How to use the reliability.Fitters.Fit_Weibull_3P function in reliability

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github MatthewReid854 / reliability / reliability / Fitters.py View on Github external
self.initial_guess = guess
        k = len(guess)
        n = len(all_data)

        delta_BIC = 1
        BIC_array = [1000000]
        runs = 0

        gamma_lower_bound = 0.95 * gamma_initial_guess  # 0.95 is found to be the optimal point to minimise the error while also not causing autograd to fail
        bnds = [(0, None), (0, None), (gamma_lower_bound, min(all_data) - offset)]  # bounds on the solution. Helps a lot with stability
        while delta_BIC > 0.001 and runs < 5:  # exits after BIC convergence or 5 iterations
            runs += 1
            result = minimize(value_and_grad(Fit_Weibull_3P.LL), guess, args=(failures, right_censored), jac=True, method='L-BFGS-B', bounds=bnds)
            params = result.x
            guess = [params[0], params[1], params[2]]
            LL2 = 2 * Fit_Weibull_3P.LL(guess, failures, right_censored)
            BIC_array.append(np.log(n) * k + LL2)
            delta_BIC = abs(BIC_array[-1] - BIC_array[-2])

        if result.success is True:
            params = result.x
            self.success = True
            self.alpha = params[0]
            self.beta = params[1]
            self.gamma = params[2]
        else:
            self.success = False
            print('WARNING: Fitting using Autograd FAILED for Weibull_3P. The fit from Scipy was used instead so the results may not be accurate.')
            sp = ss.weibull_min.fit(all_data, optimizer='powell')
            self.alpha = sp[2]
            self.beta = sp[0]
            self.gamma = sp[1]
github MatthewReid854 / reliability / reliability / Fitters.py View on Github external
def LL(params, T_f, T_rc):  # log likelihood function (3 parameter Weibull)
        LL_f = 0
        LL_rc = 0
        LL_f += Fit_Weibull_3P.logf(T_f, params[0], params[1], params[2]).sum()  # failure times
        LL_rc += Fit_Weibull_3P.logR(T_rc, params[0], params[1], params[2]).sum()  # right censored times
        return -(LL_f + LL_rc)
github MatthewReid854 / reliability / reliability / Fitters.py View on Github external
def LL(params, T_f, T_rc):  # log likelihood function (3 parameter Weibull)
        LL_f = 0
        LL_rc = 0
        LL_f += Fit_Weibull_3P.logf(T_f, params[0], params[1], params[2]).sum()  # failure times
        LL_rc += Fit_Weibull_3P.logR(T_rc, params[0], params[1], params[2]).sum()  # right censored times
        return -(LL_f + LL_rc)
github MatthewReid854 / reliability / reliability / Fitters.py View on Github external
self.alpha = sp[2]
            self.beta = sp[0]
            self.gamma = sp[1]

        params = [self.alpha, self.beta, self.gamma]
        self.loglik2 = LL2
        if n - k - 1 > 0:
            self.AICc = 2 * k + LL2 + (2 * k ** 2 + 2 * k) / (n - k - 1)
        else:
            self.AICc = 'Insufficient data'
        self.BIC = np.log(n) * k + LL2
        self.distribution = Weibull_Distribution(alpha=self.alpha, beta=self.beta, gamma=self.gamma)

        # confidence interval estimates of parameters
        Z = -ss.norm.ppf((1 - CI) / 2)
        hessian_matrix = hessian(Fit_Weibull_3P.LL)(np.array(tuple(params)), np.array(tuple(failures)), np.array(tuple(right_censored)))
        covariance_matrix = np.linalg.inv(hessian_matrix)
        self.alpha_SE = abs(covariance_matrix[0][0]) ** 0.5
        self.beta_SE = abs(covariance_matrix[1][1]) ** 0.5
        self.gamma_SE = abs(covariance_matrix[2][2]) ** 0.5
        self.alpha_upper = self.alpha * (np.exp(Z * (self.alpha_SE / self.alpha)))
        self.alpha_lower = self.alpha * (np.exp(-Z * (self.alpha_SE / self.alpha)))
        self.beta_upper = self.beta * (np.exp(Z * (self.beta_SE / self.beta)))
        self.beta_lower = self.beta * (np.exp(-Z * (self.beta_SE / self.beta)))
        self.gamma_upper = self.gamma * (np.exp(Z * (self.gamma_SE / self.gamma)))  # here we assume gamma can only be positive as there are bounds placed on it in the optimizer. Minitab assumes positive or negative so bounds are different
        self.gamma_lower = self.gamma * (np.exp(-Z * (self.gamma_SE / self.gamma)))

        Data = {'Parameter': ['Alpha', 'Beta', 'Gamma'],
                'Point Estimate': [self.alpha, self.beta, self.gamma],
                'Standard Error': [self.alpha_SE, self.beta_SE, self.gamma_SE],
                'Lower CI': [self.alpha_lower, self.beta_lower, self.gamma_lower],
                'Upper CI': [self.alpha_upper, self.beta_upper, self.gamma_upper]}
github MatthewReid854 / reliability / reliability / Probability_plotting.py View on Github external
if 'color' in kwargs:
            data_color = kwargs.get('color')
        else:
            data_color = 'k'
        xlabel = 'Time'
    elif fit_gamma is True:
        if __fitted_dist_params is not None:
            alpha = __fitted_dist_params.alpha
            beta = __fitted_dist_params.beta
            gamma = __fitted_dist_params.gamma
            alpha_SE = __fitted_dist_params.alpha_SE
            beta_SE = __fitted_dist_params.beta_SE
            Cov_alpha_beta = __fitted_dist_params.Cov_alpha_beta
        else:
            from reliability.Fitters import Fit_Weibull_3P
            fit = Fit_Weibull_3P(failures=failures, right_censored=right_censored, CI=CI, show_probability_plot=False, print_results=False)
            alpha = fit.alpha
            beta = fit.beta
            gamma = fit.gamma
            alpha_SE = fit.alpha_SE
            beta_SE = fit.beta_SE
            Cov_alpha_beta = fit.Cov_alpha_beta

        if 'label' in kwargs:
            label = kwargs.pop('label')
        else:
            label = str('Fitted Weibull_3P\n(α=' + str(round_to_decimals(alpha, dec)) + ', β=' + str(round_to_decimals(beta, dec)) + ', γ=' + str(round_to_decimals(gamma, dec)) + ')')
        if 'color' in kwargs:
            data_color = kwargs.get('color')
        else:
            data_color = 'k'
        xlabel = 'Time - gamma'
github MatthewReid854 / reliability / reliability / Fitters.py View on Github external
else:
            RC = right_censored
        self._all_data = np.hstack([failures, RC])
        if min(self._all_data) <= 0:
            raise ValueError('All failure and censoring times must be greater than zero.')

        # These are all used for scaling the histogram when there is censored data
        self._frac_fail = len(failures) / len(self._all_data)

        # Kaplan-Meier estimate of quantiles. Used in P-P plot.
        d = sorted(self._all_data)  # sorting the failure data is necessary for plotting quantiles in order
        nonparametric = KaplanMeier(failures=failures, right_censored=right_censored, print_results=False, show_plot=False)
        self._nonparametric_CDF = 1 - np.array(nonparametric.KM)  # change SF into CDF

        # parametric models
        self.__Weibull_3P_params = Fit_Weibull_3P(failures=failures, right_censored=right_censored, show_probability_plot=False, print_results=False)
        self.Weibull_3P_alpha = self.__Weibull_3P_params.alpha
        self.Weibull_3P_beta = self.__Weibull_3P_params.beta
        self.Weibull_3P_gamma = self.__Weibull_3P_params.gamma
        self.Weibull_3P_BIC = self.__Weibull_3P_params.BIC
        self.Weibull_3P_AICc = self.__Weibull_3P_params.AICc
        self._parametric_CDF_Weibull_3P = self.__Weibull_3P_params.distribution.CDF(xvals=d, show_plot=False)

        self.__Gamma_3P_params = Fit_Gamma_3P(failures=failures, right_censored=right_censored, show_probability_plot=False, print_results=False)
        self.Gamma_3P_alpha = self.__Gamma_3P_params.alpha
        self.Gamma_3P_beta = self.__Gamma_3P_params.beta
        self.Gamma_3P_gamma = self.__Gamma_3P_params.gamma
        self.Gamma_3P_BIC = self.__Gamma_3P_params.BIC
        self.Gamma_3P_AICc = self.__Gamma_3P_params.AICc
        self._parametric_CDF_Gamma_3P = self.__Gamma_3P_params.distribution.CDF(xvals=d, show_plot=False)

        self.__Expon_2P_params = Fit_Expon_2P(failures=failures, right_censored=right_censored, show_probability_plot=False, print_results=False)