ISACA COBIT 5 – Measure (BOK V) Part 7

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- January 26, 2023

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**19. Gage R&R – Number of Distinct Categories (NDC) (BOK V.C.1) **

Coming to another important aspect of measurement system, which is number of distinct categories. We did look at this number in ANOVA method. We did talk about that in that presentation in ANOVA method. Here let’s understand NDC or number of distinct categories in more detail. Before we talk of NDC or number of distinct categories, let’s understand resolution. We talked about that resolution earlier. For example, we have a class of students. In that class we have students who have height ranging from 100 height. Now, we want to measure the height of these students.

We are looking at three ways to measure that. We have a rod if that rod has height in meters only. So this rod has let me put it here. So let’s say the rod or the measuring device which we use in this case, let’s say this has readings as zero, 1 meter and 2 meters. Now, if this is the only thing which we have to measure students and our students are from 100 CM, which is 1 meter to 1. 3 meters, if I use this rod to measure, every student will have same height. Because for every student I will say this student has a height of 1 meter because I cannot go into the final detail of that.

Now, if I take another rod which has the resolution with the decimeter and decimator is 10 CM. So this rod has something, let’s say 10. This is a big reading of 1 meter. And then again 1020 30. Now, if this is the rod which I want to use here, I can classify my students into three groups. Students who have a height of 1 meter, students who have a height of 1 meter to 1. 1 meter. And then second group, 1. 1 meter to 1. 2 meters and another group of 1. 3 meters. So I can segregate these students into three categories if I have this as my measuring device. Now, if I have even more finer resolution, instead of 10 CM as the resolution, if I have 1 CM as the resolution, then I can divide my group into 30 different categories because now I can differentiate between 100 with that roar. So this was resolution. Now, what we are assuming here is that there is no variation.

And what does that mean is, let’s say if a student has a height of 101 centimeter, every time I measure that, I will measure that student as 101 centimeter only. Probably that is not the case in any measurement. Any measurement will have variation. Now, if my variation in the system is such a bad that 101 centimeter students, sometime I measure this as 98 CM, sometime I measure this as 103 CM, that’s the variation. If that variation is there in my measurement system, then I will not be able to divide my students into 30 categories. Probably I might be able to divide my students into, let’s say six categories, because my measurement itself has so much of variation that I cannot really distinguish between 10 one and 10 2 CM. This is where the concept of NDC or number of distinct categories comes into picture.

So NDC or the number of distinct categories that is given by this formula, let’s understand the formula here, and then we will go into more details of that. NDC is given by 1. 4 114, and when I say 1. 414, this is basically square root of two, then sigma of parts. What is the standard deviation of parts? In previous case, which we took the standard deviation of the heights of students. If I have heights, I list down all the heights of students, 100, 105, 120. If I take the standard deviation of those heights, that will be sigma parts and sigma gauge is the standard deviation of the gauge measurement.

That’s a measurement error. Measurement variation. Earlier on the previous slide, we did talk about this, that if we have gauge variation more, if we have a higher gauge variation, we will not be able to split our students, the group of students, into 30 categories. We might end up splitting them into six categories, because there was more variation in the gauge. And that’s why you see the gauge in the denominator higher the sigma gauge, you will have the lower value of NDC. And graphically, you can show those buckets. I will talk about buckets later on.

But if my students were from 100 to 130 CM, if this was the distribution of students height because of the gauge variation, I might not be able to split that into 30 different categories. I might be able to split them into three categories. If my gauge variation is such wide, if my gauge variation is thinner, less variation, let’s say something like this, I might be able to split my students into more than three groups, more than three buckets. Let’s move on to the next slide to have a little bit more understanding on this concept of NDC, which is number of distinct categories. So, as we talked on the previous slide, that NDC is the number of buckets in which you can naturally drop your data into. If your gauge variation is too much, you will have the less number of buckets in which you can classify your data. Now comes what is the acceptable value of NDC? And what if NDC is low? Let’s say if NDC is coming out to be low, what’s the reason of that? One reason of that could be that your gauge variation is too much, that is leading to the lower value of NDC. So for that, you might need to think about increasing the precision of your measurement tool. So, if you have a more precise tool, you will be able to reduce the variation because of the gauge variation, because of the measurement, and that will increase the NDC value.

You want higher value of NDC. Let’s be clear here, and second thing would be that in your analysis, which you did the Gauge R and R study, which you did, you probably did not include all the ranges of parts in that. If your student height was from 100 to 130, probably you just picked a sample of students who had height of 110 and 115 only. So the width of the samples which you took was less. So that means there could be a problem with your study itself. In your study, you need to make sure in Gauge R and R study, you need to make sure that whatever samples you are taking, whatever parts you are taking, that should represent the wide range of the tolerance. So you need to have some parts which are on the lower end of the tolerance, which is the lower specification limits some parts on the higher end of the tolerance. Some parts in the middle of the tolerance don’t pick up pieces just from the center of the tolerance. So that could be another thing.

So two things here. If NDC is low, that means your study was wrong. You didn’t pick the range of parts which represent the full tolerance, or your measurement device was not precise enough. What is the acceptable value? What is not acceptable value of NDC? Let’s look at that on the next slide. So NDC value of less than two is not acceptable because this cannot separate parts into even two categories. Forget about splitting the part into a number of categories. If your NDC value is two, then what your measurement system can do is your measurement system can divide the measurement into two categories only. It can just say that whether this measurement is high or this measurement is low, that’s all NDC value of three can divide your data into three groups. Let’s say low, middle and high. What you need to have is at least NDC value of five, and above represents the acceptable value of NDC for a measurement system.

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**20. Gage R&R – Crossed vs Nested Gage R&R Study (BOK V.C.1) **

When we took the example of gauge R and R using ANOVA method, we selected the cross gauge R and R study. Here on this slide, let’s understand the difference between the crossed gauge R NR study and the nested gauge R and R study. When we do cross gauge R and R study, what we do is we take three operators, we take ten parts and we ask each operator to take three measurements. So with that, we end up with 90 readings. So let me put it here. So we have three operators or the three appraisers, appraiser A, appraiser B, appraiser C. Each of these appraisers. Look at each of these ten pieces. So I have pieces piece number 12345 and so on. Let’s put it five here on this picture to make it simple. So the appraiser one looks at part number 1234 and five takes the reading, takes the reading three times. So reading number one, reading number two, reading number three.

This is by appraiser number eight, then the same ten parts. In this simple example, we have taken five here, the same five parts. Appraiser B also looks into that. Appraiser B also measures that. Appraiser C also measures these pieces. So each of these three operators or the appraisers measure ten parts three times each, leading to 90 readings. That’s what you do in cross gauge RnR study. But what happens if the test you are doing or the measurement which you are taking is a destructive one?

The example of destructive could be the paint peeling strength. You peel the paint and see how much strong that is. You cannot do the same test number of times. One operator cannot do the same test three times or even three operators cannot do this because the item will get destroyed. Let’s say if you want to find out the breaking strength of a piece. So if you take piece number one, operator number one, find operator number A, finds out the breaking strength of that, that’s it. Now, the operator A cannot find the breaking strength of that piece number 1, second time, third time.

So here now what you will do is you will take 90 pieces and 90 pieces will be tested by these three operators or appraisers and they will record the value. So here in this case, in nested one, you will have appraiser A. We’ll look at part number one, part number two, part number three and so on. And same thing with a pressure B and a pressure C also. So none of these parts will be retested by another operator. So that’s the key difference between crossed and nested gauge R and R. Crossed one is used where the test is nondestructive. Nested one is used where the test is destructive active, where only one operator measures each part because the part gets destroyed. So this completes the difference between the crossed and nested gauge RnR study.

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**21. Measurement systems across the organization (BOK V.C.2) **

In the previous topic when we talked about measurement system analysis. That measurement system analysis is not just applicable to some physical measurements. Measurements which you take for example the diameter, or the shaft, or the length of the rod, or the thickness, or the time, those are not just the measurement. There are a large number of measurements which are taken in an organization. So when you think of MSA, don’t just think of those physical measurements on the product. Even though your company is not manufacturing anything, still there will be measurements. So in this section we will be looking at those sort of measurement, what measurements which we can have in sales, in marketing, in production, and in many other functions of an organization.

So let’s look at that on next slide. But before we do that, let’s understand that that organization needs measurement to track the progress. So measurement is not just for the production, for progress measurement. Also you need to take some measurements and the measurement system analysis or the MSA which you learned earlier, the concept of those relate to any measurement in the organization. Many a time we call these measurements as KPI as well. So KPIs are key performance indicators, key performance indicators to tell how the company is progressing, how things are moving, how a particular process is behaving, whether that is giving the right result or not. All those things are measured with the help of key performance indicators or KPIs. And as I earlier said, that all functions in the organization, all functions have some or other sort of measurement in place. And we will be looking at some examples of that. And these examples might differ from company to company, the type of organization, the scale of organization, and many other factors.

So you might need to find out what are the right type of KPIs for your own organization. Another important thing is when you want to decide on what to be measured in the company. Many at times we fall into a trap to pick measurements which are easy to measure. If something is easy to measure, we love to do that because you don’t need to do anything on that. But we need to think about that, whether that measurement gives some insight into the process, whether that helps in finding out where the company is. So when you need to find out the KPI or the indicators or the measurements, make sure that your measurements are something which add value, not just because those are easy to measure. So with this as a background, let’s move on to the next slide and look at some of the examples of measurements in the organization, different functions in the organizations. So let’s start that discussion with Sales. So, if you are working in Sales department, what all measurements could be there? And depending on the type of company, these measurements might change. You might adopt some of these or you might have a totally different measurements in your sales department. So let’s look at some examples here. The first example here is number of customer complaints that will tell you how your company is performing. Sales department would be interested in finding out what sort of the complaints we are having, what level of complaints we are having, what percent of items are being returned, what percentage of sale we are getting from the returning customers. So for example, in this course, what number of students who bought my earlier course are buying my new courses? I’m interested in that because that will tell whether people are liking my courses or not.

Sales growth is another indicator. Market share, what sort of a market share this company has. Sales department might want to know that. Customer satisfaction rating, some of these indicators might overlap. But then you need to find out, depending on your company, depending on the strategy which this company has, whether the company has a strategy to increase the market share, whether the company has a strategy to increase the sale, or whether the company has a strategy to improve the customer satisfaction, whether the sale is going up or not might not matter. But maybe this company decides to have more customer satisfaction. So, depending on the company, depending on the organization, you might want to pick these or some other indicators or measurements.

These are just few examples. Let’s look at few more examples for a different department on the next slide. So, earlier we talked about measurements in the organization related to sales. Now let’s look at some of the measurements related to purchases. So, when the company buys something from suppliers, what all this company might be interested in? This company might be interested in average number of suppliers for key components. And as I earlier said, all these indicators, all these measurements depend on the company strategy. So if the company strategy is to reduce the number of suppliers for key components, they just want to have a long term relationship this company. Then this company might be interested in finding out what is the average number of suppliers for key components, number of strategic alliances which this company has formed with its suppliers. Because they are looking for long term success of this company as well as suppliers. So for that company is interested in forming strategic alliances. So what are the numbers of that? That could be one measurement.

Another measurement could be rejection rate from suppliers. So whatever material you bought from suppliers, what is the rejection rate in that? And as I earlier said, there could be number of such measurements. Let’s look at a few more examples on the next slide. So we talked about sales, we talked about purchases. Now let’s look at production, what sort of a measurement which we can have in production. And these are in addition to the physical measurements which we could have when we are making a product, the length of the product, the size of the hole, the fit up, all those measurements are different. Whether it’s a physical measurement or these management measurements, both could use MSA, that is measurement system analysis. So coming back to the topic of production measurements, you could have value added per person as a measurement.

How many employees you have and how much value this organization is producing. Dividing that, you might want to calculate value added per person. You might want to look at internal rejection or repair rate. You might want to look at work in progress, how much money is tied up as work in progress. Because that is the sort of an inventory which you want to reduce. Another measurement could be equipment utilization. What is the utilization of each of your equipment? Maybe some equipment are 50% utilized, some equipment are 10% utilized. So you might want to look at that here I will divert from this topic and talk about theory of constraint. So theory of constraints tell that you shouldn’t be looking at local optimization of your equipment. So for example, let’s take you have three pieces of machines. So machine one, machine two, machine three. So product comes to machine one, then to two, three. Suppose you find out that your machine one is underutilized, but you are still meeting whatever demand you have, whatever pull you have from customer.

So this machine is just working at 10%. Just working at 10% is enough for this machine to produce whatever customer demand is. Now if you want to optimize this and take it to 100%, that means making ten times more pieces out of this machine. Then where those pieces will go, those pieces will be piling up as an inventory here. Because your customer doesn’t demand that or your machine too doesn’t push through that. So what I want to say is when you look at equipment utilization, you should be looking at equipment utilization from the point of customer demand, not the local optimization of equipment. Local optimization of this equipment, number one, basically will lead to more inventory, more money getting held up, which doesn’t get sold. That was just some diversion from this topic of measurement system. But I thought this was important to know that when you are looking at equipment utilization or any other indicator, make sure that there are no wrong consequences of that. So if someone took this measurement equipment utilization as an indicator and started to improve that, this could have led to another problem, another problem of higher inventory.

So those were some examples of measurements which you can have in different functions. There could be many other, but these were just a few examples, few important things. When you have measurement system or when you have measurements in the company that your measurement should be free from bias, make sure that whatever you are measuring is free from bias. Because many times you will have something subjective. And when you have something subjective, something being manually entered, there is a chance that there could be bias creeping into that. For example, if you want to find out how much customer is satisfied with the quality of your product and for that you send out the quality manager to interview customer, definitely there will be some bias because quality manager of the company would want to hear positive from customer. So there is a bias here. So when you are taking measurement, make sure that you avoid such type of bias or the potential bias. Another thing is that repeatability and reproducibility.

As we learned earlier in MSA measurement system, analysis is important. And once again to remind you, repeatability is when a single operator takes the same measurement. That should be consistent. So if I go and interview or check or find out something, take one measurement, second time I check the same person, interview the same person or check the same piece, I should have the same value. That is repeatability and reproducibility is when different operators take measurement of the same piece, then it should be the same. So whether I measure or my friend measures this piece, it should give the same value. So, this is also an important in measurement system and of course we have learned about that in previous topic which was MSA. So even when it comes to organizational measurements, this is still important to make sure that your measurements are free from bias. Your measurements are repeatable and reproducible.

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**22. Metrology (BOK V.C.3) **

In the topic of measurement system, we talked about MSA which was measurement system analysis and then we talked about various measurements in the organization. Now, coming to this topic of of meteorology. Meteorology is the science of measurement and science of measurement and this would be something related to calibration this would be something related to making sure that whatever we are measuring is consistent, is right, it’s true. So, this is the science of measurements as against another term which is meteorological, which is the science of weather forecasting. We are not talking about weather forecasting here, we are talking about the science of measurements. So let’s come back to the topic of meteorology, which is the science of measurements. Meteorology involves three main activities and these are definition of internationally accepted units of measurements. So you need to have internationally acceptable unit of measurements.

What does that mean? If a person in Canada or person in India or person in Europe or person in any place in the earth says 1 meter, it’s 1 meter only and it’s the same thing, 1 meter is same thing across the globe, 1 second is same thing across the globe. And this is achieved by defining internationally accepted unit of measurements. So that’s one activity, the second activity involved with metrology is the realization of these units of measurements in practice. So that particular internationally accepted definition need to be converted to something which is physically understood. So, realization of these measurements in practice is the second part of meteorology. Third part is application of the chain of traceability linking measurements made in practice to reference standard. So, let’s understand in plain thing, you have a technical definition of 1 meter or a very technical definition of 1 second, which you will learn later on which a general person cannot understand. That’s one part, how do you define each of these measurements? The second part is how do you convert that into something which is practical? And then third part is making sure that there is a chain.

So there is a chain which connects each of these measurements to internationally acceptable standard. So, when we talk of measurement system, there are seven base units. Seven base units are meters for length, kilograms for mass, second for time, ampere for electric current, kelvin for temperature, mole for amount of substance, and candela for luminous intensity. These are seven basic measurements rest all measurements could be made from this. So, let’s say if you want to talk about area, area is meter square which is length multiplied by length, volume is length, width and height multiplication of these three. So that will be meter multiplied by meter multiplied by meter. So, out of these seven units, you can draw any other measurement from these basic or the base seven measurements. So, earlier when I was talking about that, there is some technical definition of each of these measurements.

So, for example, when we say meter long ago, quite earlier there used to be a rod, a piece of rod which was kept at a fixed temperature at one place internationally and I guess that was Geneva, that was 1 meter. So all other measurements were taken reference to that rod, that measuring rod but now that has been replaced by next definition which is here which is the distance traveled by light in vacuum in one divided by this much second. This is the definition of a meter, this is the technical definition of a meter and which is then translated to practical measurement in each country’s lab kilogram is the only thing for which you have a prototype or for which you have a piece of metal which is lying somewhere and which is a 1 kg rest. All units if you see, are something which have to be drived out. So for example meter there’s no fixed meter lying somewhere for calculating a meter you need to make sure that the light travels in vacuum in these many seconds one by this many seconds is a meter same way is for second also same way is for ampere, calvin, mole and candela. Kilogram is the only thing as of today for which there is a prototype which is lying somewhere and every kilogram has to be compared to that prototype. So as we earlier said that there are only seven base units and rest all are derived from that and those other things are known as derived units. So the derived units are calculated by the power of something, the product of something or quotients of a base unit.

So that is something which is calculated from the base unit. An example, as I earlier told you, was area volume and here is another example when you are looking at velocity you don’t have an internationally accepted definition of velocity because you have definition of length and you have definition of time. So meter per second is the unit of velocity and since you know what a meter is because that’s a fixed value and you know what the second is, then you can have an internationally acceptable derived unit of velocity from these two which are length and time. Another important topic when it comes to meter logic is a calibration because when we say that length of 1 meter there’s an internationally acceptable definition of that and then you can have that converted to a practical thing. How do we make sure that everyone in the country, everywhere, every manufacturer whosoever manufactures, whosoever has a meter rod or a tape or a ruler scale, how does this person, how does everyone make sure that a meter is meter everywhere? That is done through calibration. So in calibration, the purpose of calibration is to ensure consistency.

Consistency so that 1 meter is 1 meter everywhere and it is to determine the accuracy of instrument readings to make sure that the instrument readings are accurate and whatever measurement you are taking that measurement can be trusted. So if someone gave you 1 meter thing and which you want to use as a 1 meter in some other product. Calibration ensures that what you are receiving as a 1 meter is actually 1 meter. And it’s not something 1 meter two centimeter or 1 meter two millimeter. This is what the whole purpose of calibration is and how does this gets achieved. Let’s look at that here. So, when we talk of calibration, another important thing here is traceability. Traceability is to make sure that whatever measurement instrument you have, whether that is traceable to national or international standard. So traceability will ensure that in your company, the operator who is using a measuring tape, whether that tape is traceable to national standard or international standard, this is what is the purpose of traceability. So the definition here is that traceability is the property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibration, each contributing to measurement uncertainty. So, key thing here is unbroken chain of calibration. How does that gets done? Let’s see that. So here is the chain of unbroken documentation. So, what you have is at the top you have si unit.

And these are the units which we earlier said that 1 meter is equal to light traveling in vacuum for one divided by that many number seconds. That was a unit of length of 1 meter. From that si unit, your national lab will have a physical piece. And with that physical piece, your national lab will calibrate and issue the calibration certificate to third party laboratories in different part of country. So this is this part. So your national lab issues or calibrates the masterpieces’of third party labs. So third party laboratories might have another meter rod which they sent to the national lab. National lab will calibrate that, check that whether this confirms and issue a certificate or a piece of documentation. So with that documented calibrated rod, this third party lab will calibrate the equipment used by organizations, which is the next level organization or even the meteorological department of the organization. Because organization might not want to send their every tape to third party laboratory, they might think that okay, let’s get one instrument, one piece of equipment calibrated from third party rest all with the help of that, we can calibrate our rest of instrument. So this is what they’re doing.

Meteorological department will get that piece of rod or that piece of measurement equipment calibrated from third party lab. And with that calibrated piece, which they keep protected, they will calibrate the working instruments used in the company. So if a company has 2030 pressure gauges, so let’s say this company has 20 pressure gauges, they will have one master pressure gauge, which will be the most accurate or the most reliable thing that they will keep as one master in the meteorology department. And this master gauge, they will send it to third party lab for calibration every six months or whatever frequency is appropriate. So they will have a documented of that. And to calibrate this piece, third party will have their own master. So one master for third party lab. Third party lab. And this master will again, they will send it to the National Lab for calibration. So this is how you get the unbroken chain of documented.

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