# Variable data w/ varying sample size

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• #39278

April
Participant

What is the best chart type to construct given variable data and a varying sample size? The mean for a service process is calculated weekly with a population that varies roughly between 40 – 60. Given the varying sample size, what is the best way to calculate an upper control limit for this process? Can A and B values be used with a mean with sample sizes this large, and if so how do I use A and B values with varying sample sizes. Thank you in advance.

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#119197

Utah123
Member

Subgroup the data daily (if it makes sense), average it, and plot it on an xbar/R  if n is between 2-9 or xbar/s if greater thatn 10.  Use excel or minitab for UCL and LCL calculation.

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#119203

FTSBB
Participant

Individuals & moving range chart if you want one set of control limits for all the data.  The method mentioned by Utah calculates different control limits for each subgroup.

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#119347

April
Participant

Does it make sense for me to use the Xbar/s chart given a population mean or is this only valid for samples? Thanks

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#119352

FTSBB
Participant

The statisticians out there will probably smell blood in the water, but I almost always use the range method for estimating variation, just because it is easier to understand and compute than s.  There are (strong) arguments that show the error in the variation component using R charts are significant for n>10 {or >12 (Juran) or >15 (Wheeler)}, but I rarely use subgroups this large.  For the individuals chart, n=1.
If you’re using MINITAB, the “help” icon on each command does a good job of describing the use of each chart and also shows the equations used.  Might try reading these and decide which chart makes more sense to you.  Look at the I-MR versus the I-MR-R/S options.
Hope this helps.

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#120225

ALEK DE
Participant

FTSBB, A small correction. In I-MR , n is generally 2.

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#120245

FTSBB
Participant

For individuals chart n=1, hence the name “individual”.  The bias correction factors and control constants use the values for n=2, as you are comparing two subsequent measures.  See Understanding Statistical Process Control by Donald Wheeler, page 48, for a good example.  There are probably countless other texts on I-MR – take your pick.

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#120260

ALEK DE
Participant

Possibly it’s a different way to understand thing. My interpretation of a group is no of samples in a sub group & that’s important when we use Range as estimate of variation , d2 constatnt changes with the the no of samples in a sub group. In I/MR , moving range is generally with two subsequent data points & hence I commented ( becaz here d2 is corresponding to sample size-2). In individual chart it’s always individual – no confusion on that. Hope we are talking the same thing.
Thanks.

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