I have a component with a 2 parameter Weibull distribution and an
increasing failure rate. I have a population of these components with
a variable amount of time ac***ulated.
I have a failure threshold which I am not allowed to exceed going
forward.
Given the particular time of a specific component and the Weibull
distribution of its failure rate, how do I determine the amount of
time that I can continue to use the component before the probability
that it fails exceeds my threshold.
If they had no time ac***ulated, I know I could just look at the CDF
and determine how long the component could be used before it exceeded
the threshold. However knowing that each specific component hasnt
failed up to a given time, how do I figure out how much longer each
one will be "good"?
Sample numbers
k = 1.5
lambda = 84000
acceptable threshold = 7e-3
current time = 3000
