If you need upperlimit and lowerlimit and you already have control limit you want to evaluate, control mean and control standard deviation, this calculator does the substitution for you. It suits a quick check, a homework answer you want to confirm, or any figure you need to sanity test.
What Is the Upper Control Limit Calculator?
The upper control limit calculator turns a set of measurements into upperlimit and lowerlimit, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Upper Control Limit Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with control limit you want to evaluate set to 10, control mean set to 5, control standard deviation set to 2, the calculator returns upperlimit of 25, and lowerlimit of -15. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out upperlimit?
Enter control limit you want to evaluate, control mean and control standard deviation. The calculator then works through the relationship and reports upperlimit and lowerlimit.
What does the upper control limit actually calculate?
It takes control limit you want to evaluate, control mean and control standard deviation and converts them into upperlimit and lowerlimit using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter control limit you want to evaluate?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.