P4a. Calculate the standard deviation of the final clearance, Y. Round your answer to two decimal places.

P2a. Based on the fitted Gage R&R model, the relatively small Operator variance indicates that the operators generally measure the parts similarly; therefore, differences among operators are not an important source of measurement-system variation in this study.

P1b. What percentage of the total observed variance is attributable to the measurement system? Round your answer to the nearest whole percent. Enter the number only (for example, enter 25 rather than 25%).

Q13. A stable manufacturing process is monitored using an X̄- and S-chart with subgroups of size n = 5. The Phase I study produced the following results: Lower specification limit (LSL) = 19.50 mm Upper specification limit (USL) = 20.50 mm Grand mean = 20.30 mm Average subgroup standard deviation, S̄ = 0.120 mm c4 = 0.9400 Calculate the actual process capability, Cpk. Round your final answer to two decimal places.

A process is producing measurements that all fall within the customer’s specification limits. Therefore, the process is in statistical control.

P3a. Because the overall average bias in the calibration study is approximately zero, there is no evidence of a systematic accuracy problem with this measurement system.

A stable process has Cp = 1.50 and Cpk = 0.85. Which statement best describes the process?

A Gage R&R study is conducted in which several operators each measure every part multiple times. Match each source of variation with its interpretation in the measurement study.

P1c. Based on your analysis, which statement best evaluates the engineer’s conclusion?

A manufacturer assembles a product from several components. Each component is produced independently and meets its own specification limits. Which statement best explains why the completed assembly may still fail to meet its overall dimensional requirement?