In statistical quality control, the and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. 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).”" Uses The chart is advantageous in the following situations: The sample size is relatively large (say, n > 10— and R charts are typically used for smaller sample sizes) The sample size is variable Computers can be used to ease the burden of calculation The "chart" actually consists of a pair of charts: One to monitor the process standard deviation and another to monitor the process mean, as is done with the and R and individuals control charts. The and s chart plots the mean value for the quality characteristic across all units in the sample, , plus the standard deviation of the quality characteristic across all units in the sample as follows: . Assumptions The normal distribution is the basis for the charts and requires the following assumptions: The quality characteristic to be monitored is adequately modeled by a normally-distributed random variable The parameters μ and σ for the random variable are the same for each unit and each unit is independent of its predecessors or successors The inspection procedure is same for each sample and is carried out consistently from sample to sample Control limits The control limits for this chart type are: (lower) and (upper) for monitoring the process variability for monitoring the process mean where and are the estimates of the long-term process mean and range established during control-chart setup and A3, B3, and B4 are sample size-specific anti-biasing constants. The anti-biasing constants are typically found in the appendices of textbooks on statistical process control. NIST provides guidance on manually calculating these constants Validity As with the and R and individuals control charts, the chart is only valid if the within-sample variability is constant. Thus, the s chart is examined before the chart; if the s chart indicates the sample variability is in statistical control, then the chart is examined to determine if the sample mean is also in statistical control. If on the other hand, the sample variability is not