carta de Shewhart

Desarrollo:

Shewhart Chart
Cálculos en Mathematica

<<Statistics`ContinuousDistribution`

t=NormalDistribution[0,1]

NormalDistribution[0, 1]

Para mu=1 1-(-CDF[t,-5.417173413]+CDF[t,3.417173413]) -----> p(mu)= 0.000316405

Para mu=2 1-(-CDF[t,-6.417173413]+CDF[t,2.417173413]) -----> p(mu)= 0.00782078

Para mu=3 1-(-CDF[t,-7.417173413]+CDF[t,1.417173413]) -----> p(mu)= 0.0782161
 
 

<<Statistics`DiscreteDistribution`

bdist=NegativeBinomialDistribution[1,1-0.99999]
Quantile[bdist,0.01]
NegativeBinomialDistribution[1, 0.00001]
1005
Mean[bdist]
100000

bdist=NegativeBinomialDistribution[1,0.000316405]
Quantile[bdist,0.99]
NegativeBinomialDistribution[1, 0.000316405]
14552

bdist=NegativeBinomialDistribution[1,0.00782078]
Quantile[bdist,0.99]
NegativeBinomialDistribution[1, 0.00782078]
586

bdist=NegativeBinomialDistribution[1,0.0782161]
Quantile[bdist,0.99]
NegativeBinomialDistribution[1, 0.0782161]
56
 
 

Decimos también que los ARL para los Gráficos de Walter Shewhart son aproximadamente igual a la media ya que para una distribución binomial negativa :

                                                       mu=k*q/p

donde k será la cantidad de falsas alarmas, p la probabilidad de defectuosos y q=1-p y decimos que

                                    ARL= k/p (corregir resto de valores)
 
 

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19.may.1999

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Glosario de Carlos von der Becke.