Tools › Quality › Control › SPC and Capability › Example
Montgomery Example 6.1: X̄–R chart and Cp of hard-bake flow width
| Tool | SPC and Capability |
| Source | Montgomery, D. C. (2013). Introduction to Statistical Quality Control, 7th ed. Wiley, Hoboken, NJ. Example 6.1, Table 6.1, Appendix VI. |
| Level | Undergraduate |
Problem
Twenty-five subgroups of five flow-width measurements (microns) were taken from a hard-bake process in semiconductor manufacturing. Set up X̄ and R control charts, check the process for control and estimate its capability against specification limits of 1.00 and 2.00 µm.
Inputs to Enter
- Chart type X̄–R; 25 lines of 5 values (Table 6.1, loaded by default)
- LSL 1.00, USL 2.00
- Run rules Western Electric; Phase I revision keep all subgroups
Answers
- x̿ = 1.5056, R̄ = 0.32521 (m = 25, n = 5)
- X̄ chart: UCL 1.69325, LCL 1.31795 (book 1.693, 1.318)
- R chart: UCL 0.68749, LCL 0 (D4 = 2.114, D3 = 0)
- σ̂ = R̄/d2 = 0.32521/2.326 = 0.1398
- Cp = (2.00 − 1.00)/(6 × 0.1398) = 1.192 (book 1.19)
Notes
The tool's default inputs are this example; press Submit to reproduce it. The book rounds x̿ to 1.5056 before computing the limits; the control-chart constants are computed by the tool and agree with Appendix VI to the printed digits.