## Fitting the Repairable Systems Data of Arab, Rigdon and Basu (Zeros Trick)

2013-08-14
2013-08-14

• Alan Polansky
2013-08-14

Hello All:

I am trying to replicate the analysis of Arab, Rigdon and Basu (2012) [Journal of Quality Technology, Vol. 44, No. 1, 28-38] in JAGS. The model statement given in the paper for WinBUGS is

```model{
C<-100000000
for (i in 1:K){
for (j in 1:N[i]){

#Define PEXP likelihood using the “zeros-trick”

zeros[i,j] <- 0
zeros[i,j]~dpois(phi[i,j])
phi1[i,j] <- pow((delta[i]/mu[i])*pow(j, delta[i]-1),-1)
*exp(-x[i,j]*pow((delta[i]/mu[i])
*pow(j, delta[i]-1),-1))
phi[i,j] <- -log(phi1[i,j])+C } }

#Non-informative gamma prior distributions for
#parameters

for (i in 1:K){
mu[i] ~ dgamma(0.1,0.1)
delta[i] ~ dgamma(0.1,0.1) }
}
```

I have specified the following jags model:

```data {
for (i in 1:K) {
for (j in 1:N[i]) {
zeros[i,j] <- 0
}
}
}

model {
C<-100000000
for (i in 1:K) {
for (j in 1:N[i]) {
zeros[i,j] ~ dpois(phi[i,j])
phi1[i,j] <- pow((delta[i]/mu[i])*
pow(j,delta[i]-1),-1)*
exp(-1*x[i,j]*pow((delta[i]/mu[i])*
pow(j, delta[i]-1),-1))
phi[i,j] <- 1*log(phi1[i,j])+C
}
}
for (i in 1:K) {
mu[i]~dgamma(0.1,0.1)
delta[i]~dgamma(0.1,0.1)
}
}
```

The data are given by

```x <-
structure(c(327, 637, 278, 353, 401, 231, 125, 40, 261, 96, 36,
20, 7, 197, 990, 49, 18, 361, 6, 36, 191, 211, 159, 260, 107,
54, 107, 82, 341, 176, 277, 53, 32, 175, 171, 16, 54, 97, 51,
79, 24, 101, 332, 63, 10, 117, 350, 293, 510, 216, 132, 26, 72,
5, 110, 118, 176, 4, 303, 119, 10, 125, 247, 5, 34, 9, 9, 25,
165, 60, 45, 80, 85, 4, 454, 39, 324, 112, 27, 101, 142, 35,
2, 10, 59, 184, 39, 258, 70, 162, 16, 167, 249, 97, 57, 90, 8,
81, 212, 59, 103, 176, 34, 46, 204, 3, 11, 360, 21, 18, 182,
37, 5, 90, 152, 32, 116, 8, 3, 15, 158, 219, 30, 245, 144, 315,
44, 405, 24, 79, 80, 32, 18, 20, 32, 49, 53, 266, 0, 248, 38,
31, 84, 0, 0, 140, 10, 259, 218, 0, 0, 0, 311, 283, 122, 0, 0,
0, 61, 150, 0, 0, 0, 0, 0, 24, 0, 0), .Dim = c(6L, 28L))

N <- c(23,25,27,28,26,23)

K <- 6
```

When I run the script I get the following error:

```Welcome to JAGS 3.1.0 on Wed Aug 14 11:46:40 2013
JAGS is free software and comes with ABSOLUTELY NO WARRANTY
Compiling data graph
Resolving undeclared variables
Allocating nodes
Initializing
Reading data back into data table
Compiling model graph
Resolving undeclared variables
Allocating nodes
Graph Size: 1750
Initializing model
Error in node zeros[3,3]
Invalid parent values
Deleting model
```

This appears to be due to the large value of 990 in the data.
If I replace the data point with something smaller it seems to work fine, but there
are major convergence issues.

Questions:

1. Have I specified the model correctly?

2. What will fix the error?

Thanks for any help anyone has.