Product Engineering
Reject rate is exponential in sigma. A small tightening is never a small cost.
— currency
Cost of accepting the tighter limit without improving the process
Reject rates assume a centred, normally distributed process, which is the optimistic case on both counts. A real process drifts, and the widely used 1.5σ long-term shift would raise these ppm figures substantially; a distribution with heavier tails than normal — which most textile strength data has — raises them further, and the error is largest exactly where it matters, out at the specification limit. Treat the ppm figures as a lower bound and the cost comparison as a ratio rather than a forecast. The linear improvement cost is a planning placeholder: variation reduction gets progressively harder, so the last 10% typically costs more than the first 30%. Neither route priced here includes the cost of the customer relationship if the tighter tolerance is refused.
Specification Tolerance Cost-of-Quality Modeler — free, with the formula and a worked example, at Textile School.