Time to failure. Probability, Survival, the Hazard rate, and the Conditional Failure Probability. f(t) is the Probability Density Function (PDF). PDF f(t). Failures do not occur at fixed times. They occur randomly according to a probability distribution.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Time to failure
Probability, Survival, the Hazard rate, and the Conditional Failure Probability
f(t)
Working Age t
f(t)
T x f(t)
T
Working Age t
f(t)
T
T
T
T
T
t1
Working Age t
“The probability that an item will fail during an age interval given that the item enters (or survives) to that age interval.“
h(t) = f(t)/R(t) (Hazard, Failure rate func.)
H(t) = (R(t)-R(t+L))/R(t). (Conditional failure prob.)
f(t)= -dR(t)/d(t)
H(t) = (R(t)-R(t+L))/R(t) by L and and then applying the definition of a limit as L tends to 0.
Lim R(t)-R(t+L) = (1/R(t))( -dR(t)/dt) = f(t)/R(t) = h(t)
L0 LR(t)
F(t)=1-R(t) (Cumulative failure prob.)