![]() In the next lesson, you learn about process capability studies, which we use to address this question. But this question of whether a process is meeting specifications is important. For this reason, specification limits should not be drawn on X-bar charts. You can't compare specification limits to control limits on X-bar charts. Specification limits are the range of acceptable values for individual measurements. Specifications, on the other hand, relate to individual measurements. X-bar charts are used to plot subgroup means, and the upper and lower control limits provide a range of values for subgroup means. What about the thickness of individual parts? Your specifications for the process are 40 plus or minus 5, or 35 to 45 hundredths of an inch. So although the process is stable, the process mean is not on target. The grand mean, 41.328, is above the target of 40. This means that the process is in control, and that future performance is predictable. When you run the tests for special causes, you see that the process is stable. Together, the two charts characterize the spread and centering of thickness over time. Here are the X-bar and R charts and control limit summaries. You measure subgroups of five consecutive parts every hour for 25 hours. One of your first steps is to collect some baseline data and construct a control chart to study process variation. The target is 40 plus or minus 5 hundredths of an inch (which is about 1 centimeter). Your goals are to bring the thickness to target and to reduce variability. The critical measurement is the thickness of the part. You are on a team charged with improving the dimensional conformance of a small metal part. We then use this estimate to calculate the control limits for the X-bar chart. ![]() We use the average range to estimate the within-subgroup standard deviation. Here, we calculate the range for the first subgroup and plot this on the R chart. This chart monitors within-subgroup variability over time. The subgroup ranges or standard deviations are plotted on a second chart, either an R (or range) chart or an S (or standard deviation) chart. Because we use sample means, we place the control limits at plus or minus 3 standard errors of the mean. The center line on the X-bar chart is the average of the subgroup means, or the grand mean. We use this chart to monitor subgroup means over time. The subgroup means are plotted on an X-bar chart. Data from rational subgroups can be plotted on an X-bar and R chart or an X-bar and S chart. Because these items are close together in time, they form natural, or rational, subgroups. For example, once an hour, five consecutive items off the line are measured. For some processes, more than one item can be measured at a time.
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