Friday, October 04, 2013

Marriage 601, Lecture 231: Process capability and marriage, or, What are the odds of getting sick on a Saturday? Like one in a thousand?

From wikipedia:

The Process Capability is a measurable property of a process to the specification, expressed as a process capability index (e.g., Cpk or Cpm) or as a process performance index (e.g., Ppk or Ppm). The output of this measurement is usually illustrated by a histogram and calculations that predict how many parts will be produced out of specification (OOS).

You measure the process capability by looking at the data of the outcomes and deciding if the process is in statistical control. It helps if the process has a normal distribution. You calculate your standard deviations and your process mean and then you look to see how many of the outcomes are within your tolerance levels (that is, the upper control limit and the lower control limit).

If most of your results are clustered around zero, you have a tight process. But if a lot of your results are in the tails of the curve - more than a couple sigma out, then you have a problem.

Let's look at the outcome from my washing dishes. This is more of a binary problem, but let's introduce some nuance into it.

Let's say that I wash the dishes and then SH eats from those dishes. There are a few outcomes:

1. He does not get sick (value = 0)
2. He feels a little bit sick (value = 1)
3. He feels a lot sick (value = 2)
4. He dies (value = 3)

(BTW, I think this is a one-sided problem, as I cannot assign negative values to these outcomes, unless eating off the dishes I washed would make SH more healthy than he is already.)

If I wash dishes 100 times and SH never gets sick, then all the data points would be clustered around zero.

If I wash dishes 100 times and he mostly never gets sick - maybe he gets a little bit sick ten times, then 90 of the data points will be at zero and the remaining ten will be at one.

If I wash dishes 100 times and SH always gets sick, then all the data points will be around two. (Let's ignore the fact that none of these are normal distributions. Wait. Let's just say that this distribution comes from the overall dishwashing/health experiences of the entire population of the US and that's the standard and I want to see how I fit into it.)

You look at the results and decide if they fall into the acceptable range: between the upper control limit and the lower control limit. Those limits determine how many times can someone get sick before you change the process.

Once you have analyzed your process and discover that you do not like the results, you have two options:

1. Reduce the variability (which is when you use a six sigma project).
2. Expand the tolerance.

In any project involving SH, I can predict how he will want to proceed: He will want to reduce the variability, i.e., change the process so there are no outliers in the outcomes. That is, he would want me to take three times as long to wash dishes as I already do.

I can also predict how I would want to proceed: I say increase the tolerance. I say, SH accepts being a little bit sick very occasionally. If he doesn't like that outcome, then I say we can reduce the variability in the process by changing the process so he washes the dishes all the time.

Marry someone with the same approach to process capability as you is my advice.

1 comment:

LPC said...