def __init__(self, failures, failure_stress, right_censored=None, right_censored_stress=None, print_results=True, show_plot=True, common_shape_method='BIC'):
# input type checking and converting to arrays in preperation for creation of dataframe
if common_shape_method not in ['BIC', 'weighted_average', 'average']:
raise ValueError('common_shape_method must be either BIC, weighted_average, or average. Default is BIC.')
if len(failures) != len(failure_stress):
raise ValueError('The length of failures does not match the length of failure_stress')
if type(failures) is list:
failures = np.array(failures)
elif type(failures) is np.ndarray:
pass
else:
raise ValueError('failures must be an array or list')
if type(failure_stress) is list:
failure_stress = np.array(failure_stress)
elif type(failure_stress) is np.ndarray:
pass
else:
raise ValueError('failure_stress must be an array or list')
if right_censored is not None:
if len(right_censored) != len(right_censored_stress):
raise ValueError('The length of right_censored does not match the length of right_censored_stress')
if type(right_censored) is list:
right_censored = np.array(right_censored)
elif type(right_censored) is np.ndarray:
pass
else:
raise ValueError('right_censored must be an array or list')
if type(right_censored_stress) is list:
right_censored_stress = np.array(right_censored_stress)
elif type(right_censored_stress) is np.ndarray:
pass
else:
raise ValueError('right_censored_stress must be an array or list')
delta = max(failures) - min(failures)
xmin = min(failures) - delta * 0.2
xmax = max(failures) + delta * 0.2
xvals = np.linspace(xmin, xmax, 100)
if right_censored is not None:
TIMES = np.hstack([failures, right_censored])
STRESS = np.hstack([failure_stress, right_censored_stress])
CENS_CODES = np.hstack([np.ones_like(failures), np.zeros_like(right_censored)])
else:
TIMES = failures
STRESS = failure_stress
CENS_CODES = np.ones_like(failures)
data = {'times': TIMES, 'stress': STRESS, 'cens_codes': CENS_CODES}
df = pd.DataFrame(data, columns=['times', 'stress', 'cens_codes'])
df_sorted = df.sort_values(by=['cens_codes', 'stress', 'times'])
is_failure = df_sorted['cens_codes'] == 1
is_right_cens = df_sorted['cens_codes'] == 0
f_df = df_sorted[is_failure]
rc_df = df_sorted[is_right_cens]
unique_stresses_f = f_df.stress.unique()
if right_censored is not None:
unique_stresses_rc = rc_df.stress.unique()
for item in unique_stresses_rc: # check that there are no unique right_censored stresses that are not also in failure stresses
if item not in unique_stresses_f:
raise ValueError('The right_censored_stress array contains values that are not in the failure_stress array. This is equivalent to trying to fit a distribution to only censored data and cannot be done.')
normal_fit_mu_array = []
normal_fit_sigma_array = []
normal_fit_mu_array_common_shape = []
color_list = ['steelblue', 'darkorange', 'red', 'green', 'purple', 'blue', 'grey', 'deeppink', 'cyan', 'chocolate']
weights_array = []
# within this loop, each list of failures and right censored values will be unpacked for each unique stress to find the common sigma parameter
for stress in unique_stresses_f:
failure_current_stress_df = f_df[f_df['stress'] == stress]
FAILURES = failure_current_stress_df['times'].values
len_f = len(FAILURES)
if right_censored is not None:
if stress in unique_stresses_rc:
right_cens_current_stress_df = rc_df[rc_df['stress'] == stress]
RIGHT_CENSORED = right_cens_current_stress_df['times'].values
len_rc = len(RIGHT_CENSORED)
else:
RIGHT_CENSORED = None
len_rc = 0
else:
RIGHT_CENSORED = None
len_rc = 0
weights_array.append(len_f + len_rc)
normal_fit = Fit_Normal_2P(failures=FAILURES, right_censored=RIGHT_CENSORED, show_probability_plot=False, print_results=False)
normal_fit_mu_array.append(normal_fit.mu)
normal_fit_sigma_array.append(normal_fit.sigma)
common_shape_guess = np.average(normal_fit_sigma_array)
def __BIC_minimizer(common_shape_X): #lgtm [py/similar-function]
'''
__BIC_minimizer is used by the minimize function to get the sigma which gives the lowest overall BIC
'''
BIC_tot = 0
for stress in unique_stresses_f:
failure_current_stress_df = f_df[f_df['stress'] == stress]
FAILURES = failure_current_stress_df['times'].values
if right_censored is not None:
if stress in unique_stresses_rc:
right_cens_current_stress_df = rc_df[rc_df['stress'] == stress]
RIGHT_CENSORED = right_cens_current_stress_df['times'].values
else:
RIGHT_CENSORED = None
else:
RIGHT_CENSORED = None
normal_fit_common_shape = Fit_Normal_2P(failures=FAILURES, right_censored=RIGHT_CENSORED, show_probability_plot=False, print_results=False, force_sigma=common_shape_X)
BIC_tot += normal_fit_common_shape.BIC
return BIC_tot
if common_shape_method == 'BIC':
optimized_sigma_results = minimize(__BIC_minimizer, x0=common_shape_guess, method='nelder-mead')
common_shape = optimized_sigma_results.x[0]
elif common_shape_method == 'weighted_average':
total_data = sum(weights_array)
weights = np.array(weights_array) / total_data
common_shape = sum(weights * np.array(normal_fit_sigma_array))
elif common_shape_method == 'average':
common_shape = common_shape_guess # this was just the numerical average obtained above
self.common_shape = common_shape
# within this loop, each list of failures and right censored values will be unpacked for each unique stress and plotted as a probability plot as well as the CDF of the common sigma plot
AICc_total = 0
BIC_total = 0
AICc = True
for i, stress in enumerate(unique_stresses_f):
failure_current_stress_df = f_df[f_df['stress'] == stress]
FAILURES = failure_current_stress_df['times'].values
if right_censored is not None:
if stress in unique_stresses_rc:
right_cens_current_stress_df = rc_df[rc_df['stress'] == stress]
RIGHT_CENSORED = right_cens_current_stress_df['times'].values
else:
RIGHT_CENSORED = None
else:
RIGHT_CENSORED = None
normal_fit_common_shape = Fit_Normal_2P(failures=FAILURES, right_censored=RIGHT_CENSORED, show_probability_plot=False, print_results=False, force_sigma=common_shape)
normal_fit_mu_array_common_shape.append(normal_fit_common_shape.mu[0])
if type(normal_fit_common_shape.AICc) == str:
AICc = False
else:
AICc_total += normal_fit_common_shape.AICc
BIC_total += normal_fit_common_shape.BIC
if show_plot is True:
normal_fit_common_shape.distribution.CDF(linestyle='--', color=color_list[i], xvals=xvals)
Probability_plotting.Normal_probability_plot(failures=FAILURES, right_censored=RIGHT_CENSORED, color=color_list[i], label=str(stress))
plt.legend(title='Stress')
plt.xlim(xmin, xmax)
if common_shape_method == 'BIC':
plt.title(str('ALT Normal Probability Plot\nOptimal BIC ' + r'$\sigma$ = ' + str(round(common_shape, 4))))
elif common_shape_method == 'weighted_average':
plt.title(str('ALT Normal Probability Plot\nWeighted average ' + r'$\sigma$ = ' + str(round(common_shape, 4))))
elif common_shape_method == 'average':
plt.title(str('ALT Normal Probability Plot\nAverage ' + r'$\sigma$ = ' + str(round(common_shape, 4))))
self.BIC_sum = np.sum(BIC_total)
if AICc is True:
self.AICc_sum = np.sum(AICc_total)
else:
self.AICc_sum = 'Insufficient Data'
sigma_difs = (common_shape - np.array(normal_fit_sigma_array)) / np.array(normal_fit_sigma_array)
sigma_differences = []
for item in sigma_difs:
if item > 0:
sigma_differences.append(str('+' + str(round(item * 100, 2)) + '%'))
else:
sigma_differences.append(str(str(round(item * 100, 2)) + '%'))
results = {'stress': unique_stresses_f, 'original mu': normal_fit_mu_array, 'original sigma': normal_fit_sigma_array, 'new mu': normal_fit_mu_array_common_shape, 'common sigma': np.ones_like(unique_stresses_f) * common_shape, 'sigma change': sigma_differences}
results_df = pd.DataFrame(results, columns=['stress', 'original mu', 'original sigma', 'new mu', 'common sigma', 'sigma change'])
blankIndex = [''] * len(results_df)
results_df.index = blankIndex
self.results = results_df
if print_results is True:
pd.set_option('display.width', 200) # prevents wrapping after default 80 characters
pd.set_option('display.max_columns', 9) # shows the dataframe without ... truncation
print('\nALT Normal probability plot results:')
print(self.results)
print('Total AICc:', self.AICc_sum)
print('Total BIC:', self.BIC_sum)
def __init__(self, failures, failure_stress, right_censored=None, right_censored_stress=None, print_results=True, show_plot=True):
# input type checking and converting to arrays in preperation for creation of dataframe
if len(failures) != len(failure_stress):
raise ValueError('The length of failures does not match the length of failure_stress')
if type(failures) is list:
failures = np.array(failures)
elif type(failures) is np.ndarray:
pass
else:
raise ValueError('failures must be an array or list')
if type(failure_stress) is list:
failure_stress = np.array(failure_stress)
elif type(failure_stress) is np.ndarray:
pass
else:
raise ValueError('failure_stress must be an array or list')
if right_censored is not None:
if len(right_censored) != len(right_censored_stress):
raise ValueError('The length of right_censored does not match the length of right_censored_stress')
if type(right_censored) is list:
right_censored = np.array(right_censored)
elif type(right_censored) is np.ndarray:
pass
else:
raise ValueError('right_censored must be an array or list')
if type(right_censored_stress) is list:
right_censored_stress = np.array(right_censored_stress)
elif type(right_censored_stress) is np.ndarray:
pass
else:
raise ValueError('right_censored_stress must be an array or list')
xmin = np.floor(np.log10(min(failures))) - 1
xmax = np.ceil(np.log10(max(failures))) + 1
xvals = np.logspace(xmin, xmax, 100)
if right_censored is not None:
TIMES = np.hstack([failures, right_censored])
STRESS = np.hstack([failure_stress, right_censored_stress])
CENS_CODES = np.hstack([np.ones_like(failures), np.zeros_like(right_censored)])
else:
TIMES = failures
STRESS = failure_stress
CENS_CODES = np.ones_like(failures)
data = {'times': TIMES, 'stress': STRESS, 'cens_codes': CENS_CODES}
df = pd.DataFrame(data, columns=['times', 'stress', 'cens_codes'])
df_sorted = df.sort_values(by=['cens_codes', 'stress', 'times'])
is_failure = df_sorted['cens_codes'] == 1
is_right_cens = df_sorted['cens_codes'] == 0
f_df = df_sorted[is_failure]
rc_df = df_sorted[is_right_cens]
unique_stresses_f = f_df.stress.unique()
if right_censored is not None:
unique_stresses_rc = rc_df.stress.unique()
for item in unique_stresses_rc: # check that there are no unique right_censored stresses that are not also in failure stresses
if item not in unique_stresses_f:
raise ValueError('The right_censored_stress array contains values that are not in the failure_stress array. This is equivalent to trying to fit a distribution to only censored data and cannot be done.')
weibull_fit_alpha_array = []
weibull_fit_beta_array = []
expon_fit_lambda_array = []
color_list = ['steelblue', 'darkorange', 'red', 'green', 'purple', 'blue', 'grey', 'deeppink', 'cyan', 'chocolate']
# within this loop, each list of failures and right censored values will be unpacked for each unique stress to find the common beta parameter
for stress in unique_stresses_f:
failure_current_stress_df = f_df[f_df['stress'] == stress]
FAILURES = failure_current_stress_df['times'].values
if right_censored is not None:
if stress in unique_stresses_rc:
right_cens_current_stress_df = rc_df[rc_df['stress'] == stress]
RIGHT_CENSORED = right_cens_current_stress_df['times'].values
else:
RIGHT_CENSORED = None
else:
RIGHT_CENSORED = None
weibull_fit = Fit_Weibull_2P(failures=FAILURES, right_censored=RIGHT_CENSORED, show_probability_plot=False, print_results=False)
weibull_fit_alpha_array.append(weibull_fit.alpha)
weibull_fit_beta_array.append(weibull_fit.beta)
# within this loop, each list of failures and right censored values will be unpacked for each unique stress and plotted as a probability plot as well as the CDF of the common beta plot
AICc_total = 0
BIC_total = 0
AICc_total_weib = 0
BIC_total_weib = 0
AICc = True
AICc_weib = True
for i, stress in enumerate(unique_stresses_f):
failure_current_stress_df = f_df[f_df['stress'] == stress]
FAILURES = failure_current_stress_df['times'].values
if right_censored is not None:
if stress in unique_stresses_rc:
right_cens_current_stress_df = rc_df[rc_df['stress'] == stress]
RIGHT_CENSORED = right_cens_current_stress_df['times'].values
else:
RIGHT_CENSORED = None
else:
RIGHT_CENSORED = None
expon_fit = Fit_Expon_1P(failures=FAILURES, right_censored=RIGHT_CENSORED, show_probability_plot=False, print_results=False)
weib_fit = Fit_Weibull_2P(failures=FAILURES, right_censored=RIGHT_CENSORED, show_probability_plot=False, print_results=False, force_beta=np.average(weibull_fit_beta_array))
expon_fit_lambda_array.append(expon_fit.Lambda)
if type(expon_fit.AICc) == str:
AICc = False
else:
AICc_total += expon_fit.AICc
if type(weib_fit.AICc) == str:
AICc_weib = False
else:
AICc_total_weib += weib_fit.AICc
BIC_total += expon_fit.BIC
BIC_total_weib += weib_fit.BIC
if show_plot is True:
expon_fit.distribution.CDF(linestyle='--', color=color_list[i], xvals=xvals, plot_CI=False) # plotting of the confidence intervals has been turned off
Probability_plotting.Weibull_probability_plot(failures=FAILURES, right_censored=RIGHT_CENSORED,plot_CI=False, color=color_list[i], label=str(stress))
plt.legend(title='Stress')
plt.xlim(10 ** (xmin + 1), 10 ** (xmax - 1))
plt.title('ALT Exponential Probability Plot')
self.BIC_sum = np.sum(BIC_total)
self.BIC_sum_weibull = np.sum(BIC_total_weib)
if AICc is True:
self.AICc_sum = np.sum(AICc_total)
else:
self.AICc_sum = 'Insufficient Data'
if AICc_weib is True:
self.AICc_sum_weibull = np.sum(AICc_total_weib)
else:
self.AICc_sum_weibull = 'Insufficient Data'
beta_difs = (1 - np.array(weibull_fit_beta_array)) / np.array(weibull_fit_beta_array)
beta_differences = []
for item in beta_difs:
if item > 0:
beta_differences.append(str('+' + str(round(item * 100, 2)) + '%'))
else:
beta_differences.append(str(str(round(item * 100, 2)) + '%'))
results = {'stress': unique_stresses_f, 'weibull alpha': weibull_fit_alpha_array, 'weibull beta': weibull_fit_beta_array, 'new 1/Lambda': 1 / np.array(expon_fit_lambda_array), 'common shape': np.ones_like(unique_stresses_f), 'shape change': beta_differences}
results_df = pd.DataFrame(results, columns=['stress', 'weibull alpha', 'weibull beta', 'new 1/Lambda', 'common shape', 'shape change'])
blankIndex = [''] * len(results_df)
results_df.index = blankIndex
self.results = results_df
if print_results is True:
pd.set_option('display.width', 200) # prevents wrapping after default 80 characters
pd.set_option('display.max_columns', 9) # shows the dataframe without ... truncation
print('\nALT Exponential probability plot results:')
print(self.results)
print('Total AICc:', self.AICc_sum)
print('Total BIC:', self.BIC_sum)
print('Total AICc (weibull):', self.AICc_sum_weibull)
print('Total BIC (weibull):', self.BIC_sum_weibull)
if self.BIC_sum > self.BIC_sum_weibull:
print('WARNING: The Weibull distribution would be a more appropriate fit for this data set as it has a lower BIC (using the average method to obtain BIC) than the Exponential distribution.')