Industrial Event Takt Times (production cycle times) and Probability

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Discussion Overview

The discussion revolves around the modeling of event completion times in an industrial context, specifically focusing on the probability distributions that can accurately represent these times. Participants explore the characteristics of time distributions, particularly in relation to the assumption of normality and the implications of having a domain restricted to non-negative values.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that the event completion times should be modeled with a distribution that has a domain from 0 to infinity, questioning the applicability of the normal distribution.
  • Another participant notes that the normal distribution can still be effective when the mean is significantly above zero, despite the nature of the data being strictly positive.
  • A third participant highlights the importance of the mean and the most probable time in relation to the histogram, indicating that a small deviation can significantly impact the analysis, especially given the context of the events lasting around 8 seconds.
  • A link to the Gamma distribution is provided, suggesting it as a potential model for time distribution.

Areas of Agreement / Disagreement

Participants express differing views on the suitability of the normal distribution for modeling the data, with some supporting its use under certain conditions while others advocate for alternative distributions due to the nature of the data.

Contextual Notes

There are unresolved questions regarding the appropriateness of the normal distribution for this data set, as well as the specific characteristics of the histogram that may influence the choice of distribution model.

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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.
 
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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.
 
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.
 

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