![]() In the bag weight example above, the subgroups were formed so that the X chart examined the variation in the average bag weight for the subgroup from hour to hour while the s chart examined the variation within the subgroup from hour to hour. The subgroups should be formed with rational subgrouping in mind. The standard deviation gives a better estimate of the variation in large subgroups than the range does.ĭata has to be frequently available (multiple samples per hour, day, or week). But, you definitely should use the X-s charts when the subgroup size is 10 or more. This means they can be used in place of X-R charts all the time. You can use X-s charts for any subgroup size greater than 1. Like all control charts, they will send a signal when a special cause of variation is present. X-s charts are used to analyze a process operating over time. The process is consistent and predictable in the near future. The next result will be between 50.1 and 50.49 with a long term average of 50.3. Since the X chart is in statistical control, the variation in subgroup averages (the hour-to-hour variation) is consistent over time. We don't know what the next s value will be, but we do know that it will be between 0.06 and 0.34 with a long term average of 0.2. Since the s chart is in statistical control, this means that the variation between the individual bag weights (the within-hour variation) is consistent over time. The bagging process represented by control charts above is in statistical control. The middle line is the overall process averag the upper line is the upper control limit and the lower line is the lower control limit. This is the subgroup standard deviation (s). The standard deviation of the ten bags is calculated. The average weight of the ten bags is calculated. The ten bags are used to form a subgroup, so the subgroup size (n) is 10. This provides frequent data as well as a method of rationally subgrouping the data. Ten bags are weighed at the start of each hour. Each bag should contain a minimum of 50 pounds (lbs) of sand. A company is tracking performance of a bagging machine. The figures below are an example of an X-s chart. As for the X-R chart, frequent data and a method of rationally subgrouping the data are required to use the Xbar-s chart. The constants used to calculate the control limits and to estimate the process standard deviation are different for the X-s chart than for the X-R chart. One advantage of using the standard deviation instead of the range is that the standard deviation takes into account all the data, not just the maximum and the minimum. The major difference is that the subgroup standard deviation is plotted when using the X-s chart, while the subgroup range is plotted when using the X-R chart. Yet, the X-s chart is very similar to the X-R chart. The standard deviation is just not as easy to understand as the range. In the past, there has been reluctance to use the X-s chart in place of the X-R chart. The other chart is for the subgroup standard deviations (s). One chart is for the subgroup averages ( X). ![]() Like most other variables control charts, it is actually two charts. ![]() ![]() Time, density, weight, and length are examples of variables data. This type of control chart is used with variables data - data that is taken along a continuum. This month's newsletter introduces the X-s chart. This is where the X-s chart provides the solution. A different method is needed for the larger subgroup sizes. One problem with the X-R chart is that the range becomes a poorer and poorer measure of within-subgroup variation as the subgroup size increases. But with computer software, this is no longer an issue. This was important when the control chart calculations had to be done by hand or with a calculator. The range is an easy concept to understand - and to calculate. For the measurements within a subgroup, the range is the maximum - minimum value. This control chart uses the range to measure the variation within a subgroup. ![]() The most common control chart for years has been the X-R chart. Next month we will look at a detailed example of an X-s chart. This month we will introduce X-s charts and describe how they are constructed. But, the X-s chart might actually be the better chart to use. The X-s chart is often overlooked in favor of the X-R chart. This month's publication is the first part of a two part series on X-s charts. ![]()
0 Comments
Leave a Reply. |