Worked numbers
Shop calculators
Same formulas as the formula sheet. Degrees, not radians. Box the number before you look at the exam choices. These are study tools, not a substitute for a calibrated instrument on the floor.
Sine bar
h = L × sin θ. A 5.000 in bar at 30° needs 2.500 in of stack.
Stack h = 2.5 in
Cp and Cpk
Cp (capability index for spread only) = (USL − LSL) / 6σ. Cpk (capability index that includes centering) is the lesser of the two one-sided ratios. Do not trust either number until the process is stable.
Cp = 1.333 · Cpk = 1.333
Bonus at MMC
MMC (maximum material condition) of a hole is the smallest hole. Of a pin, the largest pin. Bonus is how far actual size is from MMC, then add it to the geometric tolerance.
MMC 0.5 · bonus 0.008 · allowed 0.018
10:1 rule
Inspection discrimination ≈ tolerance span / 10. A ±0.005 in spec is a 0.010 in span, so about 0.001 in.
Need about 0.001 in
z-score
z = (x − mean) / σ. How many standard deviations from the middle.
z = 1