Discrete Response DOE

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    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?



    Just a quick thought, are you trying to find out if one contact method or another is better at gaining a payment? If so, would it not be valid to look at the length of time between contact and payment and discover which produces the quickest payment?



    I think you are making this more complicated than it needs to be. I suppose you could run the DOE and regress your findings using binary logistical techniques, but why?

    It would be much easier to simply use a continuous metric as your RV, or better yet, give up on the DOE idea and run some simpler analytics to answer your crtiical research questions: Which method provides the shortest pay cycle?

    Good luck.

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