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 $=[0\mathrm{.}98,0\mathrm{.}95,0\mathrm{.}92]$

top$\_$reliabilities $=[0\mathrm{.}90,0\mathrm{.}85]$

bottom$\_$reliabilities $=[0\mathrm{.}95,0\mathrm{.}93]$

# Calculations and Results

series$\_$sys$\_$reliability $=$ calculate$\_$series$\_$reliability$($component$\_$reliabilities$)$

print$($f$"$Series System Reliability: $\{$series$\_$sys$\_$reliability:$\mathrm{.}4$f$\}")$

parallel$\_$sys$\_$reliability $=$ calculate$\_$parallel$\_$reliability$($component$\_$reliabilities$)$

print$($f$"$Parallel System Reliability: $\{$parallel$\_$sys$\_$reliability:$\mathrm{.}4$f$\}")$

bridge$\_$sys$\_$reliability $=$ calculate$\_$bridge$\_$reliability$($top$\_$reliabilities, bottom$\_$reliabilities$)$

print$($f$"$Bridge System Reliability: $\{$bridge$\_$sys$\_$reliability:$\mathrm{.}4$f$\}")$

Can you find the overall reliability of this system? Assume system reliability is $0\mathrm{.}95$