# Large sample size in xbar / s charts.

Six Sigma – iSixSigma Forums Old Forums General Large sample size in xbar / s charts.

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• #28905

Stan Alekman
Member

We are legally required to sample ten units at random from each production batch of approximately 5 million units, assay each unit individually, take the average, calculate the standard deviation and the %RSD, and compare the average and RSD to requirements. We want to chart the average and standard deviation but are concerned about the ten unit size. For control chart purposes, sample sizes of 3 to 5 are usually used. Larger sample sizes are usually not recommended. Can someone comment on the size and direction of the bias that may occur from sample sizes of ten in the calculation of the upper and lower control limits? And identify other problems. Thank you.
Stan Alekman

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#72745

Whitehurst
Participant

Statistically, the correct sample size is calculated by the amount of variation in your process, the confidence level you want to have in the data, and how much of a process shift you would like to detect with your sample size.  The formula is:  n= (Z^2*sigma^2)/d^2.  Once you have this information then you consider the risk,  cost, and amount of time time perform the testing.

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#72817

RR Kunes
Member

A sample size of ten is perfect for a Xbar and R chart. Use minitab or similar software to do the work for you. Remeber you do not change the control limits everytime. Collect 25 -30 subgroup samples, calculate the control limits and leave them alone unless you significantly chnage the process.
Xbar and S charts are utilized when your sample is sifficiently large to actually calculate a sample standard deviation. I would say the sample must be over 25 (or larger) to use Xbar and S.

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#72828

Ropp
Participant

Stan –
Subgroup size does detiremine sensativity of a control chart, but the formula referenced is not how to do it. The formula Joe mentioned is for calculating sample size for a t-test of means. It has no usefullness in control chart applications. Get a copy of “Advanced Topics in Statistical Process Control”  by Don Wheeler and read chapter 9 on power functions to understand this topic. Or find any good SPC book that discusses power functions( or OC curves) and ARL.
A range chart is OK or a SD chart either one for dispersion at subgroup size 10. Some authorities recommend SD charts for subgroups over 7 or 8 based on theoretical properties of the d2 method of estimating the subgroup sigma, but in practice range charts probbaly work well up to some higher sample size.
The major question I have is why do you want to control chart this information at all? What will you do with it?
If you say to do process improvement, you will have to tell what you are making that ten out of 5 million will be a fair representative sample to indicate anything. Surely you will be confounded by shifts or machines or cavaties in a mold or numerous other factors that cause  ten in five million to not be a rational subgroup.
If you just want a pretty chart to put on the wall to give an illusion that something is being done, it won’t much matter what you do. A run chart would be OK. CUSUM charts with a v-mask are much more dramatic and will serve the same purpose as far as controlling or monitoring the process. That is to say , no purpose at all.
I urge you to think through what you are doing.

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#72832

Aquinas
Member
#72845

RR Kunes
Member

The response generated by Joe is exactly why some forms of six sigma training never work.
To utilize a Z value to calculate a sample size is ludicrous. We are talking about process sampling not Hypothesis testing.
The old standard was Mil-std-105e now is is an ASQ Z1 ….
The sampling tables are based on two things. Alpha risk and Beta risk. What chance are you willing to take to accept a bad lot or accept a good lot. These sampling plans have proven statistics begind them.
But I believe your question was more about why you use an Xbar and R versus an X bar and S. For your sample size use an Xbar and R.

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#72865

Mike Carnell
Participant

dave,
Nice technical response on the control  chart.
You took off on a rant about why do it. Sentence #1 in the original question “….it’s a legal requirement.” He is just trying to comply with a law someone else put in place. Give the guy a break.

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#72890

Gabriel
Participant

Stan. It is a legal reuierment. Just do it. I see no problem at all in charting Xbar – S with subgroups of 10. Just follow the standard procedure, as described by RR Kunes. Colect 25 subgroups, calulate control limits, follow up with this control limits. The only questionable thing is why 10 every 5 Millons. May be you want to implemet a more frequent sampling. How long does it take to make this 5 millon batch? Several days, I think. If you chart Xbar and S using subgroups of 10, for example twice a shift, you will be exceding the legal requierments (for each batch you will have not 1 but many samples of 10 pieces) and this practice can give you some added value (not just meeting a legl requierement). Of course this deppends on the process and product. For example, if a destructive test is involved it may not be a good idea after all.
Good luck.
Gabriel

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#72893

Ropp
Participant

Mike –
It’s a hot button of mine. I think Stan is being fed a line of bull about “legal” requirement. He responded this morning under another thread. I am very dubious of any regulatory agency requiring a specific plan. I hope Stan responds further and clears it up.

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