CQI cheat sheet

1 inch = 25.4 mm exactly; 1 mm = 0.03937 in; 1 in = 2.54 cm.

Circle: A = πr² = πd²/4; circumference C = πd. Cylinder volume V = πr²h.

Right triangle: a² + b² = c²; sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.

Degrees to radians: rad = deg × π/180. 1 degree = 60 minutes = 3600 seconds.

Cp = (USL − LSL)/(6σ); Cpk = min(USL − μ, μ − LSL)/(3σ); Cpk can never exceed Cp.

Sample standard deviation s = √[Σ(xᵢ − x̄)²/(n − 1)]; population σ uses n in the denominator.

Worst-case tolerance stack = sum of individual tolerances; statistical stack = √(sum of squared tolerances) for independent, centered tolerances.

Temperature: °C = (°F − 32) × 5/9; °F = °C × 9/5 + 32.

Percentage = (part/whole) × 100; percent error = |measured − true| ÷ true × 100.

Traceability is an unbroken chain of calibrations, each with a stated uncertainty, linking a measurement result to a national or international standard.

Accuracy is closeness to the true value; precision is closeness of repeated readings to each other. A gage can be precise yet biased.

Gage R&R: repeatability = equipment variation (one appraiser, one gage); reproducibility = appraiser variation. %GRR = 100 × GRR ÷ tolerance (or process variation).

10:1 rule: gage discrimination (resolution) should be no more than 1/10 of the tolerance being verified.

Reference temperature for dimensional measurement is 20 °C (68 °F); steel expands about 11.7 µm/m·°C (6.5 µin/in·°F).

Typical resolution: inch micrometer 0.001 in, metric micrometer 0.01 mm, vernier caliper 0.001 in or 0.02 mm.

Sine bar: sin θ = h/L, where h is the gage block stack height and L the sine bar length. Surface roughness Ra is the arithmetic average deviation from the mean line.

Measurement uncertainty: combine Type A (statistical) and Type B (certificate, specification, judgement) into u_c; expanded U = k·u_c with k = 2 for approximately 95% confidence.

Calibration determines deviation from a standard; adjustment or repair is a separate action. An out-of-tolerance gage triggers review of product measured since the last valid calibration.

ANSI/ASQ Z1.4 governs attribute sampling by AQL; ANSI/ASQ Z1.9 governs variables sampling. Sample size and acceptance number come from lot size, inspection level, and AQL.

An OC curve plots probability of acceptance against lot fraction nonconforming. Producer's risk α = P(reject a good lot); consumer's risk β = P(accept a bad lot).

NDT selection: penetrant for nonporous surface-breaking flaws; magnetic particle for ferromagnetic surface and near-surface flaws; ultrasonic and radiographic for internal flaws; eddy current for conductive surface flaws.

An inspection plan defines the characteristic, specification, method and instrument, sample size and frequency, acceptance criteria, and record retention.

First article inspection verifies the first production part against all drawing and specification requirements before full production release.

Inspection decision errors: Type I = rejecting conforming product (false reject); Type II = accepting nonconforming product (false accept).

100% inspection is not fully reliable; effectiveness decreases with part count and fatigue, and it cannot detect flaws the method was not designed to find.

Sampling requires a random, representative sample; biased selection invalidates the OC curve and therefore the accept/reject decision.

QA is prevention-oriented and focused on processes and systems; QC is detection-oriented and focused on product against requirements.

Control limits = process mean ± 3σ, calculated from process data. Specification limits come from design or the customer. Specification limits are never plotted as control limits.

Chart selection: X̄-R for n = 2–9; X̄-s for n ≥ 10; I-MR for n = 1; p and np for nonconforming units; c and u for defect counts.

Common-cause variation is inherent and stable; special-cause variation is signalled by points beyond limits, runs, or nonrandom patterns.

Corrective action removes the root cause of an existing nonconformity; preventive action removes the cause of a potential one; containment protects the customer first.

Quality cost categories: prevention, appraisal, internal failure, external failure. External failure cost per defect is typically the highest.

Audit types: first-party = internal; second-party = supplier or customer; third-party = independent certification body such as for ISO 9001.

PDCA: Plan (define and analyse), Do (implement on a small scale), Check (verify results), Act (standardize or revise). It underlies DMAIC and 8D.