How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL

Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

Steve Prevette said:

2.66 is used in the case of the average moving range - taking the absolute value of the difference between sequential points. You are in effect using a subgroup size of 2 when you do that. d2 is 1.128, 3/1.128 is 2.66.

Click to expand...

thanks for your kindly explain, Steve

but my major query is: there is only 30 data and not have subgroup; according to your mentioned, as long as these data are sequential data, all of this situations could be served as two subgroup?
so no matter how many data, the indicate is 2.66, it's that right?

Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

ssz102 said:

thanks for your kindly explain, Steve

but my major query is: there is only 30 data and not have subgroup; according to your mentioned, as long as these data are sequential data, all of this situations could be served as two subgroup?
so no matter how many data, the indicate is 2.66, it's that right?

Click to expand...

If you plot the 30 individual points, and then average them for the baseline, and calculate the moving range for use as the UCL and LCL, then , yes, the mutliplier on the moving range is 2.66. Sometimes referred to X-individuals chart. For completeness, you should also do a Range control chart to be sure the range is stable and can be utilized as the estimator for the standard deviation.

Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

Steve Prevette said:

If you plot the 30 individual points, and then average them for the baseline, and calculate the moving range for use as the UCL and LCL, then , yes, the mutliplier on the moving range is 2.66. Sometimes referred to X-individuals chart. For completeness, you should also do a Range control chart to be sure the range is stable and can be utilized as the estimator for the standard deviation.

Click to expand...

many many thanks for your kindly response, steve

Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

Sigma = (Average Range) / d2

Or rather

Sigma = (Average Moving Range) / d2

Or using the notation above

Sigma = MR-Bar / d2

To estimate Sigma and use it in the formula for n=1 subgroup sample size Control Limits as above

Mean +/- 3 x Sigma

Or

Mean +/- 3 x (MR-Bar / d2)

Or

Mean +/- (3 / d2) x MR-Bar


Now the question is, what is the value of d2 for converting Ranges to Standard Deviation for samples of size n=2? Look in any typical Quality Control table and you will find that for n=2 then d2=1.128. This value is a characteristic of Normal Distributions.

So we have

Mean +/- (3 / 1.128) x MR-Bar


But 3 / 1.128 is 2.659 or about 2.66.

So we have

Mean +/- (2.66) x MR-Bar

Which is the magic formula