Extended Weibull model (Marshall-Olkin)



   
   [ext_weibull_ex1]
   
   model
   {
      for(i in 1 : N)
      {
      x[i] ~ dext.weib(alpha, lambda)
      }
      
      for (i in 1 : Ncen)
         {
            x.cen[i] ~ dext.weib(alpha, lambda)C(t.cen, )
         }
         
   # Prior distributions of the model parameters   
   
         alpha ~ dunif(0, 5.0)
         lambda~ dunif(0.001, 1000)
   }

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

Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84(3), 641-652.

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.

Data
list(N=21,   x=c(275, 106, 88, 13, 247,147, 28, 23, 212, 243, 181, 23, 65, 10, 2, 80, 261, 245, 173, 293, 266), t.cen = 300, Ncen = 9)
Inits for chain 1
list(alpha=0.2, lambda=200.0, x.cen = c(400, 400, 400, 400, 400, 400, 400, 400, 400))
   
Inits for chain 2
list(alpha=0.4, lambda=300.0, x.cen = c(310, 310, 310, 310, 310, 310, 310, 310, 310))



Results

The distribution of lambda is extremely skewed.
      mean   median   mode   sd   MC_error   val2.5pc   val97.5pc   start   sample   ESS
   alpha   0.3099   0.3107   0.3189   0.02356   3.369E-4   0.261   0.3523   1001   50000   4887
   lambda   246.4   190.7   101.4   181.9   2.483   49.96   760.8   1001   50000   5364

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