###################################################################
#                                                                 #
#  This program estimates the Natvig importance measure           #
#  for components in a threshold system using Monte Carlo         #
#  simulations.                                                   #
#                                                                 #
###################################################################

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]

# Threshold system weights and threshold
w = [2.0, 4.0, 2.3, 3.5, 1.9]
threshold = 5.0

# Number of components and minimal paths
num_comps = 5

# Component state vector
x = np.zeros(num_comps)

# The structure function of the threshold system
def phi(xx):
    wsum = 0.0
    for i in range(num_comps):
        wsum += w[i] * xx[i]
    if wsum >= threshold:
        return 1
    else:
        return 0

# Calculate the system lifetime given the component lifetimes
def sys_lifetime(tt):
    # Initialize component states
    for i in range(num_comps):
        x[i] = 1
    # Initialize system state and lifetime
    sys_state = phi(x)
    sys_life = 0.0
    # Determine the ordering of the failure times
    order = tt.argsort()
    # Initialize failure counter
    c = 0
    # Switch off one component at a time in the order of the failure times
    while (sys_state == 1) and (c < num_comps):
        x[order[c]] = 0
        sys_life = tt[order[c]]
        sys_state = phi(x)
        c += 1
    if sys_state == 0:
        return sys_life
    else: # This happens only for trivial systems where phi(0,...,0) = 1.
        return np.inf 

# The improvement in system lifetimes
# due to minimal repairs
z = np.zeros(num_comps)

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

# The simulated lifetimes of the components
# sampled from the conditional distribution
# given that they exceed the corresponding t
v = np.zeros(num_comps)

for k in range(num_sims):
    for i in range(num_comps):
        t[i] = weibullvariate(beta[i], alpha[i])
        v[i] = 0.0
        while v[i] < t[i]:
            v[i] = weibullvariate(beta[i], alpha[i])
    s = sys_lifetime(t)
    for i in range(num_comps):
        temp = t[i]
        t[i] = v[i]
        z[i] += (sys_lifetime(t) - s)
        t[i] = temp

# Calculate the unstandardized Natvig measure
z_sum = 0.0
z_imp = np.zeros(num_comps)
for i in range(num_comps):
    z_imp[i] = z[i] / num_sims
    z_sum += z_imp[i]

# Standardize the measure so that it adds up to 1
nat_imp = np.zeros(num_comps)
for i in range(num_comps):
    nat_imp[i] = z_imp[i] / z_sum

comp = np.linspace(1, num_comps, num_comps)

fig = plt.figure(figsize = (7, 4))
plt.bar(comp, nat_imp, color ='gray', width = 0.4)
plt.xlabel("Components")
plt.ylabel("Importance")
plt.title("Natvig importance")
plt.show()