# Discrete Response DOE Question

1. May 20, 2010

### diorio

Hi Everyone,

Im looking for some assistance on a problem that I have been working on for the last few weeks. I would like to optimise the performance of an accounts receivable department. In this dept there are several tools available to obtain a commitment to pay such as letters, phone calls, sms and others. I would like to run an experiment to determine the optimal use of these tools and I suspect that there may be some interactions between these factors.

I have researching how I can run a simple design of experiments to determine the optimal treatment. For example I could run a simple 2 level 2 factorial experiment:

Factors: Response:
Letter Call Account
Y Y Paid
Y N ?
N Y ?
N N ?

The issue that I have is that not only are my factors discrete (Y/N), my response is discrete as well (Paid/Not Paid). I am having difficulty finding an example of how to conduct a DOE with a discrete (binomial) response.

After some researching I am starting to believe I need to run multiple trials for each treatment. For example running multiple instances of: Letter Yes / Call Yes treatment so that I can obtain a resulting proportion (example: 4 of 7 customers treated in this manner paid - 57%), I have seen some places that there are suggestions to run np>5 number of treatments. If in this instance if I expect 70% proportion of people to pay, then I believe I may need to run n=5/.7=(7 to 8) trials of each treatment.

Can anyone advise if I am on the right track?

I have searched numerous six sigma and DOE references and haven't been able to reach a definitive conclusion. Is there anyone out there that could advise me or provide a similar example or book that may assist me with a discrete response DOE?

2. May 20, 2010

### zli034

You have 3 factors , i.e. letter, sms, and call, to control the incidences of get paid. Each factor has 2 level, yes/no. So you have 2x2x2=8 different treatments.

Say you decide to trial 80 customers, there are random 10 customers for each treatment. Resulting a data set of 80 rows, 4 columns. 3 columns indicate the factor used, and the last column indicates the payment.

Use ANOVA you can study the significance of the factors and their interactions.