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TL-DR:

The higher the rate of production on my expendable unit, the less overall product it seems to produce in its lifetime. I want to know how best to model this or 20 pages I could read which would tell me how I should model this; to prove or disprove my hypothesis.

Full body:

My statistics skills have atrophied in my professional career so feel free to refer me to remedial literature as a solution.
Here is my problem:

I have a unit which refines product and has a limited lifespan.
I suspect that the rate at which the product is produced is inversely proportional to the total quantity of product it produces over it's lifespan(within 2-20%).

The data I have:

  • Daily product produced
  • Date put online (brand new)
  • Date taken offline (due to failure)

My hypothesis is that if the unit produced (for example) 2 units per day it would produce more over all units than if it produced 3 units per day. Since these units run at the whim of production schedules and are subject to other factors such as quality of feed and quality of manufacturing, I am finding it difficult to tease out a solution that seems statistically sound.

My current solution is a simple multi variable regression of with $Y=\text{life span}$, $X_1=\text{average daily usage for those days online}$, $X_2=\text{total product produced}$.
Immediately typing this out I see Y and X2 should be flipped but I feel like I am not properly accounting for the day to day variations of production rates.

Please advise.

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How many units did you observe until failure? Method choice could depend on that ... if two few better to stay with simpler methods.

You should start with visualization of your data: (and show us the results) scatterplot of $Y$ versus x1, then versus x2 maybe a conditioning plot like using R) coplot(Y ~ x1 | x2, data=yourdataframe). Histograms.

In the following just some ideas: For modeling, two options: $Y$ is a survival length, so survival analysis for $Y$ with x1, x2 as predictors (and possibly others). It could well be the effect is not linear so maybe include the predictors with splines. Or a glm (generalized linear model) for $Y$ with a model for positive outcomes, maybe a gamma glm.

The other options is to model total product produces as a regression on the other variables.

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  • $\begingroup$ I observed failure in ~15 units over a 6 month period. based on the plots I made they all "appeared linear". The cost of analysis for this data would outweigh the best case determination of benefit so I'm not spending any work time on this which is why I'm not posting any graphs. I just want to stretch my stat muscles so they don't die. The GLM seems like a good idea and I will brush up on it-if you can advise a good quick start resource. My current intuition is to do regression using y=total product, X1=Lifetime(D), X2=Daily average of nonzeros/X1, X3=Log(sum of squared daily totals/X1) $\endgroup$ Jan 29 '19 at 1:39

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