Specification Tolerance Cost-of-Quality Modeler

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 6 inputs are read from the form on every keystroke: Current Tolerance (±), Proposed Tolerance (±), Process Standard Deviation, Cost per Reject, Annual Volume and Cost per 1% SD Reduction.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Additional Annual Reject Cost together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Current Sigma Level, Current Reject Rate, Proposed Reject Rate, SD Needed to Hold Capability, SD Reduction Required and Process Improvement Cost — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Additional Annual Reject Cost shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Specification Change and Economics. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Additional Annual Reject Cost in the dark results panel — that is the headline figure, expressed in currency.
4. Check the supporting rows underneath (Current Sigma Level, Current Reject Rate, Proposed Reject Rate, SD Needed to Hold Capability, SD Reduction Required and Process Improvement Cost) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Additional Annual Reject Cost before a trial is booked, so machine time and material in Product Engineering, Specifications & Feasibility are committed against a calculated figure rather than an estimate.
• Costing and quotation — Additional Annual Reject Cost is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Current Tolerance (±)) shows how much of the gap in Additional Annual Reject Cost each variable explains.
• Teaching and study — the accepted ranges bracket normal Product Engineering, Specifications & Feasibility practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• 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.
• Every input is bounded to the range normal practice occupies (Current Tolerance (±) 0.001 to 1000 units, Proposed Tolerance (±) 0.001 to 1000 units and Process Standard Deviation 0.001 to 500 units, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask