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Let X denote the lifetime of a component, with f (x) and F(x) the
An increasing failure rate function indicates that older components are increasingly likely to wear out, whereas a decreasing failure rate is evidence of increasing reliability with age. In practice, a “bathtub-shaped” failure is often assumed.
a. If X is exponentially distributed, what is r(x)?
b. If X has a Weibull distribution with parameters α and β, what is r(x)? For what parameter values will r(x)be increasing? For what parameter values will r(x) decrease with x?
c. Since
so that if a component lasts β hours, it will last forever (while seemingly unreasonable, this model can be used to study just “initial wearout”). What are the cdf and pdf of X?
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Chapter 4 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
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