Tools › Quality › Control › Dimensional Capability › Example

Montgomery Table 6.1: capability of the hard-bake flow width (Cp, Cpk, ppm)

Tool	Dimensional Capability
Source	Montgomery, D. C. (2013). Introduction to Statistical Quality Control, 7th ed. Wiley, Hoboken, NJ. Table 6.1, Examples 6.1 and 6.3, Section 8.2.
Level	Undergraduate

Problem

Twenty-five subgroups of five flow-width measurements (microns) from a hard-bake process are given with specification limits of 1.00 to 2.00 microns. Estimate the within-subgroup standard deviation from the average range and from the average standard deviation, compute Cp and Cpk, and estimate the fraction of product outside the specifications.

Inputs to Enter

Example select: Montgomery flow width, Table 6.1 (sets subgroups of 5)
Characteristic #1 Flow width, nominal 1.50, tolerance −0.50 / +0.50 (LSL 1.00, USL 2.00), 125 values in 25 rows of 5
Within sigma by R̄/d₂ (and by s̄/c₄ for Example 6.3)

Open the Dimensional Capability tool

Answers

Grand mean 1.5056, R̄ = 0.32521, σ̂ = R̄/d₂ = 0.1398
Cp = 1.192 (book 1.19), Cpu = Cpk = (2 − 1.5056)/(3 × 0.1398) = 1.179
Expected fraction out about 0.00035 (book), 350 ppm, none of the 125 values observed outside
Example 6.3: s̄ = 0.1316, σ̂ = s̄/c₄ = 0.1316/0.9400 = 0.1400

Notes

Choose the Montgomery entry in the example select, which also sets the subgroup size to 5; the default illustrative six-characteristic part is not a published example.