Seattle Concrete Company (SCC) produces bags of concrete mix for its customers. These bags have a stated weight of 40 pounds per bag. Given the steep penalties for under filling bags, SCC sets a target of 41 pounds per bag to ensure under filling due to natural variations still remain above the 40 pound threshold. Historically, they have operated with a single production shift, but have recently added a second shift to meet their growing demand. Management is interested in a full analysis of their process to ensure that the control limits and capabilities are within reason, and to ensure that the addition of a second shift isn’t causing issues to their process. To accomplish this, a data set was constructed. Ten bags were
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Once this is addressed, the R-chart should demonstrate less variability in the second shift and should resemble the one from the first shift. Looking at the X ̅- charts for both shifts, we also observe that the mean of the samples are within the upper and lower control limits. This indicates that the process average is in statistical control. The sample means for both shifts closely follow x ̿, and are consistent with the performance measure. Periodic monitoring and re-calculation of X ̅- charts are necessary to make sure processes remain in control, especially if new employees are hired or supervisors change. Since both (X ) ̅& R Control Charts seem to be under control, we have the possibility of committing a type II error, which occurs when we conclude that the process is in control and only randomness is present, when actually the process is out of statistical control. The limit at three standard deviations from the mean makes type II errors harder to detect (wide spread). SCC Management may consider reducing the control limits to two standard deviations but will cause the probability of type I errors to increase. This trade off should be taken into consideration and assessment of costs to detect an assignable cost versus the cost of not detecting it is needed.
Control Charts for Attributes: P-Chart and C-Chart
On average, 17% of the bags in shift one (Table 5 and Figure 3) are