# Inspection Detection Effectiveness and Escape Rate Calculator

> Source: https://netray.co/tools/inspection-detection-effectiveness-escape-rate-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Chain two inspection or test stages, see combined detection effectiveness, defects escaping to the customer, escape ppm and the cost of escapes.

## Category

quality

## Industry

Discrete Manufacturing

## Audience

- Quality engineer
- Supplier quality
- Inspection supervisor

## Tool

**Kind:** calculator

**Currency:** $

**Inputs:**

#### Annual volume

**Key:** volume

**Type:** number

**Default:** 250000

**Min:** 0

**Step:** 5000

**Unit:** units

#### Defect rate entering inspection

**Key:** defect_pct

**Type:** number

**Default:** 1.2

**Min:** 0

**Max:** 100

**Step:** 0.1

**Unit:** %

**Help:** Share of units that are defective before any detection stage.

#### Stage 1 detection effectiveness

**Key:** e1

**Type:** slider

**Default:** 80

**Min:** 0

**Max:** 100

**Step:** 1

**Unit:** %

**Help:** Probability stage 1 catches a defective unit. Manual visual inspection is often well below 100%.

#### Stage 2 detection effectiveness

**Key:** e2

**Type:** slider

**Default:** 60

**Min:** 0

**Max:** 99

**Step:** 1

**Unit:** %

**Help:** Probability stage 2 catches what stage 1 missed.

#### Cost per escaped defect

**Key:** cost_escape

**Type:** number

**Default:** 400

**Min:** 0

**Step:** 25

**Unit:** $

**Help:** Customer line stoppage, return, containment, charge-back and warranty.

**Outputs:**

#### Defective units entering inspection

**Key:** defects

**Expr:** volume * defect_pct / 100

**Format:** integer

#### Defects escaping stage 1

**Key:** after1

**Expr:** defects * (1 - e1 / 100)

**Format:** integer

#### Defects escaping both stages

**Key:** escapes

**Expr:** after1 * (1 - e2 / 100)

**Format:** integer

**Primary:** true

#### Combined detection effectiveness

**Key:** combined

**Expr:** if(gt(defects,0), (1 - escapes / defects) * 100, 0)

**Format:** percent

**Primary:** true

#### Escape rate

**Key:** escape_ppm

**Expr:** if(gt(volume,0), escapes / volume * 1000000, 0)

**Format:** integer

**Description:** Escaped defective units per million shipped.

#### Annual cost of escapes

**Key:** escape_cost

**Expr:** escapes * cost_escape

**Format:** currency

**Chart:**

#### Annual cost of escapes vs stage 2 effectiveness

**Type:** line

**X:** e2

**From:** 0

**To:** 99

**Steps:** 34

**Series:**

- escape_cost

**Disclaimer:** Assumes the two stages are independent. Correlated inspectors or identical methods make the real combined effectiveness lower.

## Content

**Intro:** Detection ratings in a PFMEA are only as good as the evidence behind them. This calculator shows what layered inspection actually delivers and how many defects still reach the customer.

**Sections:**

#### How to use the calculator

**Body:** Enter annual volume and the defect rate entering inspection, then the detection effectiveness of each stage. Effectiveness is the probability that a defective unit is caught. Use results from a challenge test or attribute agreement study where possible. The calculator reports defects escaping both stages, combined effectiveness, escape ppm and the yearly cost of those escapes.

#### The math

**Body:** Defects entering inspection equal volume times the defect rate. Each stage passes on the fraction it misses, so escapes equal defects times (1 minus e1) times (1 minus e2). Combined effectiveness is one minus escapes divided by defects. Escape ppm equals escapes divided by volume times one million. The model assumes stage independence, which rarely holds fully when both stages rely on the same human judgment.

**Bullets:**

- Two 80 percent stages give 96 percent, not 160 percent.
- Adding a third stage has diminishing returns.

#### Using the result for detection ratings

**Body:** Combined effectiveness helps justify a detection rating. Automated 100 percent inspection with proven capability supports a low rating; manual sampling supports a high one. Record the study that produced each effectiveness figure in the control plan so the rating survives audit. Compare against the escape ppm your customer tolerates.

#### Common mistakes

**Body:** Assuming 100 percent effectiveness for visual inspection is the classic error; fatigue and lighting reduce it. Another is applying effectiveness to sampling plans, where only a portion of units are inspected at all. For sampling, multiply effectiveness by the fraction inspected or use an acceptance sampling model instead.

**Cta:** Netray can connect inspection results and customer returns in your ERP so measured escape rates replace assumptions in your FMEA.

**Faq:**

#### How do I measure effectiveness?

**Answer:** Seed known defective units into a normal flow and count how many are caught, or run an attribute agreement analysis against a reference. Repeat across shifts and inspectors.

#### Does this apply to sampling inspection?

**Answer:** Not directly. Sampling only checks some units. Multiply the stage effectiveness by the fraction of units inspected, or use a sampling plan calculation.

#### Why is the chart curved down only slightly?

**Answer:** The cost falls linearly with stage 2 effectiveness, and stage 1 already removed most defects, so the absolute savings are smaller than the percentage gain suggests.

#### Are stages really independent?

**Answer:** Often not. If both rely on the same operator or the same misleading defect appearance, misses correlate and escapes are higher than this model shows.

## Search terms

inspection effectiveness calculator, escape rate calculator, defect escape ppm, detection rating fmea evidence, combined inspection probability of detection, visual inspection effectiveness, customer escape cost, layered inspection calculator

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