## MSA- Measurement System Analysis

MSA is defined as an experimental and mathematical method of determining the amount of variation that exists within a measurement process. MSA is used to certify the measurement system for use by evaluating the system’s accuracy, precision and stability.

### Objective of MSA:-

- To quantify the variation in measurement system.
- To ensure stability of measurement system.
- To minimize measurement system variation within total process variation.

### Statistical Properties of Measurement System (MS):-

- Adequate discrimination (Sensitivity)
:- Least count of instrument should be 1/10
^{th}of process variation (Process variation could be specification limit) - MS variation is due to common causes, not because of special causes.
- Measurement error should be small compared to tolerance spread/process variability.

### Measurement system error:-

- Location error [Accuracy, Bias, Stability, Linearity]
- Width Error [Precision, Repeatability, Reproducibility, GRR]

#### Effect of MS error on measurement decision:-

- Calling OK part NG
- Calling NG part OK
- Calling common cause as special cause
- Calling special cause as common cause

#### Understanding MS errors:-

**BIAS**: - Difference between observed value and
reference value on same characteristics and same part.

**Precision**: - It is standard deviation of MS,
smaller the spread, better is precision. It is further divided into 2 parts.

- Repeatability [Within the system variation]-Show by R chart (It is EV)
- Reproducibility [Between the system variation]- Show by average (X-bar) chart. (It is AV)
- GRR [Gage repeatability & reproducibility] – Ïƒ²(GRR)= Ïƒ²(reproducibility) + Ïƒ²(repeatability)

### MSA Acceptance criteria:-

- %R&R should be less than 10%. If more than 10 and less than 30% instrument can be accepted under some condition. But if %R&R is more than 30% than we have to reject the instrument.
- When repeatability of measurement is more than reproducibility then maintenance/Replacement of gauge is required.
- When reproducibility is more than repeatability then training to operator is required.

### What is ndc in MSA?

Ndc= Number of distinct categories (It should be more than 5). Calculated only in Variable MSA. In attribute MSA we calculate Kappa.

#### What are variation in MSA?

TV (Total Variation),

AV-Appraisal variation,

PV- Part variation,

EV- Equipment variation.

#### What is formula for R&R in MSA?

R&R= Sqr-root((EV² + AV²)

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