Statistics for Maintenance Modelling: Continuous Lifetime Distributions 1

# The Reliability Function for the Weibull Distribution¤

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The reliability (survival) function is . Hence, for the exponential distribution, .

This is shown against time below with = 2 and = 2, but you can click on the chart for an interactive version in Excel where you can experiment with different values of alpha and beta yourself.

Using Excel with the notation of this section, consider the Weibull distribution with = 3 and = 1. If an item has survived to year 2, what is the probability that it fails between years 3 and 4? Type your answer into the textbox to 3 decimal places and click the "Check Answer" button. Click the "Hint" button for some help in working out the answer. Click here to launch Excel - if this opens in Internet Explorer, click here.

Yes, that's right. The correct expression for this is (F(4) - F(3)) / R(2). Using the Weibull function with our notation in Excel produces
(WEIBULL(4,1,3,TRUE)-WEIBULL(3,1,3,TRUE))/(1-WEIBULL(2,1,3,TRUE)) = 0.203.
No, that's not right. The correct expression for this is (F(4) - F(3)) / R(2). Using the Weibull function with our notation in Excel produces
(WEIBULL(4,1,3,TRUE)-WEIBULL(3,1,3,TRUE))/(1-WEIBULL(2,1,3,TRUE)) = 0.203.