A point outside a limit suggests the stable historical model may no longer explain the process, while all points inside do not guarantee control. Runs, trends and other nonrandom patterns can also be signals. Use established chart rules with care and avoid searching for causes after every ordinary fluctuation.
NIST distinguishes chart forms for individuals, subgroup averages, ranges, standard deviations, counts and proportions. The simple mean ± kσ expression is valid only when the supplied σ belongs to the plotted quantity. Autocorrelation, changing mix or poor measurement systems can make limits misleading.
Control limits support process learning; specification limits describe required output. A process can be stable but incapable of meeting specifications, or unstable while current points remain within specifications.
Before calculating limits, establish that the baseline data come from a reasonably stable period. If assignable causes contaminate the baseline, the estimated mean and spread can be too wide or shifted. Measurement resolution and gauge variation should also be adequate for the changes the chart is meant to detect.
The multiplier balances sensitivity and false alarms. Narrower limits detect smaller shifts sooner but generate more signals from common variation; wider limits do the reverse. Run rules can improve sensitivity to sustained small shifts, but applying many rules also raises the chance of a false signal. Choose the plan before reviewing results.
Zero standard deviation places both limits at the mean, which mathematically describes no measured variation but is rarely credible for a real process. Check for rounded data, too little baseline information or a broken measurement system before using such limits. Likewise, an LCL below zero may be mathematically symmetric yet physically impossible for a nonnegative measurement. A chart-specific convention may set it to zero, but this general calculator deliberately reports the raw symmetric result so the analyst can make that documented choice.