A Python package for binary/multi state systems

Project description

relibmss

A Python package for binary/multi state systems with BDD/MDD.

Installation

pip install relibmss

Usage

Calculate the probability of a fault tree

import relibmss as ms

# Create a fault tree (binary system)
ft = ms.FTree()

# Define events (This version only supports repeated events)
A = ft.defvar('A')
B = ft.defvar('B')
C = ft.defvar('C')

# Make a tree
top = A & B | C # & is AND gate, | is OR gate

# Set probabilities
prob = {
    'A': 0.1,
    'B': 0.2,
    'C': 0.3
}

# Calculate the probability
print(ft.prob(top, prob))

# Set the interval of the probability
prob = {
    'A': (0.1, 0.2),
    'B': (0.2, 0.3),
    'C': (0.3, 0.4)
}

# Calculate the probability
print(ft.prob_interval(top, prob))

Obtain the minimal cut sets

import relibmss as ms

# Create a fault tree (binary system)
ft = ms.FTree()

# Define events (This version only supports repeated events)
A = ft.defvar('A')
B = ft.defvar('B')
C = ft.defvar('C')

# Make a tree
top = ft.kofn(2, [A, B, C]) # k-of-n gate

# Obtain the minimal cut sets
s = ft.mcs(top) # s is a set of minimal cut sets (ZDD representation)

# Convert the ZDD representation to a list of sets
print(s.extract())

Draw a BDD

import relibmss as ms

# Create a binary decision diagram
ft = ms.FTree()

# Define variables
A = ft.defvar('A')
B = ft.defvar('B')
C = ft.defvar('C')

# Make a tree
top = A & B | C

# Draw the BDD
bdd = ft.getbdd(top)
source = bdd.dot() # source is a string of the dot language

# Example: Display the BDD in Jupyter Notebook
from graphviz import Source
from IPython.display import Image, display
Image(Source(source).pipe(format='png'))

An example of a large fault tree

## This is an example of a large fault tree
## Computational time may be long (about 1 minute)

import relibmss as ms

ft = ms.FTree()
c = [ft.defvar("c" + str(i)) for i in range(61)]

g62 = c[0] & c[1]
g63 = c[0] & c[2]
g64 = c[0] & c[3]
g65 = c[0] & c[4]
g66 = c[0] & c[5]
g67 = c[0] & c[6]
g68 = c[0] & c[7]
g69 = c[0] & c[8]
g70 = g62 | c[9]
g71 = g63 | c[10]
g72 = g64 | c[11]
g73 = g65 | c[12]
g74 = g62 | c[13]
g75 = g63 | c[14]
g76 = g64 | c[15]
g77 = g65 | c[16]
g78 = g62 | c[17]
g79 = g63 | c[18]
g80 = g64 | c[19]
g81 = g65 | c[20]
g82 = g62 | c[21]
g83 = g63 | c[22]
g84 = g64 | c[23]
g85 = g65 | c[24]
g86 = g62 | c[25]
g87 = g63 | c[26]
g88 = g64 | c[27]
g89 = g65 | c[28]
g90 = g66 | c[29]
g91 = g68 | c[30]
g92 = g67 | c[31]
g93 = g69 | c[32]
g94 = g66 | c[33]
g95 = g68 | c[34]
g96 = g67 | c[35]
g97 = g69 | c[36]
g98 = g66 | c[37]
g99 = g68 | c[38]
g100 = g67 | c[39]
g101 = g69 | c[40]
g102 = g66 | c[41]
g103 = g68 | c[42]
g104 = g67 | c[43]
g105 = g69 | c[44]
g106 = ft.kofn(3, [g70, g71, g72, g73])
g107 = ft.kofn(3, [g74, g75, g76, g77])
g108 = ft.kofn(3, [g78, g79, g80, g81])
g109 = ft.kofn(3, [g82, g83, g84, g85])
g110 = ft.kofn(3, [g86, g87, g88, g89])
g111 = ft.kofn(3, [g94, g95, g96, g97])
g112 = ft.kofn(3, [g98, g99, g100, g101])
g113 = g90 & g92
g114 = g91 & g93
g115 = g102 & g104
g116 = g103 & g105
g117 = g113 | c[45]
g118 = g114 | c[46]
g119 = g107 | g108 | c[51]
g120 = g109 | g110
g121 = g66 | g117 | c[47]
g122 = g68 | g118 | c[48]
g123 = g67 | g117 | c[49]
g124 = g69 | g118 | c[50]
g125 = ft.kofn(2, [g121, g123, g122, g124])
g126 = g111 | g112 | g125 | c[52]
g127 = g115 & g120
g128 = g116 & g120
g129 = g62 | g127 | c[53]
g130 = g63 | g128 | c[54]
g131 = g64 | g127 | c[55]
g132 = g65 | g128 | c[56]
g133 = g62 | g129 | c[57]
g134 = g63 | g130 | c[58]
g135 = g64 | g131 | c[59]
g136 = g65 | g132 | c[60]
g137 = ft.kofn(3, [g133, g134, g135, g136])
g138 = g106 | g119 | g137
g139 = g62 | g66 | g117 | g129 | c[47]
g140 = g63 | g68 | g118 | g130 | c[48]
g141 = g64 | g67 | g117 | g131 | c[49]
g142 = g65 | g69 | g118 | g132 | c[50]
g143 = g139 & g140 & g141 & g142
g144 = g111 | g112 | g143 | c[52]
top = g126 & g138 & g144

bdd = ft.getbdd(top)
print(bdd.count()) # The numbers of nodes and edges in the BDD

mcs = bdd.mcs() # Obtain the minimal cut sets from the BDD directly
print(mcs.extract())

prob = {
    'c0': 0.01,
    'c1': 0.051,
    'c2': 0.051,
    'c3': 0.051,
    'c4': 0.051,
    'c5': 0.112,
    'c6': 0.112,
    'c7': 0.112,
    'c8': 0.112,
    'c9': 0.016,
    'c10': 0.016,
    'c11': 0.016,
    'c12': 0.016,
    'c13': 0.0218,
    'c14': 0.0218,
    'c15': 0.0218,
    'c16': 0.0218,
    'c17': 0.015,
    'c18': 0.015,
    'c19': 0.015,
    'c20': 0.015,
    'c21': 0.016,
    'c22': 0.016,
    'c23': 0.016,
    'c24': 0.016,
    'c25': 0.015,
    'c26': 0.015,
    'c27': 0.015,
    'c28': 0.015,
    'c29': 0.0137,
    'c30': 0.0137,
    'c31': 0.0137,
    'c32': 0.0137,
    'c33': 0.016,
    'c34': 0.016,
    'c35': 0.016,
    'c36': 0.016,
    'c37': 0.016,
    'c38': 0.016,
    'c39': 0.016,
    'c40': 0.016,
    'c41': 0.0038,
    'c42': 0.0038,
    'c43': 0.0117,
    'c44': 0.0117,
    'c45': 0.00052,
    'c46': 0.00052,
    'c47': 0.018,
    'c48': 0.018,
    'c49': 0.018,
    'c50': 0.018,
    'c51': 0.000008,
    'c52': 0.000072,
    'c53': 0.015,
    'c54': 0.015,
    'c55': 0.015,
    'c56': 0.015,
    'c57': 0.0188,
    'c58': 0.0188,
    'c59': 0.0188,
    'c60': 0.0188
}

ft.prob(top, prob)

# Set the interval of the probability
error_lower = 0.5
error_upper = 1.5

prob = {
    'c0': (0.01 * error_lower, 0.01 * error_upper),
    'c1': (0.051 * error_lower, 0.051 * error_upper),
    'c2': (0.051 * error_lower, 0.051 * error_upper),
    'c3': (0.051 * error_lower, 0.051 * error_upper),
    'c4': (0.051 * error_lower, 0.051 * error_upper),
    'c5': (0.112 * error_lower, 0.112 * error_upper),
    'c6': (0.112 * error_lower, 0.112 * error_upper),
    'c7': (0.112 * error_lower, 0.112 * error_upper),
    'c8': (0.112 * error_lower, 0.112 * error_upper),
    'c9': (0.016 * error_lower, 0.016 * error_upper),
    'c10': (0.016 * error_lower, 0.016 * error_upper),
    'c11': (0.016 * error_lower, 0.016 * error_upper),
    'c12': (0.016 * error_lower, 0.016 * error_upper),
    'c13': (0.0218 * error_lower, 0.0218 * error_upper),
    'c14': (0.0218 * error_lower, 0.0218 * error_upper),
    'c15': (0.0218 * error_lower, 0.0218 * error_upper),
    'c16': (0.0218 * error_lower, 0.0218 * error_upper),
    'c17': (0.015 * error_lower, 0.015 * error_upper),
    'c18': (0.015 * error_lower, 0.015 * error_upper),
    'c19': (0.015 * error_lower, 0.015 * error_upper),
    'c20': (0.015 * error_lower, 0.015 * error_upper),
    'c21': (0.016 * error_lower, 0.016 * error_upper),
    'c22': (0.016 * error_lower, 0.016 * error_upper),
    'c23': (0.016 * error_lower, 0.016 * error_upper),
    'c24': (0.016 * error_lower, 0.016 * error_upper),
    'c25': (0.015 * error_lower, 0.015 * error_upper),
    'c26': (0.015 * error_lower, 0.015 * error_upper),
    'c27': (0.015 * error_lower, 0.015 * error_upper),
    'c28': (0.015 * error_lower, 0.015 * error_upper),
    'c29': (0.0137 * error_lower, 0.0137 * error_upper),
    'c30': (0.0137 * error_lower, 0.0137 * error_upper),
    'c31': (0.0137 * error_lower, 0.0137 * error_upper),
    'c32': (0.0137 * error_lower, 0.0137 * error_upper),
    'c33': (0.016 * error_lower, 0.016 * error_upper),
    'c34': (0.016 * error_lower, 0.016 * error_upper),
    'c35': (0.016 * error_lower, 0.016 * error_upper),
    'c36': (0.016 * error_lower, 0.016 * error_upper),
    'c37': (0.016 * error_lower, 0.016 * error_upper),
    'c38': (0.016 * error_lower, 0.016 * error_upper),
    'c39': (0.016 * error_lower, 0.016 * error_upper),
    'c40': (0.016 * error_lower, 0.016 * error_upper),
    'c41': (0.0038 * error_lower, 0.0038 * error_upper),
    'c42': (0.0038 * error_lower, 0.0038 * error_upper),
    'c43': (0.0117 * error_lower, 0.0117 * error_upper),
    'c44': (0.0117 * error_lower, 0.0117 * error_upper),
    'c45': (0.00052 * error_lower, 0.00052 * error_upper),
    'c46': (0.00052 * error_lower, 0.00052 * error_upper),
    'c47': (0.018 * error_lower, 0.018 * error_upper),
    'c48': (0.018 * error_lower, 0.018 * error_upper),
    'c49': (0.018 * error_lower, 0.018 * error_upper),
    'c50': (0.018 * error_lower, 0.018 * error_upper),
    'c51': (0.000008 * error_lower, 0.000008 * error_upper),
    'c52': (0.000072 * error_lower, 0.000072 * error_upper),
    'c53': (0.015 * error_lower, 0.015 * error_upper),
    'c54': (0.015 * error_lower, 0.015 * error_upper),
    'c55': (0.015 * error_lower, 0.015 * error_upper),
    'c56': (0.015 * error_lower, 0.015 * error_upper),
    'c57': (0.0188 * error_lower, 0.0188 * error_upper),
    'c58': (0.0188 * error_lower, 0.0188 * error_upper),
    'c59': (0.0188 * error_lower, 0.0188 * error_upper),
    'c60': (0.0188 * error_lower, 0.0188 * error_upper)
}

result = ft.prob_interval(top, prob)
print('lower: ', result.lower)
print('upper: ', result.upper)

TODO for fault tree analysis

FTA with MCS
Importance analysis
Sensitivity analysis
Uncertainty analysis; etc.

Multi-state system

Definition of Gate

MSS does not have default gates. Users need to define gates by themselves. The operation that can be used in the definition of a gate is as follows:

Arithmetic operations: +, -, *, /
Comparison operations: ==, !=, >, <, >=, <=
Logical operations:
- mss.And: AND gate
- mss.Or: OR gate
- mss.Not: NOT gate
- mss.switch: Switch-case structure
- mss.case: Case structure

import relibmss as ms

# def for a gate with switch-case structure
def gate1(mss, x, y):
    return mss.switch([
        mss.case(cond=mss.And([x == 0, y == 0]), then=0),
        mss.case(cond=mss.Or([x == 0, y == 0]), then=1),
        mss.case(cond=mss.Or([x == 2, y == 2]), then=3),
        mss.case(cond=None, then=2) # default
    ])

Example of a multi-state system

import relibmss as ms

# Define gates
def gate1(mss, x, y):
    return mss.switch([
        mss.case(cond=mss.And([x == 0, y == 0]), then=0),
        mss.case(cond=mss.Or([x == 0, y == 0]), then=1),
        mss.case(cond=mss.Or([x == 2, y == 2]), then=3),
        mss.case(cond=None, then=2) # default
    ])

def gate2(mss, x, y):
    return mss.switch([
        mss.case(cond=x == 0, then=0),
        mss.case(cond=None, then=y)
    ])

mss = ms.MSS() # Context for the multi-state system

# Define variables

A = mss.defvar('A', 2) # 2 states
B = mss.defvar('B', 3) # 3 states
C = mss.defvar('C', 3) # 3 states

# Define a multi-state system
sx = gate1(mss, B, C)
ss = gate2(mss, A, sx)

# Define probabilities
prob = {
    'A': [0.1, 0.9],
    'B': [0.2, 0.3, 0.5],
    'C': [0.3, 0.4, 0.3]
}

# Calculate the probability
print(mss.prob(ss, prob))

Draw an MDD

import relibmss as ms

# Define gates
def gate1(mss, x, y):
    return mss.switch([
        mss.case(cond=mss.And([x == 0, y == 0]), then=0),
        mss.case(cond=mss.Or([x == 0, y == 0]), then=1),
        mss.case(cond=mss.Or([x == 2, y == 2]), then=3),
        mss.case(cond=None, then=2) # default
    ])

def gate2(mss, x, y):
    return mss.switch([
        mss.case(cond=x == 0, then=0),
        mss.case(cond=None, then=y)
    ])

mss = ms.MSS()

A = mss.defvar('A', 2)
B = mss.defvar('B', 3)
C = mss.defvar('C', 3)

# Define the order of variables
# this should be done before making MDD
mss.set_varorder({"A": 2, "B": 1, "C": 0})

sx = gate1(mss, B, C)
ss = gate2(mss, A, sx)

mdd = mss.getmdd(ss)
source = mdd.dot()

from graphviz import Source
from IPython.display import Image, display
Image(Source(source).pipe(format='png'))

Obtain the minimal vector sets

import relibmss as ms

# Define gates
def gate1(mss, x, y):
    return mss.switch([
        mss.case(cond=mss.And([x == 0, y == 0]), then=0),
        mss.case(cond=mss.Or([x == 0, y == 0]), then=1),
        mss.case(cond=mss.Or([x == 2, y == 2]), then=3),
        mss.case(cond=None, then=2) # default
    ])

def gate2(mss, x, y):
    return mss.switch([
        mss.case(cond=x == 0, then=0),
        mss.case(cond=None, then=y)
    ])

mss = ms.MSS()

A = mss.defvar('A', 2)
B = mss.defvar('B', 3)
C = mss.defvar('C', 3)

sx = gate1(mss, B, C)
ss = gate2(mss, A, sx)

mdd = mss.mvs(ss)
print(mdd.dot())

TODO

Add more examples
Add more functions for fault tree analysis
Add more functions for multi-state system analysis

License

MIT License

Project details

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0.21.0

Jul 22, 2026

0.20.1

Jul 21, 2026

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Jul 21, 2026

0.19.0

Jul 21, 2026

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Jul 21, 2026

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Jul 21, 2026

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Jul 21, 2026

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Jul 21, 2026

0.16.0

Jul 21, 2026

0.15.0

Jul 21, 2026

0.14.0

Jul 21, 2026

0.13.0

Jul 20, 2026

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Jul 19, 2026

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Jul 19, 2026

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Jul 19, 2026

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Jul 16, 2026

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Jan 27, 2025

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Jan 21, 2025

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Jan 20, 2025

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Jan 19, 2025

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Jan 19, 2025

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Jan 11, 2025

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Jan 10, 2025

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Jan 10, 2025

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Jan 8, 2025

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Jan 8, 2025

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Jan 8, 2025

0.5.2

Dec 28, 2024

0.5.1

Dec 11, 2024

0.5.0

Dec 11, 2024

0.4.4

Dec 10, 2024

This version

0.4.3

Dec 10, 2024

0.4.2

Dec 10, 2024

0.4.1

Dec 10, 2024

0.4.0

Dec 9, 2024

0.3.0

Dec 8, 2024

0.2.2

Dec 7, 2024

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relibmss 0.4.3

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relibmss

Installation

Usage

Calculate the probability of a fault tree

Obtain the minimal cut sets

Draw a BDD

An example of a large fault tree

TODO for fault tree analysis

Multi-state system

Definition of Gate

Example of a multi-state system

Draw an MDD

Obtain the minimal vector sets

TODO

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