## How Good is My Measurement System?

You just completed your ANOVA Gage R&R analysis. The results indicate that your measurement system is responsible for 40% of the process variance (GRR%). You look up the guidelines on the internet and this is what you see:

- Less than 1%: The measurement system is acceptable.
- Between 1% and 9%: The measurement system is acceptable depending on the application.
- Greater than 9%: The measurement system is not acceptable and should be improved.

You are in trouble! 40% and it can’t be greater than 9%! What will your customer say? Should you panic? Maybe so, but then again maybe not.

This is the third part of a four-part series on Gage R&R. The first part addressed what a gage R&R study is. The second part examined how to determine how much of the total process variance is due to the measurement system. This blog now takes that result and answers the following question:

*How good is my measurement system?*

The guidelines are rather arbitrary. They do not give you any meaningful insight into your measurement system. Instead, we need to move to a newer method – developed by Dr. Donald Wheeler. His methodology places a measurement system into one of four classes. These classes give us more insight into our measurement system than the rating system above. This is part of Dr. Wheeler’s Evaluating the Measurement Process (EMP). EMP classifies our measurement system based on three characteristics:

- How much the measurement system reduces the strength of a signal (out of control point) on a control chart.
- The chance of the measurement system detecting a large shift.
- The ability of the measurement system to track process improvements.

Dr. Wheeler developed this system by focusing on the Intraclass Correlation Coefficient (ρ), which is defined as:

ρ = % of Total Variance due to the Product Variance = 100(σ_{p}^{2}/σ_{x}^{2})

where σ_{x}^{2} is the product measurements (total) variance and σ_{p}^{2} is the product varariance. Note that 1 – ρ is the % of total variance due to the measurement system (σ_{e}^{2}). Dr. Wheeler analyzed what a measurement system with different values of ρ could do. Based on his analysis, he created the classes of monitors shown in the table below.

ρ | Type of Monitor | Reduction of Process Signal | Chance of Detecting ± 3 Std. Error Shift | Ability to Track Process Improvements |
---|---|---|---|---|

80% to 100% | First Class | Less than 10% | More than 99% with Rule 1 | Up to Cp80 |

50% to 80% | Second Class | From 10% to 30% | More than 88% with Rule 1 | Up to Cp50 |

20% to 50% | Third Class | From 30% to 55% | More than 91% with Rules 1, 2, 3 and 4 | Up to Cp20 |

0% to 20% | Fourth Class | More than 55% | Rapidly Vanishing | Unable to Track |

This table is adapted from Dr. Wheeler’s excellent book, EMP III: Evaluating the Measurement Process on his website (www.spcpress.com). The first column lists the value of ρ. The second column lists whether it is a First Class, Second Class, Third Class or Fourth Class monitor – with “First” being the best. As you move from a First Class to a Fourth Class monitor the % of variance due to the measurement system is increasing.

The third column shows how much of a reduction in a process signal (out of control point) there is. The fourth column lists the chance of detecting a ± 3 standard error shift within ten subgroups. This column refers to the four Western Electric zone tests.

The fifth column describes the monitor’s ability to track process improvements. This is something we don’t think about too much. As you improve your process, the % of total variance due to the measurement system increases – eventually to a point where you move from one class down to the next. The value of Cp represents the process capability when ρ is the minimum in the class.

So, what about the measurement system with a 40% GRR. This corresponds to a ρ of 60%. It is a second class monitor, that reduces signals only from 10 to 30%, still captures 88% of the signals with Rule 1 (beyond the control limits) and can track improvements up to Cp50. This is far from being an incapable measurement system, which the traditional guidelines would infer. If you want more information on this classification system and the calculations, please see one of our Evaluating the Measurement System articles in our SPC Knowledge Base.

Once you estimate your total, product, and measurement system variances, you can use the above table to interpret the results. Our next blog will take a closer look at EMP and Gage R&R.

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