv

30 kv

32 kv

68.85 | 17.05 | 194.9 | 0.4 | 3.91
426.07 | 22.66 | 47.3 | 82.85 | 0.27
110.29 | 21.02 | 7.74 | 9.88 | 0.69
108.29 | 175.88 |  | 89.29 | 100.58
1067.6 | 139.07 |  | 215.1 | 27.8
| 144.12 |  | 2.75 | 13.95
| 20.46 |  | 0.79 | 53.24
| 43.4 |  | 15.93 |