# MSA: What is ndc: Number of Distinct Characteristics

*The greatest mistake is to imagine that we never err*.: **Thomas Carlyle**** **

**Introduction**

Tolerance in any process is relevant based on its context. When we are purchasing vegetables from the market, the error of 10 grams does not matter. But when we are purchasing a gold ornament, even an error of 1 gram is very expensive. Similarly, when we withdraw money from the bank, even an error of 1 currency note is not acceptable to the bank or the consumer.

**Content: ndc – Number of Distinct Categories (MSA 4**^{th} Edition)

^{th}Edition)

- What is ndc (Number of Distinct Categories)?
- Why it is Important to Analyse the ndc in a Variable MSA Study?
- How to Effectively Understand the Purpose of ndc?
- How to interpret the results of the ndc calculation?
- What actions should be taken for ndc score <5?
- Conclusion

**Objective**

Measurement Systems Analysis, as part of the Statistical Process Control practices, has been widely used in many industries, especially those related to the automotive sector.

When the measurement of any component is conducted, there are two types of variation. The first is in the component about the standard and the second is measurement error. The key purpose of the MSA study is to identify the percentage of measurement error in the total variation. The purpose of monitoring ndc-number of distinct categories is to measure the discrimination power of the measurement system.

Once you go through the article, you will understand the meaning of ndc, what is its purpose, how to effectively interpret it and what action needs to be taken, when it is not meeting the requirement.

__Read More: __**http://bit.ly/VariableAttributeStudy**

**Definition: MSA: AIAG Manual 4 ^{th} Edition**

**Repeatability**: Variations in the measurements obtained with one measuring instrument when used several times by an appraiser while measuring the identical characteristic on the same part.

**Reproducibility**: Variation in the average of the measurements made by different appraisers using the same gauge when measuring a characteristic on a part.

**Bias:** The difference between the observed average of measurements and the reference value.

**Linearity: **The change in bias over the normal operating range. A systematic error component of the measurement system.

**Stability (Drift): **The total variation in the measurement obtained with the measurement system on the same master or parts when measuring a single characteristic over an *extended time period*. __Stability is the change in bias over time__.

**Read More: ****http://bit.ly/CommonSpecialCause**

**Detailed Information**

**What is ndc (Number of Distinct Categories)**?

The ndc is one of the criteria used by the MSA to determine the sensitivity of the measuring equipment. It indicates the “**Number of Distinct Categories**” that can be clearly distinguished by the measurement system being used.

Statistically speaking the ndc is the number of non-overlapping 97% confidence intervals that will span the expected part variation. In other words, it represents the number of groups within product or process data that the measurement system can *discern*.

In layman’s terms, using the graphical representation, the ndc tells the user how many times the GR&R curves fit within the part variation curve – *the more times the better* i.e. the more sensitive your measurement equipment is.

** ****The formula for calculation is ndc = 1.41*(PV/GR&R)**

Where:

- PV = Part Variation – the real variation of the parts manufactured
- GR&R = Gauge Variation – the variation of the measurement process

It is important to understand that GR&R measures only the variability in measurements. It does not reveal anything about their accuracy, which can only be assured through calibration, so if inaccurate (junk!) measurement data goes into the calculation in the first place, the user will get unusable results to work off.

**Why it is Important to Analyse the ndc in a Variable MSA Study**?

The key objective of any measurement system is to get accurate results so that desired actions can be taken. However, if the results are heavily influenced by the measurement error, the results can not be trusted as good parts may be rejected (Type I Error) or the bad parts be accepted (Type II Error). Example,

__Example: Type I Error (Producer Risk)__

**Measurement Error: **0.02 mm

**Dimension**: 4.90 to 5.00

**Actual Dimension**: 4.99 mm

**Due to Measurement Error, Observed**: 5.01 mm.

**Result**: Product Rejected, although OK

__Example: Type II Error (Consumer Risk)__

**Measurement Error: **0.02 mm

**Dimension**: 4.90 to 5.00

**Actual Dimension**: 4.89 mm

**Due to Measurement Error, Observed**: 4.91 mm.

**Read More: ****http://bit.ly/TypeITypeIIError**

**How to interpret the results of the ndc calculation**:

The resulting value tells the user if the measurement equipment is sensitive enough. The higher this number, the better chance the measuring instrument has in discerning one part from another, and the guidelines for interpretation are listed below:

- ndc ≥ 5 – acceptable measurement equipment
- ndc < 5 – rejected measurement equipment – more sensitive equipment needs to be used.
- ndc < 2 is considered too low to interpret because there is nothing to make comparisons between
- ndc = 2 – this is a suboptimal result as the data can only be divided into two groups (high-level and low-level data)
- ndc = 3 – this is also a suboptimal result as the data can only be divided into 3 groups, say low, middle, and high

**Read More: ****http://bit.ly/BiasLinearity**

**What Actions should be taken for ndc Scores of < 5**?

- To increase ndc you need to
**increase**your*part variation*(PV),**decrease**the*measurement variation*(GR&R), or both. - Changing the measuring instrument like switching from a caliper to a micrometer does decrease GR&R, but it may not have much of an effect if the PV is small.
- Increase the part variation so that it can represent the full spectrum of variation. Example: If the part variation is 9.8 to 10.2 mm but we have considered the components from 9.9 to 10.1, probably, the ndc will be low but when we will conduct the study by selecting components having variation from 9.8 to 10.2, the ndc will improve.
- Increase the precision of your measuring instrument like Least Count from 0.1 to 0.01 mm.

**Read More: ****http://bit.ly/SPCandMSA**

**Conclusion**:

The purpose of the MSA study is to identify the possible error emanating from the measurement system. Either the error should be within target or the user should have a justified reason to have more measurement error. Whatever decisions are being taken; it should be in context to the measurement system.

**Read More: ****http://bit.ly/CommonSpecialCause**

**References**:

MSA AIAG Manual 4^{th} Edition

Industry Experts

*This is the 207 ^{th} article of this Quality Management series. Every weekend, you will find useful information that will make your Management System journey Productive. *

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