This article might not fit into a context at first, but it is very general-purpose in terms of its applications. I’m going to fit this topic into a hypothetical scenario, which is very common in product development. Remember that this is just an example, and you can apply the principles in a variety of different situations. Also, the whole point of this exercise is to figure out how good is your verification system. You need to keep that in your mind when reading through the rest of this article.
Pretend that you want to source different parts from suppliers based on your specifications for a product development activity. In my case, I’m building a small wooden deck at my home, and I need to source a large number of steel nails of length 1" ( 2.54 cm). My formal specification is the following.
|Nail Length||2.5 cm||2.6 cm|
This table clearly shows what is acceptable and what is not. I have a reasonable room for errors for my nail suppliers’ manufacturing processes. I do not provide them any other parameters such as standard deviation or mean nail length. In many professional product development cases, they are also provided as part of the requirement specifications. Now imagine, based on this specification, my supplier provides me a sample of 10 nails from a large bag of nails. Statistically, what they just did is the process of sampling from a nail population. I need to verify the sample to ensure that it meets my requirements using some mechanism, and give a go or no-go signal back to the supplier. My verification should be devoid of any errors or process deviations.
I have decided that the precision of my nail length specification is only 1mm (refer to specification table), and the discrimination I need to use for my measurement should be higher than that. Typically this is 10% or better. So, I have decided to use a vernier calliper, which can measure upto 1/10-th of a millimetre. Secondly, I have to ensure that, the verification process should be reproduce-able regardless of who is executing it. So, I have decided that I will take help from my wife and my sister to ensure that the measurement process has reproduce-ability. Lastly, I also have to ensure that each of us should be able to repeat the verification process at any point in time. The image below shows my measurement table. I have numbered the nails, and I have devised to hold each nail in my left hand, keeping nail head towards my left, and measure by my right hand, in a well lighted environment.
Minitab is a great statistical tool that has the ability to provide you a number of statistical insights. For this use case, I’m going to use the Minitab’s Stats > Quality Tools > Gage Study > Create Gage R&R Study.
Note that I have entered all three of our names, and ensured that every part is measured at least twice. Press OK. Minitab will provide you a measurement worksheet in a randomised order of measurement activity. Note that, there are 60 entries in total. That is, 10 parts x 3 operators x 2 repetition each. The next activity is to do the measurement as listed in the worksheet. We three spent about 30 minutes to perform the measurement using the same vernier calliper and the same technique by holding each nail in our left hands, the same way. Each measurement is promptly recorded into column C4, and the worksheet is now completely filled up.
The next step is to analyse the results. Go to Stats > Quality Tools > Gage Study > Gage R&R Study (Crossed). Minitab will prepare and present you with a pack of insights in 6 different graphs.
Let’s go through these graphs and explain what each graphs are telling us about the gage study.
This graph tells us the source of variation in the measurement process. In this case, more than 90% of the variation is coming from the parts themselves. Which means that, our verification system is generally good, the variation in length is coming from the manufacturing process of these nails. That is, the nails are ’really" different from one another.
This graph tells us that, the lengths are not closely packed around the mean, there is definitely some amount of part-to-part variation. We knew this already from the earlier graph, but this graph tells even more. There is a variation in measurement for the first and third part. These two parts might need inspection to figure out why it varied when measured by three different operators. It will be investigated.
This graph tells us that Ann’s measurement has at least two outliers. This could possibly mean that she is deviating from the method of measuring which we have agreed before starting the experiment. She might have trouble holding the nail in the left hand? Could there be a difference in lighting due to which she is not able to eyeball the calliper correctly. She might need re-training to ensure that the operating procedure is followed strictly during verification. Also note that she has consistently measured lower than the other two. This is a good indicator that her measurement is biased in one direction. There is probably a need of introducing a nail holder, which any operator can use easily, and the calliper can be replaced with one which has a digital read out.
This chart tells us that for the first part, one operator has repeatedly measured higher than the rest. It provides some amount of insight that, for part-1 there is clearly an error generated by the process among as every operator deviates from each other. May be that part has a manufacturing defect, which can cause deviations to the current measuring process.
The R chart, or the Range Chart visualises how much the samples vary from each other. Note that the overall range is 0.00 - 0.04, where part-2 has literally no variation from each other, even across operators. Another insight from the R chart is that the maximum variation across parts is about 0.03812 cm. From the X-bar chart, one thing is quite clear, the mean of the 10 parts measured is 2.5378 cm, which is very close to my ideal requirement 2.54 cm. However, the mean spec limits are 2.5598 cm 2.5159 cm, which some of the parts does not respect. This indicates a higher standard deviation, which can be further investigated by calculating the basic statistical parameters. Part number 6 is a significant deviation. This demands a review of part number 6, and if in a repeated sample from the population has such deviations, then the supplier needs to relook into their manufacturing process.
The Gage Repeatability & Reproduced-ability study is a very effective way to ensure that your method of verification does not affect a part’s qualification. It can provide unique insights about the operating procedure used for verification studies and the human element involved in. The exercise is worth the time it takes, and should be considered for any product development activities.