Methods and formulas for survival probabilities in Distribution Overview Plot (Arbitrary Censoring)

Survival probabilities

The reliability function R(t), also known as the survival function S(t), represents the probability a unit survives beyond time t.


R(t) = 1 - F(t)

The reliability of a series system is the product of the reliability functions of the components because all of the components must survive in order for the system to survive. To calculate the reliability of a series system of independent components, multiply the reliability functions of all the components together.


F(t) cdf for the chosen distribution

Confidence limits for survival probabilities

The lower and upper confidence limits for the survival probabilities are defined by the following formulas:


where and (the variance of the survival probabilities) are defined as follows, based on the distribution.

Smallest extreme value, normal, lognormal, logistic, loglogistic

3-parameter lognormal, 3-parameter loglogistic


3-parameter Weibull


2-parameter exponential


zα the upper critical value for the standard normal distribution where 100α % is the confidence level.
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