Cumulative Hazard Function

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 n–1, 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).