# How many samples?

Six Sigma – iSixSigma Forums Old Forums General How many samples?

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• #27449

Brett G
Participant

Our plant manufactures 200,000 square yards of fabric per day. The fabric is shipped in rolls that are 125 feet long. Currently, we randomly sample ten (10) rolls per day and perform various tests on the specimens obtained from the sample rolls.

My question is this:

To be 95% confident that the results of my sampling for the day is indicative of that of the population for the day – how big of a sample should I take in a day (how many square yards or how many rolls, etc.).

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#67273

Grant Blair
Participant

Ten samples will get you within 1 standard deviation
of the average. If that’s close enough for you, then you’re o.k.

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#67274

ROSS
Member

Hi Grant,

I’m new to sampling…how did you go about determining the number of samples needed based on the situation? Should I use minitab or something like that to determine?

Thanks,
Tony

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#67275

Grant Blair
Participant

I wish it were that easy. Determining sample size depends on three things:
How close do I want estimate the true value?
Closer means take more samples.
How much risk am I willing to take?
Most people set this at 5%. This means if did this 20 times, I would be wrong 1 time. You can also say, I want to be 95% confident (1- % risk).
Use more samples to lower your risk.
How variable is the process I’m sampling?
Have to know a sigma. Higher the sigma, more samples you have to take.
Now, I’ve seen consultants make a lot of money calculating sample size,but I’ve always heeded the advice of an old friend who said “when in doubt, take 10 samples…you can sample the world with 10”.
This is based on a mathematical “trick”. When you set the difference you’re willing to detect at 1 sigma,
then the terms cancel out of the equation, and you will find that ~10 samples will work at 95% confidence.
Ten is also an interesting sample size when you are using control charts, but that’s another story.
Hope this piques your interest…a good statistics course will cover this in more detail (not all of them do, unfortunately!)

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#67278

“Ken”
Participant

Brett,

What is the purpose of the sampling? For instance, are you sampling to make an acceptance decision? Are you sampling to make and estimate? or, are you sampling to conduct a comparison test? Essentially, what is the objective of the sampling?

Ken

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#67284

Marc Richarsdon
Participant

I would like to put a finer point on what Grant wrote. He said “This means if did this 20 times, I would be wrong 1 time.” In actuality, a 5% confidence level means that if you employ this sampling plan 20 times, you just don’t know whether you are right or not one of the times you use it. In other words, it’s not that you will be wrong, it’s that you’re uncertain. Also, keep in mind that you can’t know when that one time is. It could be the first or the last of the 20 samples or anywhere in between.

Marc Richardson,
Sr. Q.A. Engineer

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#67286

“Ken”
Participant

Without knowledge on Brett’s specific objective, how can we determine if the confidence of the test is the desired probability? If a comparison is made perhaps the power of the test is a more important probability to prescribe.

I belive the selection of the sampling plan should speak to both quantities. But, they each may be different for different objectives. For comparison discrimination, such as in exploratory studies, higher power would be desired. For estimation work, such as in confirmation studies, higher confidence is desired. The test will determine the balance.

Without knowing the purpose of the test how can we adequately prescribe a sample?

If Brett is doing acceptance sampling, then he is trying to make a decision with high confidence. If Brett is comparing the performance of one roll of fabric to the others, then he may need higher power.

(my one-cent worth)

Regards,

Ken

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#67288

Neil Polhemus
Participant

You can sample the world with 10? An election poll with 10 respondents? A sample of 10 items from a lot of 10,000? Not my world.

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#67289

Grant Blair
Participant

I’m reading in Brett’s message that he just wants to know if everything he made that day is o.k.
Actually, sample size is the least of his worries:
How are rolls sampled randomly? Is a random numbers table used? Non-random sampling is a typical source of incorrect data.
Forget about no. of square yards…you can only sample the END of a roll of fabric. How do you know the rest of the roll is o.k.
What about differences across the width of the fabric?
This can really kill you, especially if you’re dyeing this fabric.
10 samples may make some people unconfortable, but one of the products my company made contained miles of yarn on each tube and one machine could produce hundreds each day. Sampling 10 tubes a week
worked fine, if you did it right.
Would also suggest a control chart might be useful here. Subgroup size of 10 gives excellent results.

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#67296

Grant Blair
Participant

Sounds like you’re someone who insists on counting every dimpled chad.};->
Census last year was good \$\$\$, thanks to guys like you…especially since they finally had to call in the statisticians to develop a sampling plan which corrrected the so-called 100% count.

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#67297

Anonymous
Participant

Ignore the comments of the “experts” on steriods above. More important to one up one another. Go read Juran’s QC Handbook on sample size. It is better advice than you will get from these Cheeseheads.

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#67300

Anonymous
Participant

G,

There’s one thing you can’t do is read Brett’s mind. You really don’t know what he wants. Better to have Brett tell us.

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#67323

Anonymous
Participant

Gary C., is that you???

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#67325

Gary Cone
Participant

Dear Anonymous,

I am flattered that you would attribute such a direct comment to me, but not me this time. I live too close to Wisconsin to be throwing those comments. I usually offend the west coast types.

I do however agree with the offer of a reference instead of an opinion.

Thank you again.

Gary

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#67351

Brett G.
Participant

My primary concern for the sample size (actually, sampling frequency) is to just ensure that given the “population” size for the day – am I sampling enough so that the results of the tests are representative of the population.

We’ve addressed other concerns such as ensuring true randomness, considering variation within (across the width of our fabric) each sample, control charts, etc.

We actually do use a sampling frequency of ten rolls per day currently. Because an n of ten is somewhat large, we are not using an X bar R chart, but instead an X bar S chart. We are happy with what our control chart is doing for us – we were concerned as to “is ten samples enough or should we be obtaining thirty (or so) samples each day (and have three points plotted per day on our control charts).

Thanks for the help – and insight.

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#67354

Grant Blair
Participant

You’re doing it exactly right. Don’t change a thing.
Since I mentionned in my post taking 10 samples per week, just wanted to raise a word of caution. You need to be really comfortable with your process. The process used in my example started with sampling every shift, which is where you were thinking about, then was moved to every day. Move to once per week was
based on a years of experience and data indicating stability.

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#67356

“Ken”
Participant

Brett,

Thanks for following up before this discussion spun to far out of control…

The primary question appears to be associated with the “frame” underwhich your sample is selected. The frame defines the sampling frequency, how the rolls are selected, and how each are measured for example. The selection of ten rolls throughout the day, about one roll per hour, tells me that you may expect the process to change on the order of every 2 or 3 days. When considering how frequent to select these samples, two concerns should be addressed:

1. How frequent you expect the process to change.
2. How tightly you want to control the process.

My question would be: How frequent does this process change when looking at past control charts? For instance, if the mean change frequency with all process controls in place is on the order of months, then perhaps you could try relaxing the sampling period from every hour to every two hours. However, if the process exhibits weekly inconsistent behavior, then you may want to increase the sampling frequency to every 1/2 hour to get a finer resolution on the timing of the causes. In this case, it’s not a confidence you’re looking to assess, it’s an observation of the change in the process.

For concern number 2 above, we are asking how tight you want to place the control limits to observe a change. To determine this criteria, one needs to know the capability of the process, Cp, and how well they want to control the average shift in the process from the desired target. In your case, with a sample size of 10 rolls per day you should be able to detect a minimum change in the process of 1 sd from the target within 2 periods, i.e 2 days. Relaxing the daily sampling to 5 would take about 5 periods, 5 days, before you would observe the same shift in the process.

To determine the impact, you need the capability of the process. For example, if your process had a Cp of about 1.7, and you used a 10 roll sample per day, then it would take you about 2 days to detect a shift of 1 sd that would produce about a 0.135% defect rate if this shift persisted.

So, in the final analysis the number of samples used per day depends upon: the process stability(frequency to unstable observations), process variability(tied to capability), and the level of control desired, with all other sampling frame factors you discussed earlier assessed correctly.

If you’re interested in the calcs for above, send me an email.

Reg

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#67357

“Ken”
Participant

Brett,

A minor correction to my previous post. A process with a Cp=1.7 is about 5 sigma, not a 4 sigma process as I originally used. The defect rate would go from 1350dpmo to about 32dpmo. These estimates obviously assume the data are distributed normally.

Ken

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