Thread: What type of distribution

1. What type of distribution

Hello I am a novice in probabilities and statistics and I am working on a data mining project

I am currently analysing the reliability of medical equipment

I have been using the central limit theorem to qualify the uncertainty of the mean value of my statistical findings

My question relates to failure rate and how to quantify uncertainty associated with the calculate of the failure rate (especially for small sample sizes)

A numerical example would demonstrate that clearly:

I have 1000 physiological monitors in my asset list and last year 400 repairs were performed on them (a failure rate of 400/1000=0.4)

Some of these physiological monitors did not break at all last year and some broke more than once

Therefore my data look like that in terms of number of correctives being performed per physiological monitor last year:
(0,1,0,0,0,0,3,2,1,0,0,0.......)

Do the rules of the central limit theorem apply when quantifying the uncertainty associated with the 0.4 failure rate

What probability distribution better characterises the failure data?

Many Thanks
Regards
Dora

2. Re: What type of distribution

Common count distribution to model frequencies will be Binomial, Poisson, and Negative Binomial, which correspond to different situation - mean > variance, men = variance, and mean < variance.

Of course you should consider the physical nature of the generation of data, and maybe some other discrete distribution will be more appropriate.

Last but not least, your distribution maybe zero-inflated, which is common in these kinds of failure data.

3. Re: What type of distribution

Here is a good overview of the reliability analysis of repairable systems. It is different from that of non-repairable systems because only the initial failure is governed by a distribution (e.g., Weibull, etc.). Subsequent failures follow a Power Law model.

4. Re: What type of distribution

Thanks very much

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