X̅ and R chart
In statistical process monitoring (SPM), the formula_3 and R chart is a type of scheme, popularly known as control chart, used to monitor the mean and range of a normally distributed variables simultaneously, when samples are collected at regular intervals from a business or industrial process. It is often used to monitor the variables data but the performance of the formula_3 and R chart may suffer when the normality assumption is not valid. This is connected to traditional statistical quality control (SQC) and statistical process control (SPC). However, Woodall noted that "I believe that the use  of control charts and other monitoring methods should be referred to as “statistical process monitoring,” not “statistical process control (SPC).”" The chart is advantageous in the following situations: The "chart" actually consists of a pair of charts: One to monitor the process standard deviation (as approximated by the sample moving range) and another to monitor the process mean, as is done with the formula_3 and s and individuals control charts. The formula_3 and R chart plots the mean value for the quality characteristic across all units in the sample, formula_8, plus the range of the quality characteristic across all units  in the sample as follows: The normal distribution is the basis for the charts and requires the following assumptions: The control limits for this chart type are: As with the formula_3 and s and individuals control charts, the formula_3 chart is only valid if the within-sample variability is constant. Thus, the R chart is examined before the formula_3 chart; if the R chart indicates the sample variability is in statistical control, then the formula_3 chart is examined to determine if the sample mean is also in statistical control. If on the other hand, the sample variability is "not" in  statistical control, then the entire process is judged to be not in statistical control regardless of what the formula_3 chart indicates. Limitations. For monitoring mean and variance of normal distribution, the combination of formula_19 S chart is usually better than that of formula_19and R chart. Moreover, changes in mean affect R or S chart and changes in standard deviation affects formula_19chart. Noting this, several authors recommend using a single chart that can simultaneously monitor formula_22and S.