CAN'T MISS: Conquer Any Number Task by Making Important Statistics Simple. Part 7. Statistical Process Control: x–s Control Charts

Abstract

Statistical process control (SPC) can be thought of as the frequent monitoring of processes using inferential statistics. The feature that distinguishes SPC from the typical use of inferential statistics for analyzing populations is that in the former frequent samples are taken over time, whereas in inferential statistics a single sample is generaLLy taken before and after some intervention or treatment. An x-s control chart is used to monitor a continuous variable that reflects the output of a process. The x-s control chart is a graph that includes serial sample means (x) as the variables of interest, a centerline that represents the grand mean of the samples (x), and upper control limit (UCL) and lower control limit (LCL) that represent three standard errors (SEx) above and below the centerline. An x-s control chart is used to estimate with 99.7% confidence that the population mean of a continuous output variable was within the interval defined by the UCL and LCL during a period of baseline monitoring. It is further assumed that if the process remains stable, future population means wiLL remain between the control Limits for additional process outputs. Control charts allow the evaluation of both common- and special-cause variation. AnaLysis of the common-cause variation aLLows an assessment of the current process performance. Special-cause variation is identified when there is a sample mean that is beyond the UCL or LCL.