###################################################################
#                                                                 #
#  This program plots I_B^{(i)}(t) as a function of t for a       #
#  system  with given minimal path sets using Monte Carlo         #
#  simulations of the component lifetimes and calculating the     #
#  resulting system lifetime.                                     #
#                                                                 #
###################################################################

from math import *
from random import *
import matplotlib.pyplot as plt
import numpy as np

# Time parameters
max_t = 120
steps = 120

# Number of simulations
num_sims = 100000

# Weibull-parameters for the components
alpha = [2.0, 2.5, 3.0, 1.0, 1.5]
beta = [50.0, 60.0, 70.0, 40.0, 50.0]

# Number of components and minimal paths
num_comps = 5
num_paths = 4

# Birnbaum measures
IB = np.zeros((num_comps, steps))

# A component is identified as critical when t is in [L, U)
L = np.zeros(num_comps)
U = np.zeros(num_comps)

# Minimal path sets
paths = [{1,4}, {1,3,5}, {2,3,4}, {2,5}]

# Calculate the system lifetime given the component lifetimes
def sys_lifetime(tt):
    sys_life = 0.0
    for j in range(num_paths):
        path_life = np.inf
        for i in paths[j]:
            if tt[i-1] < path_life:
                path_life = tt[i-1]
        if path_life > sys_life:
            sys_life = path_life
    return sys_life

# The simulated lifetimes of the components
t = np.zeros(num_comps)

# Time steps
time = np.linspace(0.0, max_t, steps)

# Run simulations
for k in range(num_sims):
    for i in range(num_comps):
        t[i] = weibullvariate(beta[i], alpha[i])
    for i in range(num_comps):
        temp = t[i]
        t[i] = np.inf
        U[i] = sys_lifetime(t)
        t[i] = 0
        L[i] = sys_lifetime(t)
        t[i] = temp
    for step in range(steps):
        for i in range(num_comps):
            if L[i] <= time[step] and time[step] < U[i]:
                IB[i][step] += 1

# Calculate average importance values
for step in range(steps):
    for i in range(num_comps):
        IB[i][step] = IB[i][step] / num_sims

fig = plt.figure(figsize = (7, 4))
for i in range(num_comps):
    plt.plot(time, IB[i], label='IB(' + str(i+1) + ", t)")
plt.xlabel('Time')
plt.ylabel('Importance')
plt.title("Importance as a function of time")
plt.legend()
plt.show()