Comments on: Oh Snap! We Sent Bad Product to Our Customer: Fun with the Hypergeometric Distribution

By: Robert

Robert — Tue, 01 Sep 2009 13:15:48 +0000

So why talking about fixing the inspection system? If 36 products out of 1000 are busted, there is room for improvement on the manufacturing side…
Or was this about explaining the distribution in a simple way?

By: Sowrirajan

Sowrirajan — Fri, 21 Aug 2009 02:35:20 +0000

Hi
There seem to a basic problem with the sampling method they used.
Sampling methods use certain sample size formulae that are developed for well defined static population situations.
Though random sampling can be applied to stable processes we use systematic or sub-group sampling with clear time order to represent the process behaviour precisely.
Representativeness is the most important aspect of sampling.
Ron can correct me if i have faltered in my assessment please.

By: Ron Pereira

Ron Pereira — Wed, 19 Aug 2009 15:33:52 +0000

Gagandeep, the key to this analysis – and really any analysis that attempts to “infer” something from a sample of data is to ensure you do a good job sampling.

My example here was made up… but in order to do what I describe for real you’d need to have confidence in your sampling plan… also, you must know how many defects or defectives we’re starting with in order to infer anything.

So, if you don’t have any data on how many defects or defectives a process has this must be your first step. Go to gemba and observe first… Mintab second. Make sense?

By: Gagandeep S. Datta

Gagandeep S. Datta — Wed, 19 Aug 2009 15:20:01 +0000

Ron

I have a leading question to this … suppose we did not have the defectives count in the population (which 99.9% is true!). i.e.,

- the number of defectives in the sample = 0
- the size of the sample = 100
- the number of defectives in the population = “unknown”
- the population size = 1000

What I have boserved is that many examples assume ” the number of defectives in the population = the size of the sample” i.e.,

- the number of defectives in the sample = 0
- the size of the sample = 100
- the number of defectives in the population = 100
- the population size = 1000

Why is this so the case?

For e.g., suppose we want the probability of getting 3 winning numbers in a lottery of 49 numbers where we draw 6 numbers. This is equivalent to saying, any 3 from 6 in 49 of 1/49% (2.04%).

The resulting excel formula and result is =HYPGEOMDIST(3,6,6,49) = 1.77%

The reason I am seeking this is because Minitab asks for Sample-Size, Population-Size and Population-Defectives, REALITY is that we have defectives IN samples and NOT in populations (populations which are theoretically and practically infinite!).

Seek clarity.

Gagandeep

By: Ron Pereira

Ron Pereira — Wed, 19 Aug 2009 12:34:40 +0000

Thanks for the excellent analysis, Gagandeep! I, and I’m sure those without Minitab access, appreciate the time you took to share this!

By: Gagandeep S. Datta

Gagandeep S. Datta — Wed, 19 Aug 2009 10:56:51 +0000

When we talk of hyper-geometric distribution, we require the following data to establish a probability:
• the number of successes in the sample
• the size of the sample
• the number of successes in the population
• the population size

In excel the formula is entered as HYPGEOMDIST(the number of successes in the sample, the size of the sample, the number of successes in the population, the population size)

Let me first illustrate using a lottery example. For e.g., If we want the probability of getting 3 winning numbers in a lottery of 49 numbers where we draw 6 numbers, it is equivalent to saying, “any 3 from 6 in 49 of 1/49% (2.04%),” which in excel translates to: =HYPGEOMDIST(3,6,6,49) = 1.77%

So in the example stated by you, in this scenario,
- the number of defectives in the sample = 0
- the size of the sample = 100
- the number of defectives in the population = 36
- the population size = 1000

Which in excel translates to: =HYPGEOMDIST(0,100,36,1000) = 2.09676%

By: Anonymous

Anonymous — Tue, 11 Aug 2009 01:24:28 +0000

Do defects occur completely randomly or in clusters? If the latter i would think entirely random sampling might not be the most efficient.

By: Anonymous

Anonymous — Tue, 11 Aug 2009 01:20:08 +0000

If you were making teh widgets in lots of 10, testing every 10th wouldnt be the smartest idea. 10mod10=0

By: Jeff Hajek

Jeff Hajek — Sat, 08 Aug 2009 06:56:29 +0000

This article only talks about one shipment to one customer. The sampling plan is undoubtedly used on all of the shipments. So, out of every fifty shipments, it is likely that one will look good and actually be bad (consumer’s risk, or beta risk).
If this were the only inspection that happened and it had a problem, the most likely scenario is that there is a problem with the inspection process. I would look at that first.
On the other hand, if there were 49 other inspections that turned out right (i.e. properly categorized the lot), the sampling process might not be broken. Sampling is a shortcut, and carries risk. Every sampling plan will, eventually, have this kind of problem. Even with a sample size of 999, there is still a chance, no matter how small, that the one that isn’t inspected will be the one that is defective. That’s why sampling isn’t used for critical functions, like airport security.
There’s another important task, though. We don’t know how long ago the problem happened. Since there is only a 1 in 50 (ish) chance that this happened to the very first customer, the producer probably needs to be looking at prior shipments too.
The good news, though, is that the article mentions that a permanent fix (poka yoke) was put in place. It sounds like the company is on the right track–preventing defects at the source.

By: Ron Pereira

Ron Pereira — Tue, 04 Aug 2009 22:36:48 +0000

Hi everyone, thanks for your great and thought provoking comments. I really appreciate them.