The depth of a keyway is an important part quality characteristic. Samples of size n = 5 are taken every four hours from the process, and 20 samples are summarized in the following table.

(a) Using all the data, find trial control limits for XÌ… and R charts. Is the process in control?

(b) Use the trial control limits from part (a) to identify out-of- control points. If necessary, revise your control limits.

Then estimate the process standard deviation.

(c) Suppose that the specifications are at 140 ± 2. Using the results from part (b), what statements can you make about process capability? Compute estimates of the appropriate process capability ratios.

(d) To make this a 6-sigma process, the variance σ² would have to be decreased such that PCR_k = 2.0. What should this new variance value be?

(e) Suppose that the mean shifts to 139.7. What is the probability that this shift is detected on the next sample? What is the ARL after the shift?

Transcribed Image Text:

Sample 1 139.7 1.1 139.8 1.4 3 140.0 1.3 140.1 1.6 139.8 0.9 139.9 1.0 139.7 1.4 140.2 1.2 139.3 9. 1.1 140.7 10 1.0 11 138.4 0.8 138.5 12 0.9 137.9 13 1.2 14 138.5 1.1 15 140.8 1.0 16 140.5 1.3 17 139.4 1.4