# sample size and subgroup size

Six Sigma – iSixSigma Forums Old Forums General sample size and subgroup size

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• #37689

Dmitry
Participant

I have read notes and comments made about sample size and subgroup size and I understand the importance of both parameters for interpretation of the results. These parameters are different depends upon the type of process, level of confidence you want to achieve and size of population.  In production world we have to statistically evaluate the whole population (for instance, the total quantity of customer order) and at the beginning we need to choose the amount parts we need to take for our analysis (sample) and, then, choose the subgroup size for selected sample size. We know only the total amount of population (total parts in order),  parameter(s) we need to monitor, and, of course, the level of confidence (mostly it is 95%). Does anybody know, how to calculate the required sample size and subgroup size for chosen sample in this case? And, what approach we have to use to resolve that?

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#111393

Ken Feldman
Participant

A few questions first:
1.  Do you wait until you have produced the entire customer order before taking your samples from that batch?
2.  Do you take samples from the process during the run of the customer order?
3.  What are the parameters that you are measuring, are they continuous or discrete?
You have also forgotten to mention the importance of desired precision and estimated population variation in addition to the confidence.  All three factors are needed to estimate the sample size.

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#111394

Dmitry
Participant

Thank you, Darth, for respond. Trying to answear your quastions. I am taking samples during the process run (but, of course, I need to know my sampling size beforethe run). I am measuring ID of cylindrical parts. And, of course, I need to measure specific spot of ID to avoid variation due to difference in location of measurements. Total tolerance can be either 0.0005″ or 0.001″, depending on the part (drawing requirement). Well, I thing, it is continuous parameter. Beside that, sometimes, I have to measure AOL (overall lenght), and total tolerance of it usually bigger: from 0.002″ to 0.005″

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#111397

Ken Feldman
Participant

About how large is a run?
About how long does a run last?
It appears that you are trying to do two things.  You seem to want to monitor the process over the length of the run to see if the process is exhibiting common cause or special cause variation.  You also seem to want to make an inference about a product parameter.  By doing so, you will likely come up with some confidence interval around your sample mean and determine if your run is within tolerance.
It sounds like you are trying to use a Systematic Sampling scheme, that is some fixed number per time period so that the total sampled will equal your total sample size.
To determine your sample size, you will need some estimate of the standard deviation of your parameter as well as some degree of precision which might be your tolerance.
Is all this making sense to you?

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#111402

Dmitry
Participant

Yes, you are right. I am trying to monitor the process over the length of run. And it is important to “cover” first and last pieces. I am trying to see of my process is within control limits and fluctuating around the center line on control chart (I use usually Xbar/R chart). My run can be from may be 100 pieces to 5000 the maximum. Usually it is up to 1000. It is hard to say how long it is going to last. I remember, if it is close to the max (50000) it might be around a week if 3 shifts are working (8hours/shift). I use subgroup size 5 every 1/2 hour for orders up to 1000. And it is fixed number during specific run.But, besides that, I need to sample order that has already been made (not during the run). In this way I need to know how many pieces I need to take for analysis and, then, what subgroup size I need to use, when I start processing that sample size. Usually I take around 30-40 sample and process this sample with subgroup size 3 or 5. I draw Xbar/R chart, calculate control limits to see if process is under control. I do normality test. Then, I build histogram and calculate Cp/Cpk for two subgroup sizes to see if how much the difference for Cp/Cpk. I just wondering about how is it right to do and be more specific about sampling and subgrouping.You said about confidence interval. If I know my total tolerance for chosen parameter, should my confidence interval be equal or close to that number? And, talking about standard deviation, do you mean the standart deviation around the mean for all collected data during the run (which will help me to determine the sample size)?

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#111470

Johnny Guilherme
Participant

Dmitry
Why not go to valid sampling plans i.e. “ANSI/ASQ Z1.9-1993 Sampling procedures and tables for inspection by variables for percent nonconforming”. For the batch size and the inspection level desired plus the AQL value for the type of defect, major, minor or crtical the tables will indicate what sample to pull and what your acceptance criteria will be.
For inprocess control (over length of run) you can decide on the sample size and frequency. Typically what I have used is a sample size of 5(you can also use 4 or even 3). The frequency is decided by yourself. Typically if your process is new, then maybe sample more often. Once the process is under control you can reduce the frequency for pulling your sample.
Hope this helps-(if I have understood your question correctly??)
Johnny

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#111484

Brian.P.M.
Participant

Dmitry,
A far as sampling the completed run and building an Xbar/R chart after the fact, the horizontal axis on the chart is time and unless the parts you are sampling are time ordered the chart will be meaningless. I believe that you can still create the histogram and do the capability studies IF the process is known to be in control. But since you are drawing from a lot that wasn’t control charted you really can’t be sure of those assumptions or the results of the capability studies.
Hope this helps some.
Brian.P.M.

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