Modified Weibull model



   [modifiedweibull_ex1]
   

   model
   {
      for( i in 1 : N )
      {
      x[i] ~ dweib.modified(alpha, beta, lambda)
      }
      
   # Prior distributions of the model parameters   
   
         alpha ~ dunif(0.001, 1.0)
         beta ~ dunif(0.001, 1.0)
         lambda~ dunif(0.001, 1.0)   
   }

The data set is taken from Aarset (1987).

Lai, C.D. , Xie, M. and Murthy, D.N.P. (2003). A modified Weibull distribution, IEEE Trans. Reliab., 52, 33–37.

Ng, H.K.T. (2005). Parameter estimation for a modified Weibull distribution, for progressively type-II censored samples, IEEE Trans. Reliab., 54, 374–380.

Aarset, M.V.(1987). How to identify bathtub hazard rate. IEEE Trans Reliab., 36(1), 106 –108.

The MLE’s ( Lai et al., 2003) are  
alpha = 0.0876,    beta = 0.389;   lambda = 0.01512

The linear regression estimates (Ng, 2005) are  
alpha = 0.0624,    beta = 0.355,   lambda = 0.02332

Data
list( N=50, x = c(0.1, 0.2, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 3.0, 6.0, 7.0, 11.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 21.0, 32.0, 36.0, 40.0, 45.0, 45.0, 47.0, 50.0, 55.0, 60.0, 63.0, 63.0, 67.0, 67.0, 67.0, 67.0, 72.0, 75.0, 79.0, 82.0, 82.0, 83.0, 84.0, 84.0, 84.0, 85.0, 85.0, 85.0, 85.0, 85.0, 86.0, 86.0))
Inits for chain 1
list(alpha=0.1, beta= 0.1 , lambda=0.1)
   
Inits for chain 2
list(alpha=0.2, beta= 0.5 , lambda=0.2)



Results

[modifiedweibull_ex2]