An X-bar and R chart was prepared for an operation using twenty samples with five pieces in each sample; X-bar was found to be 33.6 and R-bar was 6.20.
During production, a sample of five was taken and the pieces measured 36, 43, 37, 25, and 38. At the time, this sample was taken:
To determine whether the sample mean and range are within the control limits, we need to calculate both the sample mean and the sample range, and then compare them to the control limits derived from the X-bar and R-bar values. The sample mean is calculated as the average of the sample values: (36 + 43 + 37 + 25 + 38) / 5 = 35.8. The sample range is the difference between the maximum and minimum values: 43 - 25 = 18. The control limits for the X-bar chart can be calculated using the formula: X-bar ± A2 * R-bar, where A2 is a constant based on the sample size (for sample size 5, A2 is approximately 0.577). Thus, the upper control limit (UCL) for the X-bar chart is 33.6 + (0.577 * 6.20) = 37.18, and the lower control limit (LCL) is 33.6 - (0.577 * 6.20) = 30.02. Since the sample mean of 35.8 is within these control limits, the sample mean is within control limits. The control limits for the R chart can be calculated using the D3 and D4 constants (for sample size 5, D3 is 0 and D4 is 2.114). Thus, the upper control limit (UCL) for the R chart is 2.114 * 6.20 = 13.11, and the lower control limit (LCL) is 0 * 6.20 = 0. Since the sample range of 18 is outside the upper control limit of 13.11, the sample range is not within control limits. Therefore, the correct answer is that only the range was outside control limits.
Only the range was outside control limits