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Fit_Weibull_Power_Exponential

class reliability.ALT_fitters.Fit_Weibull_Power_Exponential(failures, failure_stress_1, failure_stress_2, right_censored=None, right_censored_stress_1=None, right_censored_stress_2=None, use_level_stress=None, CI=0.95, optimizer=None, show_probability_plot=True, show_life_stress_plot=True, print_results=True)

This function will Fit the Weibull_Power_Exponential life-stress model to the data provided. Please see the online documentation for the equations of this model. This model is most appropriate to model a life-stress relationship with thermal and non-thermal stresses. It is essential that you ensure your thermal stress is stress_thermal and your non-thermal stress is stress_nonthermal. Also ensure that your temperature data are in Kelvin.

Inputs: failures - an array or list of the failure times. failure_stress_1 - an array or list of the corresponding stress 1 (thermal stress) at which each failure occurred. This must match the length of failures as each failure is tied to a failure stress. failure_stress_2 - an array or list of the corresponding stress 2 (non-thermal stress) at which each failure occurred. This must match the length of failures as each failure is tied to a failure stress. right_censored - an array or list of all the right censored failure times right_censored_stress_1 - an array or list of the corresponding stress 1 (thermal stress) at which each right_censored data point was obtained. This must match the length of right_censored as each right_censored value is tied to a right_censored stress. right_censored_stress_2 - an array or list of the corresponding stress 1 (non-thermal stress) at which each right_censored data point was obtained. This must match the length of right_censored as each right_censored value is tied to a right_censored stress. use_level_stress - [stress_1, stress_2]. A two element list or array of the use level stresses at which you want to know the mean life. Optional input. print_results - True/False. Default is True show_probability_plot - True/False. Default is True show_life_stress_plot - True/False. Default is True CI - confidence interval for estimating confidence limits on parameters. Must be between 0 and 1. Default is 0.95 for 95% CI. optimizer - ‘TNC’, ‘L-BFGS-B’, ‘powell’. Default is ‘TNC’. These are all bound constrained methods. If the bound constrained method fails, nelder-mead will be used. If nelder-mead fails the initial guess (using least squares) will be returned with a warning.

Outputs: a - fitted parameter from the Power_Exponential model c - fitted parameter from the Power_Exponential model n - fitted parameter from the Power_Exponential model beta - the fitted Weibull_2P beta loglik2 - Log Likelihood*-2 (as used in JMP Pro) loglik - Log Likelihood (as used in Minitab and Reliasoft) AICc - Akaike Information Criterion BIC - Bayesian Information Criterion a_SE - the standard error (sqrt(variance)) of the parameter c_SE - the standard error (sqrt(variance)) of the parameter n_SE - the standard error (sqrt(variance)) of the parameter beta_SE - the standard error (sqrt(variance)) of the parameter a_upper - the upper CI estimate of the parameter a_lower - the lower CI estimate of the parameter c_upper - the upper CI estimate of the parameter c_lower - the lower CI estimate of the parameter n_upper - the upper CI estimate of the parameter n_lower - the lower CI estimate of the parameter beta_upper - the upper CI estimate of the parameter beta_lower - the lower CI estimate of the parameter results - a dataframe of the results (point estimate, standard error, Lower CI and Upper CI for each parameter) goodness_of_fit - a dataframe of the goodness of fit criterion (Log-likelihood, AICc, BIC). change_of_parameters - a dataframe showing the change of the parameters (alpha and beta) at each stress level. mean_life - the mean life at the use_level_stress (only provided if use_level_stress is provided). alpha_at_use_stress - the equivalent Weibull alpha parameter at the use level stress (only provided if use_level_stress is provided). distribution_at_use_stress - the Weibull distribution at the use level stress (only provided if use_level_stress is provided). probability_plot - the figure object from the probability plot (only provided if show_probability_plot is True) life_stress_plot - the figure object from the life-stress plot (only provided if show_life_stress_plot is True)

static LL(params, t_f, t_rc, S1_f, S2_f, S1_rc, S2_rc)
static logR(t, S1, S2, a, c, n, beta)
static logf(t, S1, S2, a, c, n, beta)