# Gummi Bear Measurement Systems Analysis: Type 1 Gage Study

Gummi bears have more to teach us about measurement systems analysis.

Today, we’ll look at doing a Type 1 Gage Study, which compares the measurement variation to the specifications for your process, to judge whether a gage is measuring well enough. The Type 1 Gage Study is a starting point because it evaluates accuracy, precision, and consistency, but only for a single case. Later, we’ll look at the Gage Linearity and Bias Study and the Gage R&R Study.

I’ve mentioned that we will study the effect of different factors on how far a gummi bear flies, but the real goal of knowledge about factor effects is usually to minimize, maximize, or target a response variable. My target will be a CD. Choosing a target lets me provide specifications for the Type 1 Gage Study.

- Sadly, we still don’t need the catapult, and we only need one gummi bear. Here’s what you do:
- Place the gummi bear at a spot where you know the distance from your starting point. I'm using the diagonal distance of my computer monitor, 23 inches.

Measure the location of the gummi bear 25 times.

This can seem a little tedious because the Type I Gage Study is evaluating a measurement tool. Most rulers and tape measures are very accurate in this day and age, so I’m going to choose a tool that makes the measurement process harder: a 6-inch protractor. Here's what I got:

Order | Measurement |
---|---|

1 | 22.7500 |

2 | 22.6875 |

3 | 22.9375 |

4 | 22.7500 |

5 | 22.8125 |

6 | 22.6875 |

7 | 22.7500 |

8 | 22.7500 |

9 | 22.8125 |

10 | 22.6875 |

11 | 22.7500 |

12 | 22.9375 |

13 | 22.8750 |

14 | 22.8750 |

15 | 22.6875 |

16 | 22.8750 |

17 | 22.8125 |

18 | 22.6875 |

19 | 22.8125 |

20 | 22.7500 |

21 | 23.0000 |

22 | 22.8750 |

23 | 22.8125 |

24 | 22.7500 |

25 | 22.8750 |

Now we can use this data to perform a Type 1 Gage Study in Minitab Statistical Software:

- Choose
**Stat > Quality Tools > Gage Study > Type 1 Gage Study**. - In
**Measurement Data**, enter the column where you have your measurements. - In
**Reference**, enter the known distance to the gummi bear. Mine was 23 inches. - In
**Upper spec – lower spec**, enter 4.5, for the diameter of a CD. You can enter a different number if you choose a different target. Click**OK**.

My results looked like this:

The most interesting part to me was that my bias was negative: my measurements were too short. I had thought that the measurements would be thrown off most by not moving the protractor in a straight line, so I would end up with measurements that were too long. As it turned out, the real problem was twofold:

- My protractor didn’t go all the way back into the corner of the computer monitor.

- From the tip of my fingernail to the rounded part of my fingernail is a longer distance than I’d expected when you add it in 3 times.

You’ll make all kinds of unexpected discoveries when you use measurement systems analysis. The practice that you get collecting simple data to build your confidence will help you think about the issues you will encounter in more complex quality improvement tasks.

In my next post, I’ll look at how bias might shrink or grow depending on how large a measurement you take using a Gage Linearity and Bias Study.

Name: Jason Wei• Wednesday, July 4, 2012hello

thanks for the work youhave done. But I still want to kwon how the number of 21.21% (%var) is caculated.

thanks very much.

Name: Cody Steele• Thursday, July 5, 2012Hi Jason,

That's a great question. The easiest method to tell you is that the %Var(Repeatability and Bias) value is K/Cgk.

K is a percentage of the tolerance that you want to use for deciding if your gage is capable. In this example, I used 20%.

Cgk is the calculated statistic that considers whether the gage is capable with respect to both bias and variability. In this example, Minitab prints 0.94.

But Cody, you'll say, I put 20/.94 into my calculator and got 21.28, not 21.21.

This is rounding error in Cgk. To get a more accurate value, you can calculate Cgk with the formula in this PDF:

http://www.minitab.com/support/documentation/Answers/Type%201%20Gage.pdf

You will get 0.942862531. When you do 20/.942862531, you'll get the 21.21 in Minitab's output.

I appreciate your thirst for knowledge! Thanks for reading.

Name: Sumit• Saturday, November 10, 2012I have done Type 1 Gage capability study using Minitab 15 with one operator measuring the product 30 times.

The USL-LSL=0.6 i.e. +/-0.3

In reference i have taken median of all 30 values , is my approach correct if not what should be the reference value .

Thanks in anticipation

Name: Cody Steele• Monday, November 12, 2012Hi Sumit,

In Minitab 15, you can find a good description of the reference value in the Statistical Glossary. Choose the Help menu, then Glossary. Enter "reference value" as the keyword to find.

The reference value is typically known before you collect the measurement data. If you do not have a reference value, then you cannot calculate the bias. However, not all of the calculations depend on the reference value. You can still determine the percent of variation due to repeatability and the Cg statistic.

Minitab's StatGuide provides common guidelines for the interpretation of these statistics. Right-click in the output and choose StatGuide from the menu that appears.

Hopefully, that gets you started. Thanks for reading!

Name: dennis• Sunday, February 3, 2013Tappi T1200 use repeatability % over mean of set of data to check whether two sets of data really different or just due to variation. How can I use repeatability of Minitab for same purpose ?

Name: Cody Steele• Monday, February 4, 2013Hi Dennis,

As I understand Tappi T1200, you use it to compare measurements from within a lab and between labs to look for differences. The repeatability is the variation in measurements by the same lab. The reproducibility is the variation in measurements from different labs. I think you can try an ANOVA analysis to do this.

Set up your data with a column that identifies the labs, a column that identifies the materials, and a column of measurement data.

1. Choose Stat > ANOVA > General Linear Model

2. In Responses, enter your column of measurements.

3. In Model, enter the columns that identify the labs and the materials.

4. Click OK.

Part of the output is an ANOVA table. I'll paste one here, although I'm not sure how good it will look in plain text:

Analysis of Variance for Measurement, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P

Lab 8 1844.1 334.0 41.8 2.79 0.008

Linerboard 2 46629.7 46629.7 23314.8 1558.22 0.000

Error 91 1361.6 1361.6 15.0

Total 101 49835.4

Here, the error row represents the repeatability. The row about the labs tells you whether the means from the labs are different, taking the repeatability into account.

I know there can be subtle difference in the math based on whether your data are test results or determinations. Other output from Genereal Linear Model could also help--like comparisons and factor plots.

I hope that helps! Let me know how it goes.

Name: Shruti• Tuesday, June 11, 2013I have done type 1 gage capability study on some probes. The Cgk values are coming aroung 80. what does it imply? Is such a high value acceptable?

Name: Cody Steele• Thursday, June 13, 2013Hi Shruti,

High values of capability metrics like CGK are good. In most cases, values in excess of 1.33 are acceptable, so a CGK close to 80 should be wonderful. But let's talk about what that implies.

I assume that you have used the Minitab default settings: the precentage of the tolerance allowed for measurement variation is 20, and 3 standard deviations represents 1/2 the process spread. Then a CGK value of 80 implies that 20% of your tolerance, adjusting for bias, is 80 times greater than the variation of the measurement process. The probes seem to be capable of measuring very precisely under conditions with relatively small variation.

Because the purpose of the Type I Gage Study is to evaluate the gage for one operator and one measurement, you'll have to consider whether you need to study other sources of variation. A Gage Linearity and Bias Study evaluates how your probes perform over the entire range of measurements that you need them to make. A Gage R&R Study evaluates variation between different parts and variation between operators.

Thanks for sharing your experience! I hope this helps.