X-bar_and_s_Charts.docx - NCSS Statistical Software NCSS.com Chapter 243 X-bar and s Charts Introduction This procedure generates X-bar and s(standard

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NCSS Statistical Software NCSS.com Chapter 243 X-bar and s Charts Introduction This procedure generates X-bar and s (standard deviation) control charts for variables. The format of the control charts is fully customizable. The data for the subgroups can be in a single column or in multiple columns. This procedure permits the defining of stages. For the X-bar chart, the center line can be entered directly or estimated from the data, or a sub-set of the data. Similarly sigma may be estimated from the data or a standard sigma value may be entered. A list of out-of-control points can be produced in the output, if desired, and means and standard deviation values may be stored to the spreadsheet. X-bar and s Control Charts X-bar and s charts are used to monitor the mean and variation of a process based on samples taken from the process at given times (hours, shifts, days, weeks, months, etc.). The measurements of the samples at a given time constitute a subgroup. Typically, an initial series of subgroups is used to estimate the mean and standard deviation of a process. The mean and standard deviation are then used to produce control limits for the mean and standard deviation of each subgroup. During this initial phase, the process should be in control. If points are out-of-control during the initial (estimation) phase, the assignable cause should be determined and the subgroup should be removed from estimation. Determining the process capability (see R & R Study and Capability Analysis procedures) may also be useful at this phase. Once the control limits have been established of the X-bar and s charts, these limits may be used to monitor the mean and variation of the process going forward. When a point is outside these established control limits it indicates that the mean (or variation) of the process is out-of-control. An assignable cause is suspected whenever the control chart indicates an out-of-control process. 243-1 © NCSS, LLC. All Rights Reserved.
NCSS Statistical Software NCSS.com X-bar and s Charts Other Control Charts for the Mean and Variation of a Process The X-bar and s charts are very similar to the popular X-bar and R charts, the difference being that the standard deviation is estimated from the mean standard deviation in the former, and from the mean range in the latter. The X-bar and s charts are generally recommended over the X-bar and R charts when the subgroup sample size is moderately large ( n > 10), or when the sample size is variable from subgroup to subgroup (Montgomery, 2013). Two additional control charts available for monitoring the process mean are the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts. The CUSUM and EWMA charts differ from the X-bar charts in that they take into account the information of previous means at each point rather than just the current mean. The CUSUM and EWMA charts are more sensitive to smaller shifts in the mean since they use the cumulative information of the sequence of means. However, CUSUM and EWMA methods also assume a reliable estimate or known value for the true standard deviation is available.