def intensity_function(t, failure_model, T=list(), ϵ=1e-8):
"""
t : time of interest.
gamma: shape parameter of the Weibull distribution with expectation 1.
alpha: shape parameter of the power law trend function.
beta : scale parameter of the power law trend function.
T : time-to-failure data.
"""
model = failure_model[0]
gamma, alpha, beta = failure_model[1]
if T[0] != 0:
T = [0] + T
else:
pass
if model == "WPLP":
if t == 0:
if beta < 1 or gamma < 1:
return float("inf")
else:
0
else:
return (alpha * gammafunction(1 + 1 / gamma)
)**gamma * gamma * beta * t**(beta - 1) * (
t**beta - T[N(t - ϵ, T)]**beta)**(gamma - 1)
elif model == "NHPP":
return alpha * beta * t**(beta - 1)
elif model == "HPP":
return alpha
elif model == "WRP":
return (alpha * gammafunction(1 + 1 / gamma))**gamma * gamma * t * (
t - T[N(t - ϵ, T)])**(gamma - 1)
def interval_predictor(last_failure, failure_model, ε_1=.025, ε_2=.025):
gamma, alpha, beta = failure_model[1]
phi = (alpha * gammafunction(1 + 1 / gamma))**gamma
T_L = (last_failure**beta +
(1 / phi * log(1 / (1 - ε_1)))**(1 / gamma))**(1 / beta)
T_U = (last_failure**beta +
(1 / phi * log(1 / (ε_2)))**(1 / gamma))**(1 / beta)
return [T_L, T_U]
def next_ttf(previous_ttf, final_failure_model, CRN=None):
gamma, alpha, beta = final_failure_model[1]
U = uniform.rvs(random_state=CRN)
tmpA = previous_ttf**beta
tmpB = 1 / (alpha * gammafunction(1 + 1 / gamma))
tmpC = log(1 / (1 - U))**(1 / gamma)
tmpD = (tmpA + tmpB * tmpC)**(1 / beta)
return tmpD
def weibull_dist_func(x, failure_model):
gamma, alpha, beta = failure_model[1]
return 1 - exp(-(x * gammafunction(1 + 1 / gamma))**gamma)
def alpha_value(gamma, phi):
return phi ** (1/gamma) / (gammafunction(1+1/gamma))