Weibull Distribution Unusual Application

#1
I am trying to use a Weibull Distribution to understand something in my business. The process essentially involves a machine breaking and it goes into a "Broken" status. The Broken Status lasts for a finite amount of time, ending when it the machine is fixed. This is the length of time.

This is different than what I typically see Weibull used. I typically see it used in applications for Reliability, where the values within the distribution are the times that it takes something to BREAK, not get fixed.

I have computed Weibull Parameters that describe the distribution of the lengths of time it takes machines to get fixed. They are characteristically less than 1, indicating so called 'infant mortality' is present. Here is my question:

Imagine that we want to estimate the mean time it takes a machine to get repaired. Let's say the mean time is 5 hours. So at T=0, we expect the machine to be fixed at T=5.

Which of the two statements is applicable to my data, noting that infant mortality is present?
A) At T=3, we now expect that the machine will take LESS than 5 MORE hours to fix, so we update the estimated time of repair to T = 3 + x, where x is a number < 5
B) At T=3, we now expect that the machine will take GREATER than 5 MORE hours to fix, so we update the estimated time of repair to T = 3 + x, where x is a number > 5

Thank you for your thoughts in advance!
 

Miner

TS Contributor
#2
All of the tools and analyses that are typically associated with reliability will work equally well with any "event in time", so don't worry about whether you can use it for repairs instead of failures. In fact, there is a Mean Time to Repair (MTTR) metric that is an equivalent to the MTBF/MTTF metrics, so your application is not new.

The hard part to wrap your head around is converting the traditional reliability terms into something that makes sense to your usage. For example, you have a shape parameter less than 1, which you called infant mortality. In the traditional reliability context, this makes sense, but not in your context. Instead, you need to convert this into a decreasing repair rate. I would interpret this to mean that the farther you progress in time (i.e., T=3) the more difficult the repairs are likely to be and the longer the repair will probably take.
 
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