Generalized Power Weibull model



   [gpweibull_ex1]
   
   

The data set gives 100 observations on breaking stress of carbon fibres, Nichols and Padgett (2006).

Nichols, M.D. and W.J. Padgett, W.J. (2006). A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International, 22, 141-151.


   model
   {
      for( i in 1 : N )
      {
      x[i] ~ dgp.weib(alpha, theta)      
      }
      
   # Prior distributions of the model parameters      
         
         alpha ~ dunif(0, 20)
         theta~ dunif(0, 20)      
   }


Data
list( N=100, x=c(3.70, 2.74, 2.73, 2.50, 3.60, 3.11, 3.27, 2.87, 1.47, 3.11,
4.42, 2.41, 3.19, 3.22, 1.69, 3.28, 3.09, 1.87, 3.15, 4.90,
3.75, 2.43, 2.95, 2.97, 3.39, 2.96, 2.53, 2.67, 2.93, 3.22,
3.39, 2.81, 4.20, 3.33, 2.55, 3.31, 3.31, 2.85, 2.56, 3.56,
3.15, 2.35, 2.55, 2.59, 2.38, 2.81, 2.77, 2.17, 2.83, 1.92,
1.41, 3.68, 2.97, 1.36, 0.98, 2.76, 4.91, 3.68, 1.84, 1.59,
3.19, 1.57, 0.81, 5.56, 1.73, 1.59, 2.00, 1.22, 1.12, 1.71,
2.17, 1.17, 5.08, 2.48, 1.18, 3.51, 2.17, 1.69, 1.25, 4.38,
1.84, 0.39, 3.68, 2.48, 0.85, 1.61, 2.79, 4.70, 2.03, 1.80,
1.57, 1.08, 2.03, 1.61, 2.12, 1.89, 2.88, 2.82, 2.05, 3.65))
Inits for chain 1
list(alpha=0.5, theta=2.0)
   
Inits for chain 2
list(alpha=2.5, theta=11.0)



Results

[gpweibull_ex2]

MAP estimates are

[gpweibull_ex3]
   

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