What should I use for Variable Sample with Size 3, 4, and 5 - xbar-R or xbar-S?

[sunff114]

According to Montgomery (1996), if we have variable sample sizes, we should use xbar-s chart, rather than xbar-r chart, because r chart will produce a changing center line (but i don't understand how).

The data we collected consists of 4 samples of size 3, 1 sample of size 1 and 47 samples of size 5, so most samples have size of 5.

Should i use xbar-R because of the small sample size(3,4,5)? I know Minitab can take care of it with variate UCL and LCL.

or

Should i delete those samples with 3 or 4 so that we can have constant sample size 5?

or

Should i use xbar-S chart because of the variable sample size?

I did all of the three ways, the results shows little or no difference probably because the process is stable. I prefer not to delete samples with size 3 and 4, and use xbar-R chart to analyze, but i am trying to search papers online to surpport this method. i didn't find it.

Dear experts, please give me some suggestons!

 

[kaikai]

From statistical standpoint, xbar-s chart is preferable to xbar-R chart.
Because R uses only 2 data of each group but s uses all data of each group.

 

[Bev D]

What kaikai said is correct, although at those small sample sizes the improvement is not very helpful - it doesn't change the action you would take.

And your instinct to keep the smaller sampels in your data is correct. Minitab (or JMP) will adjust the control limits appropriately for each sample size. It will do this for both R charts and S charts...you are safe either way.

 

[sunff114]

Thanks, KaiKai.

But for small sample size, say n<5, the range method works pretty well for estimating the standard deviation. If n>10, then the range method lost its efficiency rapidly and regular standard deviation (s chart) comes into play.

 

[sunff114]

Thanks, Bev D! I am a newbie for SPC, always questions.