SFWRENG 4E03 Lecture Notes - Lecture 13: Survival Analysis, Bathtub Curve, Pareto Distribution
11 Oct 2016
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Cdf f(x) f(x) t t, t + t. F (cid:314) f, t (cid:314) x, x (cid:314) h h t x. Page 1 of 4 f x f x lim x. X is dfr iff h(t) is non-increasing in t. X is ifr iff h(t) is non-decreasing in t. You can be both if you have a constant failure rate. Most manufactured goods have a lifetime that can be modelled as a bathtub curve. Everything has a decreasing failure rate because of manufacturing bugs, then have a stable low failure rate and spike up after a certain time period due to aging. If dfr, never replace it until it fails, since the longer it lasts, the less likely it is to survive. Pareto distribution is dfr e. g. x ~ uniform(a, b) is x ifr, dfr, both, neither. Neither: when there are parts that increase and parts that decrease h t f.
