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Deming kp Rule Calculator: Inspect Everything or Nothing?

W. Edwards Deming's kp rule says that if the cost of inspecting a piece is less than the expected cost of letting a defective through, inspect every piece; otherwise inspect none. Real inspectors miss defects, so this version builds that in.

Your numbers

Process percent defective

1.5 %

Annual volume

units

Cost to inspect one piece (k1)

Cost when a defective reaches the next stage (k2)

Rework, line stoppage, warranty or customer cost for one escaped defective.

Inspection effectiveness

85 %

Share of defectives the inspection actually catches.

Your results

Break-even defect rate

2.3%

Above this rate, 100 percent inspection costs less than shipping defectives.

Saving from 100 percent inspection

-$6,025

Negative means do not inspect everything; use sampling or fix the process.

Defect fraction

0.015

Effectiveness fraction

0.85

Annual cost with no inspection

$13,500

Annual cost with 100 percent inspection

$19,525

Decision code (1 = inspect all, 0 = do not)

A simplified cost model. It ignores sampling plans and the value of fixing the root cause, which is usually the better answer.

Save results:

Annual cost: no inspection vs 100 percent inspection

Sweeps Process percent defective from 0.1 to 10, holding your other inputs fixed.

Measure your real cost of escapes

Optional: a review of how to extract rework, scrap and return costs from your ERP to set k2.

Optional. The tool and every export work without this. No spam.

How to use it

Enter the current defect rate, annual volume, what inspecting one piece costs, and what one escaped defective costs the next stage or customer. Then set inspection effectiveness. A visual inspector might catch 80 to 90 percent; an automated gauge may catch nearly all. The calculator returns the break-even defect rate, both annual costs and the saving. The chart shows the two cost lines and where they cross.

k2 should be the full cost of an escape, not only the part price.
Use measured effectiveness from a seeded defect test if you have one.
Run the chart across your best and worst months of p.

The rule and its formula

With perfect inspection the rule is simple: inspect all when p is greater than k1 / k2. With imperfect inspection that only catches a fraction e of defectives, the break-even becomes p = k1 / (e x k2). Cost with no inspection is volume x p x k2. Cost with 100 percent inspection is volume x (k1 + p x (1 - e) x k2), because you pay to inspect every piece and still pass on the defectives you miss.

Reading the result

At the defaults, break-even is about 2.3 percent. The process runs at 1.5 percent, so screening everything would cost more than the escapes it prevents, and the saving is negative. If the same process drifted to 5 percent, 100 percent inspection would clearly win. Either answer should trigger a root cause effort, because inspection never makes parts better.

Common mistakes

Underestimating k2 is the most common error: escapes to a customer cost far more than a rework hour. Another is assuming 100 percent inspection is 100 percent effective; fatigue makes repeated visual screening less reliable. Finally, the rule is a decision about economics only. Safety critical or regulated characteristics may require full inspection regardless of the numbers.

Frequently Asked Questions

What is the Deming kp rule?

It compares the cost of inspecting one piece with the expected cost of a defective passing on. If inspection is cheaper than the expected loss, inspect everything; if not, inspect nothing and work on the process. Sampling is a middle path.

Why include inspector effectiveness?

Because 100 percent inspection is never 100 percent effective. Missed defectives still carry the escape cost, so break-even moves to a higher defect rate than the simple k1 / k2 formula suggests.

What if the answer is to inspect nothing?

It means the defect rate is low enough that screening costs more than escapes. It does not mean you can stop checking the process. Use process control and periodic audits to catch any drift.

Does this replace a sampling plan?

No. Sampling plans fit the middle range where lots are usually good but not certain to be. This calculator frames the two extremes and tells you whether either one is justified.

We can help pull your real escape and rework costs from ERP and quality data so k1 and k2 are measured, not guessed. Ask for a quick review.

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