# Short notes on measurement system analysis

Mar 23, 2021

## 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):-

:- Least count of instrument should be 1/10
th 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

### 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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