Industrial Event Takt Times (production cycle times) and Probability

[SSGD]

Background:

I am a Mechanical Engineer working as an Industrial Engineer. I have collected some data that is the amount of time that an event took to complete. I first assumed it would be normally distributed, but after plotting a histogram and a normal distribution with the data, I doubt that the set follows a normal distribution. So let's do a little thought experiment.

What is the probability of the event taking from -2 to 0 second? I would say it would be zero.
What is the probability of the event taking taking from negative infinity to zero seconds? I would say it would be zero.

So I think it is save to say that the domain of the distribution is from 0 to infinity.

Question:

What are some models tailored for time distribution? I would say a time distribution should have a domain that goes from 0 to infinity.

 

[Dr. Courtney]

There are several approaches to this problem, but when the mean is more than a couple standard deviations above zero, there are occasions when the normal distribution still works well even though the values really can only be positive.

 

[SSGD]

Yeah the mean and the most probable time are close by looking at the histogram vs the normal distribution, but still about a second or so, which is actually a big issue for this study. We perform a lot of these evenst which last about 8 seconds. So 1 second is about 15% of the total time. I am about 2 to 3 STD from zero. I should plot it and post it. It starts off very close to zero for about 6 sec. Then sharp peak about 7 seconds and a slower decline to zero.

 

[Dr. Courtney]

https://en.wikipedia.org/wiki/Gamma_distribution