How many samples?

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

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

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

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.

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.

Gary C., is that you???

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.

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