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GPPQE: Data Analysis, Sampling, and Statistical Methods

GPPQE · Work through your exam, one topic at a time.

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Data Analysis, Sampling, and Statistical Methods

Domain 7 - Data Analysis, Sampling, and Statistical Methods

This domain tests the statistics a quality professional actually uses: descriptive statistics, control charts, capability, acceptance sampling, and the rules around out-of-specification data.

Core rules

  • Descriptive statistics: mean, median, standard deviation, range, coefficient of variation. A CV is meaningless on a single result; it needs replicate data.
  • Control charts separate common-cause from special-cause variation. For individuals data use I-MR; for subgroups use Xbar-R. Apply run rules (for example 8 or 9 points on one side of the centreline, or six trending points) to detect shifts - but only after confirming the limits are appropriate.
  • Capability: Cp compares specification width to process spread; Cpk also accounts for centring. Cpk = min(USL − mean, mean − LSL) / 3σ. A Cpk of 1.33 is a common minimum expectation; 1.67 is stronger. Ppk uses the overall standard deviation and is the better measure for a new process.
  • Acceptance sampling per ISO 2859-1 / ANSI/ASQ Z1.4: AQL is a quality level acceptable as a process average, not a target defect rate. Switching rules (normal, tightened, reduced) are part of the standard and are examinable.
  • OOS investigations follow a documented two-phase process (laboratory investigation, then full investigation). Outlier tests such as Grubbs may support an assignable cause but must never be used to invalidate an OOS result on their own.

Worked example

Fill weight has specification 95–105 mg, mean 100 mg, and within-subgroup σ = 1.0 mg. Cp = 10/6 = 1.67. Cpk = min(105−100, 100−95)/3 = 5/3 = 1.67. The process is centred and capable. If the mean drifts to 102 mg, Cpk = min(3, 7)/3 = 1.0 - below the usual 1.33 expectation, even though no individual result may yet be out of specification. That is the argument for monitoring capability, not just OOS counts.

Traps that cost marks

  • Averaging retest results to make an OOS disappear, or retesting until a pass is obtained.
  • Using an outlier test to discard a failing result without an assignable laboratory cause.
  • Confusing Cp and Cpk; Cp ignores centring.
  • Treating AQL as a permitted defect rate in the market.
  • Applying variable charts to attribute data, or ignoring switching rules.