# Short notes on measurement system analysis

## 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:-

1. To quantify the variation in measurement system.
2. To ensure stability of measurement system.
3. To minimize measurement system variation within total process variation.

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

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

### Measurement system error:-

1. Location error [Accuracy, Bias, Stability, Linearity]
2. Width Error [Precision, Repeatability, Reproducibility, GRR]

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

1. Calling OK part NG
2. Calling NG part OK
3. Calling common cause as special cause
4. 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.

1. Repeatability [Within the system variation]-Show by R chart (It is EV)
2. Reproducibility [Between the system variation]- Show by average (X-bar) chart. (It is AV)
3. GRR [Gage repeatability & reproducibility] – σ²(GRR)= σ²(reproducibility) + σ²(repeatability)

### MSA Acceptance criteria:-

1. %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.
2. When repeatability of measurement is more than reproducibility then maintenance/Replacement of gauge is required.
3. 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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