Ranks

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Cumulative Distribution Function

Cumulative Hazard Function

Weibull Distribution

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Often, reliability confidence limits are added to probability plots. Upper and lower confidence limits are often approximated by 5% and 95% ranks. These ranks can be taken from the expression

where wa is the 100(1-a )% nonparametric confidence limit,
j is the failure order,
n is the total number of data points, both censored and uncensored, and
F_a,_v1,v2  is the critical value from the F distribution.

When multiple censored data are encountered, the modified failure orders will not be integers, and the rank values will have to be interpolated. The rank values are not plotted against the corresponding failure time. Any deviation of the failure time from the best-fit straight line through the data is considered sampling error, and the time the rank values are plotted against is found by moving parallel to the x-axis until the best-fit straight line is intersected.