###################################################################
#                                                                 #
#  This program plots h(p(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

# 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


# 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 upper percentile levels
q = np.zeros(num_sims)

# The simulated system lifetimes
s = np.zeros(num_sims)

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

for k in range(num_sims):
    q[k] = 1.0 - k / num_sims
    for i in range(num_comps):
        t[i] = weibullvariate(beta[i], alpha[i])
    s[k] = sys_lifetime(t)


s.sort()

fig = plt.figure(figsize = (7, 4))
plt.plot(s, q, label='h(p(t))')
plt.xlabel('Time')
plt.ylabel('Reliability')
plt.title("System reliability as a function of time")
plt.legend()
plt.show()