Using this code

import numpy as np # Importing the NumPy library for numerical calculations

def calculate

$\_$

series

$\_$

reliability

$($

reliabilities

$)$

:

$$

$"$

$"$

$"$

$$ Calculates the overall reliability of components connected in series.

$$ Args:

$$ reliabilities: A list of individual component reliabilities

$($

each between

$0$

$$and

$1$

$)$

$.$

$$ Returns:

$$ The overall reliability of the series system

$($

a value between

$0$

$$and

$1$

$)$

$.$

$$

$"$

$"$

$"$

$$ overall

$\_$

reliability

$=$

$$np

$.$

prod

$($

reliabilities

$)$

$$ # Calculate the product of individual reliabilities

$$ return overall

$\_$

reliability

def calculate

$\_$

parallel

$\_$

reliability

$($

reliabilities

$)$

:

$$

$"$

$"$

$"$

$$ Calculates the overall reliability of components connected in parallel.

$$ Args:

$$ reliabilities: A list of individual component reliabilities

$($

each between

$0$

$$and

$1$

$)$

$.$

$$ Returns:

$$ The overall reliability of the parallel system

$($

a value between

$0$

$$and

$1$

$)$

$.$

$$

$"$

$"$

$"$

$$ unreliabilities

$=$

$1$

$-$

$$np

$.$

array

$($

reliabilities

$)$

$$ # Calculate unreliabilities

$($

$1$

$-$

$$reliability

$)$

$$ overall

$\_$

unreliability

$=$

$$np

$.$

prod

$($

unreliabilities

$)$

$$ # Calculate the product of unreliabilities

$$ return

$1$

$-$

$$overall

$\_$

unreliability # Subtract overall unreliability from

$1$

$$to get reliability

def calculate

$\_$

bridge

$\_$

reliability

$($

top

$\_$

reliabilities, bottom

$\_$

reliabilities

$)$

:

$$

$"$

$"$

$"$

$$ Calculates the reliability of a standard bridge structure.

$$ Args:

$$ top

$\_$

reliabilities: A list of reliabilities of components in the top path.

$$ bottom

$\_$

reliabilities: A list of reliabilities of components in the bottom path.

$$ Returns:

$$ The overall reliability of the bridge system

$($

a value between

$0$

$$and

$1$

$)$

$.$

$$

$"$

$"$

$"$

$$ top

$\_$

path

$\_$

reliability

$=$

$$calculate

$\_$

series

$\_$

reliability

$($

top

$\_$

reliabilities

$)$

$$ bottom

$\_$

path

$\_$

reliability

$=$

$$calculate

$\_$

series

$\_$

reliability

$($

bottom

$\_$

reliabilities

$)$

$$ return calculate

$\_$

parallel

$\_$

reliability

$($

$[$

top

$\_$

path

$\_$

reliability, bottom

$\_$

path

$\_$

reliability

$]$

$)$

$$# Treat paths as parallel

# Example Usage

component

$\_$

reliabilities

$=$

$[$

$0$

$.$

$9$

$8$

$,$

$0$

$.$

$9$

$5$

$,$

$0$

$.$

$9$

$2$

$]$

$$

top

$\_$

reliabilities

$=$

$[$

$0$

$.$

$9$

$0$

$,$

$0$

$.$

$8$

$5$

$]$

$$

bottom

$\_$

reliabilities

$=$

$[$

$0$

$.$

$9$

$5$

$,$

$0$

$.$

$9$

$3$

$]$

$$

# Calculations and Results

series

$\_$

sys

$\_$

reliability

$=$

$$calculate

$\_$

series

$\_$

reliability

$($

component

$\_$

reliabilities

$)$

print

$($

f

$"$

Series System Reliability:

$\{$

series

$\_$

sys

$\_$

reliability:

$.$

$4$

f

$\}$

$"$

$)$

$$

parallel

$\_$

sys

$\_$

reliability

$=$

$$calculate

$\_$

parallel

$\_$

reliability

$($

component

$\_$

reliabilities

$)$

print

$($

f

$"$

Parallel System Reliability:

$\{$

parallel

$\_$

sys

$\_$

reliability:

$.$

$4$

f

$\}$

$"$

$)$

bridge

$\_$

sys

$\_$

reliability

$=$

$$calculate

$\_$

bridge

$\_$

reliability

$($

top

$\_$

reliabilities, bottom

$\_$

reliabilities

$)$

print

$($

f

$"$

Bridge System Reliability:

$\{$

bridge

$\_$

sys

$\_$

reliability:

$.$

$4$

f

$\}$

$"$

$)$

Can you find the overall reliability of this system? Assume each node has an individual reliability of $0\mathrm{.}95$