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# System prepended metadata

title: EPS Homework

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# EPS Homework

## 1. Dependability:

### a.)
S1, S2 -> Sensors

P1 -> Processor

![](https://i.imgur.com/ehrcMu8.png)

R<sub>S1</sub> = 0.89

R<sub>S2</sub> = 0.95

R<sub>P1</sub> = 0.85


R<sub>SYS</sub> = (1-(1-R<sub>S1</sub>)&times;(1-R<sub>S2</sub>)) &times; R<sub>P1</sub> 

R<sub>SYS</sub> = (1-(1-0.89)&times;(1-0.95)) &times; 0.85

R<sub>SYS</sub> = (1-(0.11)&times;(0.05)) &times; 0.85

R<sub>SYS</sub> = (1-0.0055) &times; 0.85

R<sub>SYS</sub> = 0.9945 &times; 0.85


<u>R<sub>SYS</sub> = 0.845325</u>


### b.)
S1, S2 -> Sensors

Pnew1, Pnew2 -> Processor



![](https://i.imgur.com/7ImnXyt.png)

R<sub>S1</sub> = 0.89

R<sub>S2</sub> = 0.95

R<sub>Pnew1</sub> = 0.80

R<sub>Pnew2</sub> = 0.80

R<sub>P_Parallel</sub> = 1 - (1-R<sub>Pnew1</sub>)&times;(1-R<sub>Pnew2</sub>)

R<sub>P_Parallel</sub> = 1 - (1-0.8)&times;(1-0.8)

R<sub>P_Parallel</sub> = 1 - (0.2)&times;(0.2)

R<sub>P_Parallel</sub> = 1 - 0.04

R<sub>P_Parallel</sub> = <u>0.96</u>


R<sub>SYS</sub> = (1-(1-R<sub>S1</sub>)&times;(1-R<sub>S2</sub>)) &times; R<sub>P_Parallel</sub>

R<sub>SYS</sub> = (1-(1-0.89)&times;(1-0.95)) &times; 0.96

R<sub>SYS</sub> = (1-(0.11)&times;(0.05)) &times; 0.96

R<sub>SYS</sub> = (1-0.0055) &times; 0.96

R<sub>SYS</sub> = 0.9945 &times; 0.96


<u>R<sub>SYS</sub> = 0.95472</u>


The setup from b.) is more reliable.

### c.)
S1, S2 -> Sensors

P1 -> Processor

&lambda;<sub>S1</sub> = 0.5 &times; 10<sup>-5</sup>

&lambda;<sub>S2</sub> = 0.8 &times; 10<sup>-5</sup>

&lambda;<sub>P1</sub> = 0.3 &times; 10<sup>-5</sup>



&lambda;<sub>sys</sub> = &lambda;<sub>S1</sub> + &lambda;<sub>S2</sub> + &lambda;<sub>P1</sub>

&lambda;<sub>sys</sub> = 0.5 &times; 10<sup>-5</sup> + 0.8 &times; 10<sup>-5</sup> + 0.3 &times; 10<sup>-5</sup>

&lambda;<sub>sys</sub> = (0.5 + 0.8 + 0.3) &times; 10<sup>-5</sup>

<u>&lambda;<sub>sys</sub> = 1.6 &times; 10<sup>-5</sup></u>


MTTF = 1/&lambda;

MTTF = 1 / (1.6 &times; 10<sup>-5</sup>)

MTTF = 1 / (1.6 &times; 10<sup>-5</sup>)

MTTF = 10<sup>5</sup> / 1.6

<u>MTTF = 6.25 &times; 10<sup>4</sup></u>


t = 1 year = 365 &times; 24h = 8760h

R<sub>sys</sub>(1 year) = e<sup>-&lambda;<sub>sys</sub>t</sup> 

R<sub>sys</sub>(1 year) = e<sup>-1.6 &times; 10<sup>-5</sup>&times;8760</sup>

R<sub>sys</sub>(1 year) = e<sup>−14016 &times; 10<sup>-5</sup></sup>

R<sub>sys</sub>(1 year) = e<sup>−0.14016</sup> 

<u>R<sub>sys</sub>(1 year) = 0.869219149 = 86.9219149%</u>

