Question

A component has an exponential failure time distribution with a mean time to failure of 35 days. (a) Find the probability that the component is still operating after 35 days. (b) Find the probability that the component fails within 40 days. (c) If six of these components are placed in series, find the probability that the system is still operating after 5 days?

Answer 1

Mean $m=\dfrac{1}{35}$

(a) Probability that the components is still operating after 35 days-

$P(X>35)=e^{-mx}=e^{-\frac{1}{35}\times 35}=e^{-1}=0.3678$

(b) Probability that the component fails within 40 days-

$P(X<40)=1-e^{-m\times 40}=1-e^{-\frac{1}{35}(40)}=1-e^{-1.1428}=0.681$

(c) If six of these components are placed in series,

Mean m$=\dfrac{6}{35}$

The probability that the system is still operating after 5 days-

$P(X>5)= e^{-mx}=e^{-\frac{6}{35}(5)}=0.4243$