CQT cheat sheet

Cost of quality = prevention + appraisal + internal failure + external failure; prevention and appraisal are conformance costs, while failure costs are nonconformance costs.

Pareto principle: roughly 80% of effects come from about 20% of causes; a Pareto chart ranks categories in descending frequency to isolate the vital few.

PDCA: Plan (define objectives and processes), Do (implement), Check (monitor and measure against requirements), Act (standardize or correct).

Common cause-and-effect categories: man, machine, material, method, measurement, environment (5M1E).

Flowchart symbols: oval = start/stop, rectangle = process step, diamond = decision, parallelogram = input/output, arrow = flow direction.

Control chart limits (±3 sigma) are computed from actual process variation; a run chart shows only a center line and time-ordered points.

Histograms reveal distribution shape (skew, bimodality, spread); scatter diagrams show the association between two variables but not causation.

5S sequence: sort, set in order, shine, standardize, sustain.

Force field analysis weighs driving forces against restraining forces when evaluating a proposed change.

Mean x̄ = Σx/n; median = middle value of ordered data; mode = most frequent value; range R = maximum − minimum.

Sample standard deviation s = √[Σ(x − x̄)²/(n − 1)]; the n − 1 divisor corrects bias when estimating population variance.

Cp = (USL − LSL)/(6σ); Cpk = min[(USL − μ)/(3σ), (μ − LSL)/(3σ)]; Cpk is never greater than Cp, with equality only when centered.

X̄–R chart constants for subgroup n = 5: A2 = 0.577, D3 = 0, D4 = 2.114; UCL_x̄ = x̄̄ + A2·R̄, LCL_R = D3·R̄, UCL_R = D4·R̄.

Chart selection: variable data → X̄–R or X̄–s; nonconforming units → np (constant n) or p (variable n); defect counts → c (constant area) or u (variable area).

Empirical rule for normal data: about 68.3% of values within ±1σ, 95.4% within ±2σ, 99.7% within ±3σ.

Central limit theorem: sample means approach a normal distribution with mean μ and standard error σ/√n as sample size grows.

Sampling plan risks: producer's risk α rejects a lot of acceptable quality; consumer's risk β accepts a lot of poor quality; AQL and LTPD anchor the OC curve.

Binomial distribution models the count of nonconforming units in n trials; Poisson models defect counts when defects are rare and independent.

ANSI/ASQ Z1.4 selects a plan from lot size and AQL; general inspection level II is the default, levels I and III change sample size, and special levels S-1 through S-4 apply to small samples.

Switching rules: normal → tightened when 2 of 5 consecutive lots are rejected; tightened → normal after 5 consecutive lots accepted on original inspection; normal → reduced after 10 consecutive accepted lots meeting the defect limit.

Defect classes: critical (safety or hazard), major (likely functional failure), minor (appearance or slight deviation).

100% inspection suits critical characteristics and small lots but cannot assure zero defects because of inspector error and fatigue.

Inspection stages: receiving, in-process, final, and source inspection, the last performed at the supplier's facility before shipment.

Common NDT methods: visual, liquid penetrant, magnetic particle (ferromagnetic materials only), ultrasonic, radiographic, eddy current.

Attribute gauging (go/no-go) yields accept or reject only; variable gauging yields a measured value and more information per part.

First article inspection verifies the first production unit against all drawing and specification requirements before full production is released.

Destructive testing requires sampling because tested units cannot be sold; specimens must represent the lot being evaluated.

Traceability requires an unbroken, documented chain of calibrations linking instrument readings to national or international standards such as SI or NIST.

Calibration compares an instrument's indication with a reference of known value; adjustment alters the instrument and is a separate action, not a requirement for calibration to be valid.

Accuracy is closeness to the true value (bias); precision is agreement among repeated readings (repeatability).

Gage R&R: GRR = √(EV² + AV²); %GRR = 100 × GRR ÷ total variation (or tolerance); ≤10% acceptable, 10–30% marginal, >30% unacceptable.

Repeatability is equipment variation measured by one appraiser; reproducibility is the variation between appraisers.

Linearity is the change in bias across the measuring range; stability is the change in bias over time; hysteresis is the difference between increasing and decreasing readings.

Gauge resolution should be about one-tenth of the tolerance, and a test uncertainty ratio of 4:1 or better is commonly required.

Uncertainty budget: Type A from statistical analysis plus Type B from certificates and reference data, combined as u_c = √(Σu_i²); expanded U = k·u_c with k = 2 gives about 95% confidence.

Reference conditions are often 20 °C; thermal error is estimated as length × coefficient of expansion × temperature difference.

ISO 9001:2015 rests on seven quality management principles, applies risk-based thinking, follows PDCA, and does not require a documented quality manual.

Audit types: first-party (internal), second-party (customer auditing supplier), third-party (independent certification body).

Document hierarchy: quality policy/manual → procedures → work instructions → records and forms.

Corrective action eliminates the cause of a detected nonconformity; correction fixes the existing condition; preventive action addresses a potential nonconformity.

Document control requires approval before issue, review and update as needed, revision status identification, and controlled distribution; records are retained rather than revised.

ISO 9000 provides fundamentals and vocabulary, ISO 9001 states requirements, ISO 9004 gives guidance for sustained success, and ISO 19011 covers auditing.

Related standards: ISO 14001 environmental, ISO 45001 occupational health and safety, IATF 16949 automotive, AS9100 aerospace.

Management review inputs include audit results, customer feedback, nonconformities, and process performance; outputs include improvement decisions and resource needs.

The 8D sequence: team, problem description, containment, root cause, corrective action, verification, prevention, and recognition.