# Gage R&R Calculator (Average and Range Method)

> Source: https://netray.co/tools/gage-rr-average-and-range-method-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Turn the averages from a variable gage R&R study into EV, AV, GRR, part variation, %GRR and number of distinct categories.

## Category

quality

## Industry

Discrete Manufacturing

## Audience

- Quality engineer
- Metrology technician
- Supplier quality

## Tool

**Kind:** calculator

**Inputs:**

#### Trials per appraiser

**Key:** trials

**Type:** select

**Default:** 3

**Options:**

##### 2 trials

**Value:** 2

##### 3 trials

**Value:** 3

**Help:** How many times each appraiser measured each part.

#### Number of appraisers

**Key:** ops

**Type:** select

**Default:** 3

**Options:**

##### 2 appraisers

**Value:** 2

##### 3 appraisers

**Value:** 3

#### Number of parts

**Key:** parts

**Type:** select

**Default:** 10

**Options:**

##### 5 parts

**Value:** 5

##### 6 parts

**Value:** 6

##### 7 parts

**Value:** 7

##### 8 parts

**Value:** 8

##### 9 parts

**Value:** 9

##### 10 parts

**Value:** 10

#### Average range (R-bar)

**Key:** rbar

**Type:** number

**Default:** 0.0184

**Min:** 0

**Step:** 0.0005

**Unit:** mm

**Help:** Average of the appraisers' average ranges across all parts.

#### Appraiser average difference (X-bar diff)

**Key:** xdiff

**Type:** number

**Default:** 0.0105

**Min:** 0

**Step:** 0.0005

**Unit:** mm

**Help:** Largest appraiser average minus smallest appraiser average.

#### Range of part averages (Rp)

**Key:** rp

**Type:** number

**Default:** 0.248

**Min:** 0

**Step:** 0.005

**Unit:** mm

**Help:** Largest part average minus smallest part average.

#### Tolerance (USL minus LSL)

**Key:** tol

**Type:** number

**Default:** 0.5

**Min:** 0

**Step:** 0.01

**Unit:** mm

**Help:** Total tolerance of the characteristic being measured.

**Outputs:**

#### K1 constant

**Key:** k1

**Expr:** if(eq(trials,2),0.8862,0.5908)

**Format:** decimal

#### K2 constant

**Key:** k2

**Expr:** if(eq(ops,2),0.7071,0.5231)

**Format:** decimal

#### K3 constant

**Key:** k3

**Expr:** if(eq(parts,5),0.403,if(eq(parts,6),0.3742,if(eq(parts,7),0.3534,if(eq(parts,8),0.3375,if(eq(parts,9),0.3249,0.3146)))))

**Format:** decimal

#### Equipment variation, EV (repeatability)

**Key:** ev

**Expr:** rbar * k1

**Format:** decimal

#### Appraiser variation, AV (reproducibility)

**Key:** av

**Expr:** sqrt(pow(xdiff * k2, 2) - pow(ev, 2) / (parts * trials))

**Format:** decimal

#### Repeatability and reproducibility, GRR

**Key:** grr

**Expr:** sqrt(pow(ev, 2) + pow(av, 2))

**Format:** decimal

#### Part variation, PV

**Key:** pv

**Expr:** rp * k3

**Format:** decimal

#### %GRR of total variation

**Key:** pct_tv

**Expr:** 100 * grr / sqrt(pow(grr, 2) + pow(pv, 2))

**Format:** percent

**Primary:** true

**Description:** Under 10% is generally acceptable, 10% to 30% is marginal, over 30% is not acceptable (AIAG MSA guidance).

#### %GRR of tolerance (6 sigma)

**Key:** pct_tol

**Expr:** 100 * 6 * grr / tol

**Format:** percent

**Primary:** true

#### Number of distinct categories (ndc)

**Key:** ndc

**Expr:** floor(1.41 * pv / grr)

**Format:** integer

**Description:** 5 or more is the usual requirement.

**Chart:**

#### %GRR of total variation vs average range

**Type:** line

**X:** rbar

**From:** 0.005

**To:** 0.05

**Steps:** 19

**Series:**

- pct_tv

**Disclaimer:** Uses the AIAG MSA average and range method with sigma-based K constants. Confirm acceptance criteria against your customer requirements. Study design and the graphical checks still need a human review.

## Content

**Intro:** The average and range method is the classic hand-calculable gage R&R study for variable data. You collect measurements, reduce them to three summary numbers, and this calculator does the rest: repeatability, reproducibility, part variation, %GRR and ndc.

**Sections:**

#### How to use it

**Body:** Run the study first: 2 or 3 appraisers, 5 to 10 parts that span the real process spread, and 2 or 3 trials each, measured in random order. From your data sheet take R-bar (the average of the appraisers' average ranges), X-bar diff (the spread between appraiser averages) and Rp (the spread of part averages). Enter them with the study design and the tolerance. The tool selects the K constants for you and returns every standard output. The sweep chart shows how quickly %GRR climbs as repeatability worsens.

#### The formulas behind it

**Body:** EV = R-bar x K1, where K1 depends on trials. AV = square root of ((X-bar diff x K2) squared minus EV squared divided by (parts x trials)), where K2 depends on appraisers. GRR is the square root of EV squared plus AV squared. PV = Rp x K3 with K3 set by the number of parts. Total variation is the square root of GRR squared plus PV squared. ndc is 1.41 times PV over GRR, rounded down. If the AV expression goes negative it is set to zero, which is standard practice.

**Bullets:**

- %GRR under 10%: acceptable
- 10% to 30%: may be acceptable depending on cost and risk
- Over 30%: improve the measurement system
- ndc of 5 or more: system can distinguish part groups

#### Common mistakes

**Body:** The most common failure is choosing parts that all look alike, which shrinks PV and inflates %GRR. Pick parts that cover the full process range. Others: measuring in part order instead of random order, letting appraisers see earlier readings, using a gage with too coarse a resolution (aim for resolution under one tenth of the tolerance), and judging only against total variation when the customer cares about tolerance. Report both percentages. For non-replicable or attribute checks, use a different method such as attribute agreement analysis.

**Cta:** If your gage study data lives in a QMS or ERP inspection module, Netray can help pull it into a repeatable MSA report without retyping.

**Faq:**

#### What is an acceptable %GRR?

**Answer:** AIAG MSA guidance treats under 10% as acceptable, 10% to 30% as conditionally acceptable depending on application, cost and risk, and over 30% as unacceptable. Many customers also require ndc of 5 or more. Always check your customer-specific requirements.

#### Average and range or ANOVA?

**Answer:** Average and range is quick and easy to do by hand but cannot separate the part-by-appraiser interaction. ANOVA is more rigorous and is preferred when software is available. For a routine check or a quick supplier review, average and range is usually enough.

#### Should I use 5.15 or 6 sigma?

**Answer:** Older MSA editions used 5.15 sigma (99%) spread, while the current convention is 6 sigma (99.73%). This calculator uses sigma-based constants and a 6 sigma spread for the tolerance percentage. If your customer still asks for 5.15, scale the tolerance result by 5.15 over 6.

#### How many parts and trials do I need?

**Answer:** The common design is 10 parts, 3 appraisers and 3 trials, which gives 90 readings. Fewer parts or trials reduce confidence in the estimates. Never go below 5 parts, and make sure the parts represent the actual process spread.

## Search terms

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