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

Question

The failure density function of a random variable T is given by
$f(t) = \begin{Bmatrix} 0.011e^{-0.011t} &, t \geq 0 \\ 0 & , otherwise \end{Bmatrix}$

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

29 Feb 2024

Answer :

Word Count : 290

The given failure density function is: \[ f(t) = \begin{cases} 0.011e^{-0.011t}, & t \geq 0 \\ 0, & \text{otherwise} \end{cases} \] This represents an exponential distribution with failure rate $ \lambda = 0.011 $. Using this, we can compute the required values. --- ### (i) Reliability of the Component Reliability $ R(t) $ is given by the survival function: \[ R(t) = P(T > t) = \int_t^\infty f(x) dx = e^{-\lambda t} ________ _________ _____ ________ __________.
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		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	Duration of Automatic Signal (in ms)
	a	b	c	d
1	195	201	194	201
2	204	190	199	195
3	195	197	205	201
4	211	198	193	180
5	204	193	197	200
6	200	202	195	200
7	196	198	197	196
8	201	197	206	207
9	200	202	204	192
10	203	201	209	192

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