# Fit_Lognormal_Exponential¶

class reliability.ALT_fitters.Fit_Lognormal_Exponential(failures, failure_stress, right_censored=None, right_censored_stress=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 Lognormal-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 temperature. It is recommended that you ensure your temperature data are in Kelvin. If you are using this model for the Arrhenius equation, a = Ea/K_B. When results are printed Ea will be provided in eV.

Inputs: failures - an array or list of the failure times. failure_stress - an array or list of the corresponding stresses (such as temperature) 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 - an array or list of the corresponding stresses (such as temperature) 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 - The use level stress 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 Exponential model b - fitted parameter from the Exponential model sigma - the fitted Lognormal_2P sigma 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 b_SE - the standard error (sqrt(variance)) of the parameter sigma_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 b_upper - the upper CI estimate of the parameter b_lower - the lower CI estimate of the parameter sigma_upper - the upper CI estimate of the parameter sigma_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 (mu and sigma) at each stress level mean_life - the mean life at the use_level_stress (only provided if use_level_stress is provided) mu_at_use_stress - the equivalent Lognormal mu parameter at the use level stress (only provided if use_level_stress is provided) distribution_at_use_stress - the Lognormal distribution at the use level stress (only provided if use_level_stress is provided) probability_plot - the axes handles for the figure object from the probability plot (only provided if show_probability_plot is True) life_stress_plot - the axes handles for the figure object from the life-stress plot (only provided if show_life_stress_plot is True)

static LL(params, t_f, t_rc, T_f, T_rc)
static logR(t, T, a, b, sigma)
static logf(t, T, a, b, sigma)