Quality Engineering
What to master
Two halves: control and improvement. Control means statistical process control - variable charts (X-bar and R, X-bar and s) and attribute charts (p, np, c, u), rational subgrouping, control limit formulas (X-bar limits = X-double-bar +/- A2 x R-bar; R chart UCL = D4 x R-bar), and out-of-control rules (points beyond limits, trends, runs). Improvement means process capability (Cp = (USL - LSL)/(6 sigma); Cpk = min[(USL - mu), (mu - LSL)]/(3 sigma)), MSA and gauge R&R, acceptance sampling (AQL, LTPD, OC curves, producer's and consumer's risk), DOE and Taguchi methods, Six Sigma DMAIC, and the seven basic quality tools.
Traps
- Confusing specification limits (from design) with control limits (from the process).
- Calling a process capable just because it is in statistical control.
- Using the standard deviation of individual readings when an R-bar/d2 estimate is required.
- Mixing up p (fraction defective), c (count per unit, constant opportunity), and u (count per unit, varying opportunity).
- Reporting Cpk greater than Cp; that is impossible - check the arithmetic.
- Reading an OC curve's y-axis as defect rate when it is the probability of acceptance.
Worked example
A process has mu = 50, sigma = 2, USL = 56, LSL = 44. Cp = 12/12 = 1.00 and Cpk = min(6, 6)/6 = 1.00. If the mean drifts to 52, Cp is still 1.00 but Cpk = min(4, 8)/6 = 0.67 - the classic off-center penalty.
Rule of thumb
Cpk of at least 1.33 is the usual minimum for an existing process; 1.67 for new or safety-critical processes.