Weibull 0 time failures

I'm having a lot of trouble trying to analyse the following times to failure, due to their being dead-on-arrival failures. The only way I can analyse them is to set the zero values to an extremely small number e.g 0.001. All the examples I have seen where people are using Weibull analysis there are never 0 time failures. Am i analysing this sample correctly? 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.20000 23.80000 24.80000 46.40000 51.50000 56.00000 59.50000 64.60000 72.50000 74.00000 78.30000 79.30000 84.80000 91.00000 100.20000 102.90000 104.40000 109.90000 113.80000 123.30000 123.60000 132.40000 133.00000 137.80000 157.80000 165.00000 172.00000 174.30000 182.00000 182.00000 183.30000 184.70000 184.80000 188.80000 189.00000 189.40000 198.00000 201.40000 201.70000 203.00000 208.00000 212.30000 213.70000 214.80000 215.50000 215.50000 220.70000 224.00000 225.30000 229.00000 238.00000

Thank you in advance

Answer 1

[Andrew Newell]

I assume you were trying to fit the data using something like

parmhat = wblfit(data);

I tried a few experiments and it doesn't seem to matter whether you replace the zeros by 0.001, 0.1, or just leave them off, as in the example below. I also did a quantile-quantile plot, which shows that the Weibull distribution agrees pretty well with the data except for the zeros and the largest values.

[parmhat,parmci] = wblfit(data(10:end));
syntheticData = wblrnd(parmhat(1),parmhat(2),length(data),1);
qqplot(data,syntheticData)

[bym]

if I plot the data using probplot and censoring the 0 values, there is a distinct 'dogleg' in the data at about 183. This is indicative of different failure modes, you may want to fit two distributions: 1 to data <183 and another to data >183.

my 2 cents

[Andrew Newell]

For that matter a simple histogram suggests a distribution with two peaks.

[Matt]

Many thanks for the help, I'm going to go with fitting two distributions to the data.

Thanks