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:

An interesting thing nowadays is that in Excel spreadsheet is is actually easier to calculate s, not the moving range. Yet, we stick to using moving ranges.

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Not only is standard deviation easier to calculate, it is a better, more accurate way than the range (or moving range). You see books with rules of thumb like "Use s whe the subgroup is at least 10 because it is more accurate". In truth, s is always better than r (except for n=2, when they tie). The difference between the two is small for small n, but why not use the better method.

For manual plotting, I can see using Xbar-R, but with a computer, Xbar-S is better for getting the proper control limits.


Tim

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

OK now lets see if I have this right r- is not as accurate as s so we should use s rather than r-. So are we all doing it wrong?

I am trying on writing a training paper on SPC to both operators and technicans and from experiance I just know what the questions will be as some of the questions have been fun so far this is how I feel trying to explain the simplest of things to them.

beofre I do this any one got:
1. A copy of an x bar r chart with the formulae on it
2. A simple guide to SPC

Thanks ever so

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

Andy, IMHO there is no right or wrong control limits as far as they show the behabiur of the process.

(broken link removed)

"S" insteed of "Ranges", as better could be based on the idea that more data give a more precise estimate, but each tool has it's own application on wich it's the best option. MR is better for continuos process, and "S" is a good idea if the data is logically related to a group of data.

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

to be statistically correct, the standard deviation is a better estimator of the variation than the Range any time n>2. HOWEVER, for all practical purposes when n is <10 the Range is useful. Particularly if you are doing manual charts where the operator must calcualte the points by hand, the range is a better choice. however, if you have a large sample size, you should use the standard deviation - the estimate is much better, d2 values for 11-25 are tough to find, and it is hard for the operator to accurately find the min and max value.

if you are using computer software - there is no reason to use the range.

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

Many thanks as for feeling charitable I will be posting several packs I have written soon just as soon as I have used them on test subjects. They will range from SPC to FMEA to Design For Six Sigma

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

Bev D said:

of course the LCL and UCL do not provide an assessment for capability. But, the OP had a very limited and specific question. I answered that question but only after thinking about it for awhile as the OP had obviously not researched the question on their own and provided so little information on his issue that any answer we could give would be highly likely to be mis-used.

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This is true. It is not clear if these represent one point is time, random sampling, time series samples from a process etc. Tensile testing should provide a normal distribution, as the variation is typically a 'natural variation'. That would support most of the calculations mentioned in the responses. But, under non-normal circumstances, these calculations may not apply. So, for those reviewing this thread, control limits are not representative of capability for X-bar R charts, but are used for precision machining, where capability= (USL-LSL)/(UCL-LCL) due to the uniform distribution. Also, UCL and LCL are set by the user, typically centered at 75% of the specification, not calculated using the formulas in this thread.

Just wanted to make sure that those reviewing this thread based on its title are not left with the impression that the control limit calculations can be rubber stamped to every situation.

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

i have an other question on these tables. can anyone provide me with these constant tables for A2, D2, D3, C4 etc.. maybe they are posted somewhere online? because all the tables that i've found only go until subgroup size 15 or so and i need them for higher subgroup sizes...

thx in advance

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

zlatanibra said:

i have an other question on these tables. can anyone provide me with these constant tables for A2, D2, D3, C4 etc.. maybe they are posted somewhere online? because all the tables that i've found only go until subgroup size 15 or so and i need them for higher subgroup sizes...

thx in advance

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Duncan's book "Quality Control and Industrial Statistics" tables them to 25. It also provides the formulas for estimating the constants. Might also want to look at ASTM Manual on Quality Control of Materials (pg 115)

May I ask why you are doing control charting with subgroups that large?

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

I posted the table of factors (up to n=25) and formulas in a previous thread titled Formulas for Factors d2 and d3 for range charts
Formulas for Factors d2 and d3 for range charts

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

2.66=3/1.128