The failure density function of a random variable T is given byCal

Question

The failure density function of a random variable T is given by
$f(t) = left{egin{matrix} 0.011e^{-0.01t}, & tgeq 0 \ 0, & otherwise end{matrix}ight.$
Calculate, the
i) reliability of the component.
ii) reliability of the component for a 100 hour mission time.
iii) mean time to failure (MTTF).
iv) median of the random variable T.
v) life of the component, if the reliability of 0.96 is desired.

14 Feb 2023

Answer :

Word Count : 237

The failure density function of a random variable T is given by:

f(t) = { 0.011e^(-0.01t), t >= 0
{ 0, otherwise

i) The reliability of the component is given by the survival function:

R(t) = P(T > t) = ∫f(t)dt from t to infinity
= ∫0.011e^(-0.01t)dt from t to infinity
= -0.0011e^(-0.01t) from t to ________ ___ ___ _____ __________ _______ ________ _________.
__________ ____ ___ __________ ________.
__________ ______ _________ _____ ________ __________ ____ __________ ___ _____ _______ _________.
_______ _____ _________ ___ __________ _________ __________ ___ ________ _________ ______.
________ __________ _____ ________ ___ __________ ______ ________.
______ _______ _______ ______ _____ ______ _________.
___ ___ _________ __________ ______ ____ ______ _______ ________ ____ _____ ________.
_____ ___ _____ _____ ____ __________ ____ ____ _____ _________ ___.
_________ _______ _______ ____ __________ ___ ________ _________ ___ ___.
___ ________ _______ _______ ____ _______ ______.
______ ____ _____ ___ _______ _____ _____ ______ __________ ______ ________.
________ ________ ___ ____ ___ __________ _________.
______ __________ ____ _______ ____ _______ ____ _____ __________ _________.
_____ ________ _________ _________ ______ ________ _______ _________ __________ _____ _____ ___.
________ _____ _____ _______ _____ _______.
________ _____ _________ _____ ______ ___ _____ _________ _____.
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Failure Number			1	2	3	4	5		6	7		8	9	10
Operating Time (in hours)			3	5	31	51	76		116	140		182	250	302

		Player B
		B₁	B₂	B₃	B₄	B₅
Player A	A₁	3	4	5	–2	3
Player A	A₂	1	6	–3	3	7

Subgroup Number	Number of Mobile Phones Inspected	Number of Defective Mobile Phones
1	100	3
2	100	6
3	100	4
4	100	6
5	100	20
6	100	2
7	100	6
8	100	7
9	100	3
10	100	0
11	100	6
12	100	15
13	100	5
14	100	7
15	100	6