Reliawiki - Otra mirada al parámetro beta de weibull - trabajando en google colab

Supongamos que un ingeniero de pruebas obtuvo los datos de vida que se muestran en la Tabla 1. Según Según la experiencia previa, se debe utilizar la distribución Weibull de 2 parámetros para ajustar los datos. El análisis utilizando Weibull++ muestra que β = 0,9812 y η = 73,6036, como se muestra en la Figura 1.

Tabla 1: Datos de falla

Estado (F o S)	Es hora de declarar	Índice de artículos
F	2	1
S	3	2
F	5	3
S	7	4
F	11	5
S	13	6
S	17	7
S	19	8
F	23	9
F	29	10
S	31	11
F	37	12
S	41	13
F	43	14
S	47	15
S	53	16
F	59	17
S	61	18
S	69	19
F	75	20

from reliability.Distributions import Weibull_Distribution

import matplotlib.pyplot as plt

dist = Weibull_Distribution(alpha=73.6036, beta= 0.9812)  # this created the distribution object

dist.PDF()  # this creates the plot of the PDF

plt.show()

# sub grupo 1: 3,7,13,19,29,37,43,53,61,75

# sub grupo 2: 2,5,11,17,23,31,41,47, 59,69

from reliability.Fitters import Fit_Weibull_2P

import matplotlib.pyplot as plt

data_1 = [3,7,13,19,29,37,43,53,61,75]

wb = Fit_Weibull_2P(failures=data_1)

plt.show()

Results from Fit_Weibull_2P (95% CI):

Analysis method: Maximum Likelihood Estimation (MLE)
Optimizer: TNC
Failures / Right censored: 10/0 (0% right censored) 

Parameter  Point Estimate  Standard Error  Lower CI  Upper CI
    Alpha         37.1085         8.81965   23.2899   59.1262
     Beta         1.39557         0.36808  0.832238   2.34021 

Goodness of fit    Value
 Log-likelihood -44.5643
           AICc   94.843
            BIC  93.7338
             AD  1.42278 

from reliability.Fitters import Fit_Weibull_2P

import matplotlib.pyplot as plt

data_2 = [2,5,11,17,23,31,41,47, 59,69]

wb = Fit_Weibull_2P(failures=data_2)

plt.show()

Results from Fit_Weibull_2P (95% CI):
Analysis method: Maximum Likelihood Estimation (MLE)
Optimizer: TNC
Failures / Right censored: 10/0 (0% right censored) 

Parameter  Point Estimate  Standard Error  Lower CI  Upper CI
    Alpha         32.7011         8.52932   19.6132   54.5229
     Beta         1.27127        0.335708   0.75763   2.13313 

Goodness of fit   Value
 Log-likelihood -43.802
           AICc 93.3182
            BIC 92.2091
             AD 1.42135 

Grupos 1 y 2 juntos

from reliability.Fitters import Fit_Weibull_2P

import matplotlib.pyplot as plt

data_3 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 43, 53, 59, 61, 62, 69, 75]

wb = Fit_Weibull_2P(failures=data_3)

plt.show()

Results from Fit_Weibull_2P (95% CI):
Analysis method: Maximum Likelihood Estimation (MLE)
Optimizer: TNC
Failures / Right censored: 21/0 (0% right censored) 

Parameter  Point Estimate  Standard Error  Lower CI  Upper CI
    Alpha         36.5097          6.1597     26.23    50.818
     Beta         1.35493        0.248815   0.94538   1.94191 

Goodness of fit    Value
 Log-likelihood -93.6314
           AICc   191.93
            BIC  193.352
             AD  1.01308