Techniques
Cumulative Distribution Function
Weibull Distribution
Normal Distribution
Lognormal Distribution
Exponential Distribution
Exam
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Hazard plotting utilizes a non-parametric estimated of the cumulative of the hazard
function. Once this estimate is obtained, a hazard plot can be constructed for the
distribution of interest. The cumulative hazard function is estimated
by the cumulative of the inverse of the reverse ranks. For a data set of n points
ordered from smallest to largest, the first point has a rank of n, the second n1,
etc.
Example
Twelve items were tested with failures occurring at times
of 43 hours, 67 hours, 92 hours 94 hours, and 149 hours. At a time of 149 hours, the
testing was stopped for the remaining seven items. Estimate the cumulative hazard
function.
Solution
The cumulative hazard function estimates are shown in
the table below. Note that h(t) = 1/(Reverse Rank).
Time to Fail |
Reverse Rank |
h(t) |
H(t) |
43 |
12 |
0.0833 |
0.0833 |
67 |
11 |
0.0909 |
0.1742 |
92 |
10 |
0.1000 |
0.2742 |
94 |
9 |
0.1111 |
0.3854 |
149 |
8 |
0.1250 |
0.5104 |
149+ |
7 |
|
|
149+ |
6 |
|
|
149+ |
5 |
|
|
149+ |
4 |
|
|
149+ |
3 |
|
|
149+ |
2 |
|
|
149+ |
1 |
|
|
|