Technical Mathematics for Quality Inspectors
What is actually tested
Technical math on the CQI exam is applied, not abstract: converting units, working with tolerances, reading control charts, and computing capability. Be fluent with fractions, decimals, and percent conversions; ratio and proportion; geometry (perimeter, area, volume, circumference, angles); right-triangle trigonometry; and descriptive statistics.
Statistics you must own
Distinguish population notation (μ, σ) from sample notation (x̄, s); the sample standard deviation divides by n−1. Know mean, median, mode, and range, and how a single outlier moves each one. For a normal distribution: ±1σ ≈ 68.27%, ±2σ ≈ 95.45%, ±3σ ≈ 99.73%.
Control limits for subgroup averages use the standard error, not the individual-value spread: UCL = x̄̄ + A₂R̄, which corresponds to x̄̄ + 3s/√n. Using x̄̄ + 3s is the single most common trap in charting questions.
Capability traps
Cp measures spread only: (USL − LSL)/6σ. Cpk measures spread and centering: min[(USL − x̄), (x̄ − LSL)]/3s. A process can show Cp = 2.0 and Cpk = 0.6 if it is badly off-center; always report the smaller index.
Worked example
USL = 10.20, LSL = 9.80, x̄ = 10.05, s = 0.040. Upper half: (10.20 − 10.05)/(3 × 0.040) = 0.15/0.12 = 1.25. Lower half: (10.05 − 9.80)/0.12 = 0.25/0.12 = 2.08. Cpk = min(1.25, 2.08) = 1.25, while Cp = 0.40/0.24 = 1.67. Rule of thumb: carry four decimal places through the work and round only the final answer - premature rounding is the most frequent arithmetic error.