Fitting discrete data in time

Question

Hi everyone,

I'm hoping some kind folks on this community can point me in the right direction for this analysis, like suggestions for techniques or JMP example literature (JMP 13). I'm a bit new to this and looking for direction.

I have a discrete "damage severity ranking" (ranging from 0, 1, 2, 3, 4, with 4 being most severe and zero being brand new) and a corresponding "days in use" (continuously ranging from 0 to 450 days). The idea being that my item grows in damage over time, but each snapshot in time will have a different distribution of damage. For example, at 0 days, everything is expected to be brand new, but at 450 days, we could have 20% being level 4 damage.

Ultimately I would like to:

* Determine distribution for 0-4 damage ranking within certain time blocks, like 0 to 30 days, 30 to 60, 360-400 etc. (maybe like weibull parameters, or lognormal parameters? Other suggestions?)

* Extrapolate these trends to know damage distribution at 1500 days.

Data is very simple, takes this format:

Item #, Days in use, damage severity rank

1, 45, 1

2, 95, 3

3, 188, 3

4, 153, 2

5, 421, 4

6, 355 , 4

7, 75, 2

etc...

stephen_pearson · Answer

There is some key information missing to be able to give constructive help:
How many units existed at time 0?
Are all the units from the same lot?
Do you have more than 1 snapshot in time of the gradings, e.g. are more new units entering the field as others are retired?
Will a unit be returned to you as soon as it is damaged or can some time pass? e.g. How is the data censored?

rsellers87 · Answer

Howdy,

I want to bump this thread and give more background. I'm still looking for some direction.

When a unit is graded for damage, it is "retired" (in other words, the product is returned to us, and we grade it. the product will not see more field use).

A couple notes

* Time is continuous, it could be 23 days, 411 days, 96 days, etc.

* Damage is graded as: 0 = new, 1 = like new, 2 = fair, 3 = poor, 4 = very poor

I want to know what the 50 percentile grade is over time, and the 90 percentile grade over time.

Then extrapolate these percentiles to 3 years (~1100 days). Basically, how can we understand the 'long tail' of heavy users, and convey this visually.

dale_lehman · Answer

Somebody who knows more than me will have to steer you (and I'm sure they will), but a few thoughts come to mind.  First, your data is censored - at any point in time, lack of damage merely means damage has not occured yet - but it might (will) occur later.  However, I don't think a standard survival analysis will work, since I've only worked with 0,1 censored variables and you seem to have different levels of damage.  Hopefully, someone can shed light on how to handle that complication.

Second, I don't see why you want to put the time variable into time blocks.  You have a continuous measure of time, so I would not group it into the blocks.  You might try any of the classification models (logistic, partitions, neural nets, etc.) with the ordinal damage variable as the response and the time variable (and perhaps others) as independent variable.  That would seem the most straightforward way to model this.