# [R] Suggestions as to how to proceed would be appreciated...............

Bernard McGarvey mcg@rvey@bern@rd @end|ng |rom comc@@t@net
Sun May 22 19:39:54 CEST 2022

```I work in aspects of Cold Chain transportation in the pharmaceutical industry. These shippers are used to transport temperature sensitive products by surrounding the product load box with insulating materials of various sorts. The product temperature has lower and upper allowed limits so that when the product temperature hits one of these limits, the shipper fails and this failure time is teh shipper duration. If the shipper is exposed to very low or very high ambient temperatures during a shipment then we expect the duration of the shipper to be low.

The particular problem I am currently undertaking is to create a fast way to predict the duration of a shipping container when it is exposed to a given ambient temperature.

Currently we have the ability to predict such durations using a calibrated 3D model (typically a finite element or finite volume transient representation of the heat transfer equations). These models can predict the temperature of the pharmaceutical product within the shipper over time as it is exposed to an external ambient temperature profile. .

The problem with the 3D model is that it takes significant CPU time and the software is specialized. What I would like to do is to be able to enter the ambient profile into a spreadsheet and then be able to predict the expected duration of the shipper using a simple calculation that can be implemented in the spreadsheet environment. The idea I had was as follows:

1. Create a selection of ambient temperature profiles covering a wide range of ambient behavior. Ensure the profiles are long enough so that the shipper is sure to fail at some time during the ambient profile.

2. Use the 3D model to predict the shipper duration for the selection of ambient temperature profiles in (1). Each ambient temperature will have its own duration.

3. Since only the ambient temperatures up to the duration time are relevant, truncate each ambient profile for times greater than the duration.

4. Step (3) means that the ambient temperature profiles will have different lengths corresponding to the different durations.

5. Use the truncated ambient profiles and their corresponding durations to build some type of empirical model relating the duration to the corresponding ambient profile.

Some other notes:

a. We know from our understanding of how the shippers are constructed and the laws of heat transfer that some sections of the ambient profile will have more of an impact on determining the duration that other sections.
b. Just correlating the duration with the average temperature of the profile can predict the duration for that profile to within 10-15%. We are looking for the ability to get within 2% of the shipper duration predicted by the 3D model.

What I am looking for is suggestions as to how to approach step (5) with tools/packages available in R.

Bernard McGarvey, Ph.D.

Parenteral Supply Chain LLC

Bernard.First.Principles using gmail.com mailto:Bernard.First.Principles using gmail.com

(317) 627-4025

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