DelayN with leakage?

[kleemax]

A conveyor is similar to a fixed delay (infinit order delay) but with leakage.
I need something similar but for a Delay of higher but not infinite order, a Delay N with leakage.

Background: I'm trying to model heating systems in homes. They are being installed and after an average lifetime of x years they are being exchanged for a new one (outflow). I am using a the order of the Delay N to model the spread of the heating systems dying around the average lifetime. The problem is that some heating systems get lost earlier (e.g. when a house is torn down, because of laws mandating it etc.) The Delay N function in Vensim has no way of leaking the material in transition. But I need just that.
The orders are rather high (e.g. 48) so I am reluctant to model the aging chain by hand, esp. since I also need to calibrate the order.
It would be cool, if a solution allowed for negative leakage (inflows) as well, but that’s not a requirement because I don't have that problem now.

Any ideas on how to do this simpler than modeling lots of aging chains by hand greatly appreciated.

Max Kleemann

[tomfid]

Would DELAY CONVEYOR work? That has leakage. https://www.vensim.com/documentation/in ... nveyor.htm

[kleemax]

Thank you for your reply Tom.
Delay Conveyor has an infinite order. I need a Delay of finite order with leakage. Therefore I don't see how Delay Conveyor could help. Do you?
¿:-)Max

[tomfid]

Sorry - haste makes for dumb answers.

I can't see a way to do it without using arrays. What's the time horizon and mean time to failure? What makes the order so high? I wouldn't expect equipment to fail that way. Or is it a mix of failures and rules, such that things are replaced when they fail (low order) or reach 30 years age (high/discrete order)?

[tomfid]

It seems like an array would be a reasonable solution, as long as your model isn't too big overall.

For example, you could have a fixed-length array (say 100 levels) and vary the delay per level. That would allow you to vary the de facto delay order over any given horizon. Then, once calibrated, you could shorten the array if possible.

[kleemax]

resp. your reply form 28. Jan:
I have data on the minimum and maximum lifetimes of heating systems. The data is from questionnaires. It may be a mix of failures and other reasons but still my impression even for modern heating systems is that they don't fail for the first decade or so. I have assumed that 5% are over the max and 5% are under the min. (Not sure if that is reasonable but I haven't found info on how many % people usually exclude if you ask them about min and max) Then I have calibrated the order to make the distribution fit this.

resp. your reply from Feb 1st.:
I'm not sure if I understand correctly, I'd vary the delay ORDER for each level of the array meaning that the total order is the sum of the orders of the stocks in the array. And each level in the array would have a leakage outflow. But if I want to vary the order of each of the stocks in the delay I would still have to base the outflow of the stock on its inflow and then again I have the problem that the leakage outflow is connected to a stock that has no influence on the outflow in the aging chain, it would again be a stock that only does accounting. And that accounting would again be wrong because the outflow that is part of the higher order delay is not properly taking account of the leakage outflow.

I think it would work if I simply model an aging chain as an array, and then vary the actual number of stocks in this aging chain by changing the subscripts. Because then every stock only has a first order delay, so the stocks actually influence both the leakage and the aging chain outflows. But then I could not calibrate the order as I could do with DelayN.

[tomfid]

It seems like a funny dataset - I wouldn't think people would have accurate perceptions of lifetimes for durable equipment. Plus, as you point out, their confidence bounds may be uncalibrated.

Anyhow, I wouldn't think that a variable delay order between levels was desirable. Even if the leakage problem could be solved, aging is a deterministic process, and you wouldn't want any dispersion.

If it were a standalone model, I would tend to model this with a chain of first-order processes, using lag=time step=1, so that it was effectively discrete time. You could also use SHIFT IF TRUE if it has to reside in some larger model.

I assume you know this (later in the SDR):
http://www.systemdynamics.org/conferenc ... /P1064.pdf

Another option would be to use an array by model year or year of installation, rather than by age. That way you don't have to move things between cohorts, but you can still have an age-specific failure rate. That's how I'd do this in Ventity, I think. In Vensim, you'd be wasting some space for inactive model years, but the penalty might not be very great.