ASQ CQA – 5. Quality Tools and Techniques Part 11

27. 5D3 Outliers

The next topic in process variation is outliers. So here as CQA, you are expected to understand the significance and impact of outliers. But before we do that, let’s understand what an outlier is. An outlier is an extreme value. So if we just take the same example of me traveling from my home to office, most of the time I was able to reach my office between 610 and 650 and one day if I reach 730, that was outlier. That was significantly different from other readings.

So these extreme values are called as outliers. So as an auditor, whenever you are looking at data and you see some data, some information which is an outlier, which is an extreme value, then probably you might want to investigate, check that why this outlier is and whether the auditor has looked into that and took some action for that particular outlier. So this is how an outlier is significant for an auditor. So when you have an outlier, basically that means that there is some special cause here. So you might want to investigate or you might want to see whether the auditor has investigated that.

Even in the case of measurement of central tendency, there also we talked about mean mode and median and we said that mean is affected by outliers. So if there is an extreme value, the mean is significantly impacted by that. The median is not impacted by an outlier. So for example, if I have a data here which tells that travel time from home to office in minutes on number of days, ten minutes, eleven minutes, ten, 812, eleven. And then I have one reading which is 65 minutes.

So 65 minutes is obviously an outlier. So in case I need to find out that what is the average time I take to travel in that case, one thing I could do is I could take average of these numbers, but average of these numbers will be impacted by this one number, which is 65. 65 will significantly impact the average value. But then that 65 was because of a special cause. So that is the reason probably I might consider removing 65 from the data once I have identified the cause of that, once I have taken action for the that. So probably I might want to remove this number from this data and take the average of rest of these numbers excluding 65.

28. 5E2 Types of Sampling

Say if 1 million pieces of these items come to the factory, then are you going to measure all of these 1 million items to understand what is the current status of this particular supplier? Probably no. You will be just taking some samples and based on those samples you will be making judgment what is the quality of the supplier. So you need to take sample when things are in large number, when there’s a lot of costs, cost and the time involved in checking or measuring everything.

So now after understanding why we need sampling, now let’s understand two broad categories of sampling. One is the probability sampling and the second is non probability sampling. In probability sampling, the most important thing is every item in the population has equal chance of being selected. This is the key difference between the probability and non probability sampling. And this is one of the important aspect because based on this sample you want to make a judgment about the population. You want to make judgment about the big lot from which you have taken sample.

So probability sampling is important once you want to make judgment about the population. On the other hand, when it comes to non probability samples, non probability samples are samples where the probability of selection cannot be accurately determined. So it’s not very clear whether this was random, whether everything had equal chance. That is not possible in case of non probability sampling and in non probability sampling, as you are not randomly selecting.

So these samples generally may not represent the population because what you are doing in non probability sampling is you just took some samples for your own convenience, whatever is convenient to you, but that might not represent the whole population. So this is the difference between probability and non probability samples. In case of probability sampling, we can have simple random sampling, systematic random sampling, stratified random sampling, cluster sampling. In case of non probability we can have accidental convenience sampling, or judgmental sampling, or quota sampling. Let’s talk about probability sampling first, starting with a simple random sampling. In simple random sampling, each item in the population has equal chance of being selected.

This is the best thing which you can do because if each item in the population has equal chance of being selected, then your sample, whatever you have selected, will actually represent the population. So your sample will be the representative of the whole population. So you can make very good judgment about the population looking at the sample. The example of this could be using random tables. So there are tables where you can have random numbers. So based on that you pick those items. So let’s say if you have 100 students, or let’s say if you have 100 items which have been produced, which of these items to be picked? You take a random table and random table will tell you that. Pick item number 46, item number 37, item number 86. Whatever numbers.

These are, these numbers can be randomly generated in Microsoft Excel as well. You can use that or you can have draw off lot. So if you have to select five items out of these hundreds, then what you can do is on a piece of paper, you make small chips, each having number one to 101 to three four, and then randomly pick those pieces of paper. And based on that, you will decide that. Okay, the first item is 46. So I pick item number 46. So this will be a random selection. So this is simple random sampling. Now coming to the second type of probability sampling which is systematic random sampling here what we do is we select one item at a regular interval through the ordered list. So let’s say if you have a machine which keeps on producing item and then we randomly select one number, let’s say we randomly select number six. That means every six piece which comes out of that machine will be checked. So this is systematic random sampling.

The third type of probability sampling is stratified random sampling. When we say stratified is basically dividing things into subgroups. So what we do in stratified random sampling is we divide our population into subgroups. So very simple example of this is let’s say if we have to select ten people randomly from a country, from a city, from a town, that what we can do is we can stratify. Here by stratification we mean that we can decide that out of these we will pick five males and five females just to avoid any bias related to sex. You don’t want to select let’s say eight male and two female if you have to study just ten people because that will not be a good representation. So here just to make sure that you pick equal proportion because male and female in a town are more or less in the same proportion. So in the same proportion you pick those people as a part of sample as well.

So this was stratified random sampling. The fourth type of probability sampling is cluster sampling and cluster means again something like a group. So here you cluster the population in certified random sampling. Basically what you did was you made a group in the sample here in cluster sampling you make groups in the population itself. So rather than selecting ten people you can decide that okay, I will be picking two persons from each of these five states. So here what you have done is you have divided the population into clusters. This might not be as perfect as simple random sampling but sometimes depending on the situation, you might have to choose cluster sampling or stratified random sampling. After talking about four types of probability sampling now let’s talk about three types of non probability sampling here. The first one here is the accidental or the convenience sampling. Convenience means whatever is convenient to the person who is picking samples. So what researcher or the person who is picking samples here does is whatever is convenient to this person, this person picks that. And that is the reason we say that this is a non probability sampling here.

Each item is not having equal chance of getting selected. In this case, the sample might not be a good representative of the population. The example of this could be instead of randomly selecting customers who are visiting the store, the researcher or the person who is taking this interview will randomly pick five people. When this person visits the store, whatever, first five people come to store, this person will interview them. So this is convenience. Convenience could be. Let’s say if you receive a truckload of items in the factory and what you do is anything which is near to the door which is easily accessible, you pick some items from that and take those as sample.

Because this is convenient sampling. Rather than looking at the whole lot and looking at the random selection, you just pick whatever comes convenient to you. So this is one type of non probability sampling. The second one is judgmental sampling. In judgmental sampling, the person who is picking makes their own judgment and based on that they pick sample. Let’s say if I’m doing an audit and I’m looking at number of documents, I just make a judgment about selection, for example, and I say, okay, let me see all the documents which have been released in last one week. So rather than selecting those documents randomly, I just make a judgment and look at all the documents which were released in the last five days or six days.

29. 5E1 Acceptance Sampling Plans

Sampling. Let’s take an example. So let’s consider a case where we are manufacturing something and we have a supplier which is supplying us items on a regular basis. So this particular supplier has now supplied us 1000 items in a truck. Now truck is standing in front of the factory receiving gate and we need to receive this 1000 items. One option could be truck. Check each of these thousand items one by one. And if these thousand items are acceptable, you accept those. But that is something which might not work in many cases. In many cases you just need to have some sample. You just check some sample and based on that you decide whether you accept the whole lot or not. This is what we do in acceptance sampling. So instead of checking 1000 pieces, what we do is we check number of pieces, certain number of pieces. In this example, let’s say we randomly pick 80 pieces from the truck and we check 80 items. Once we check 80 items, we see whether three or less are defective or not.

So out of 80 items, there could be zero defective. Everything is fine. There could be one defective, two defectives or three defectives accept the lot if there are three or less items which are rejected. And you will reject the lot if there are four or more items which are rejected. And now you might want to say that why do we accept one, two or three items defective? Everything should be fine. But then these items are non critical items. So many of the times when you use acceptance sampling you use that when the item is not very critical. If the item is critical, then you need to check 100% of the items. The example here you could take is let’s say these are apples or oranges which we are receiving for our store. And one or two or three of those oranges or apples might not meet our criteria. These might be smaller in size, these might not be properly ripe, then we still accept that lot. So one thing which we need to understand is that acceptance sampling is used when the item is not very critical. And we accept some level of defects, some level of nonconformity in those items. Once you’re doing sampling, you really cannot expect 100% good items because then you cannot do sampling. You will need to go for 100% inspection in that case. Now let’s come back to our topic of acceptance sampling where we accept the lot if the number of defectives are three or less. And now the question would be where from these 80 PCs have come? Why didn’t we check, let’s say, 100 items out of 1000 items? Or why didn’t we just check four items? There are certain rules and certain standards for that. These are based on number of criteria. We will briefly touch upon those.

But let’s understand that when we are doing sampling there could be two types of sampling, attribute sampling and variable sampling. Attribute sampling is pass and fail. This is the example which we took earlier when we were checking 80 pieces. In those 80 PCs, we just checked whether the item is passed or item is fail. This is attribute sampling. For attribute sampling, the standard which we have is mill standard 10 five and mill standard 10 five has been withdrawn. So that’s not applicable. But 10 five is easily accessible. You can download that by searching this standard and you can download this standard from Internet. This is freely available.

Then the second standard which is valid is Ncasq Z 1. 14. So this is the standard which is issued by the American Society for Quality. So Z 1. 4 is for attribute sampling. And then in attribute sampling we have another standard or another criteria which is dodge roaming tables as against attribute sampling. The other type of sampling is variable sampling. In variable sampling, we are not checking whether the item is good or bad. What we are doing here is we are taking the actual measurement, let’s say in that case of apple or oranges, if we have the size or the weight of each of these oranges. So what we will do is we will take the weight of these items and we will record this weight. And based on this weight we will judge whether to accept or reject the whole lot.

That will be the variable sampling where we will take measurement or where we take the dimension of the items which we are checking, not just pass and fade. For variable sampling, the standard are mill standard 4114, just like the previous standard which was mill standard 1054. 114 is also withdrawn, but you can still download that by searching on Internet and this is freely available. Another standard for variable sampling is Ncasq Z 1. 9, for which you need to pay and you can download that standard as well. That standard will give you a lot of details which will help you in deciding how many pieces you need to pick for the sampling and what is the acceptance or rejection criteria. So once again, Z 1.

4 is for attribute sampling and Z 1. 9 is for variable sampling. So these are the two standards which are current. Now, let’s quickly take an example and understand how do we use these tables and standards. So, once again, I’m not going into too much of details, I’m just looking at this at a very superficial level. So, when we were talking about attribute sampling, we picked 80 pieces, we rejected the lot. If there were three or less items which were rejected. If there were four or more defective items, we rejected the whole lot. Now, how do you decide that? You decide that based on number of factors.

You need to decide on the level inspection level. Inspection level could be one, two, three or s one, s two, s three or s four. This basically tells us how much items you want to select, how much deeper you want to go. Level one will require a lot more items to be sampled. Level S one, S two, S three and S four will require very minimum number of items to be selected. So depending upon the risk level, you might want to decide on the level. And then you need to define acceptable quality limit to what level of defectives you can accept. Let’s say here in this case, we decided the AQL level of 1. 5%, that means up to 1. 5% defectives. We are good. And then you have different types of sampling plan, single sampling, double sampling and multiple sampling plan. In single sampling you take sample one time, let’s say we picked 80 items and we checked those, this was a single sampling plan. Double sampling plan will be instead of 80. Let’s say that we just picked 40 items and based on the results of these 40 items, we will pick one more sample and then similarly there are multiple sampling plans as well. And then we need to understand the reduced, normal and tightened inspection.

So how much relationship you have with the supplier, you might want to decide which level you are, the reduced level, the normal level or the tightened level. You go for reduced level when you are very confident of the quality of a particular supplier. You have taken lots and lots of items from this supplier and you have tested number of these, everything was fine. So you go for reduced. If you are using this particular supplier for the first time, you might want to start with the normal inspection level. And if you have found few defective lots previously, then you might want to tighten the inspection. So these are few things which you need to decide for your acceptance sampling plan. So here, let’s take an example, the same example which we took earlier. The lot size is 1000, the lot size is 1000.

So we had 1000 items in the truck and we decided that we will be using general inspection level two. As we earlier talked, there are number of inspection level one, two, three, S one, S two, S three, s four. And we decided that we will go with inspection level two. And then we have decided that we will go with AQL level of 1. 5%. And based on this, using these tables on the left, you will come out with this acceptance sampling plan where you will take 80 random samples and accept the lot. If there are three or less items which are rejected and you will reject the lot. If there are four or more items which are rejected, then let’s quickly look at these two tables, how you go about that. So what you do is the first thing, what you want to do is look at the lot size. And based on lot size which is here, 500 to 1200, our lot size was 1000. And based on that, with the general inspection level two, we come out with the letter code. Letter code here is J.

Based on that letter code J. Here we look at the second table and we find out that we need to pick 80 items. And this gives us three and four as the pass and fail, accept and reject criteria. For 1. 5% AQL you will not be expected to look at these tables in CQA exam. Obviously, when you go for CQE certified Quality Engineer there you need to learn a lot about this particular topic. But for CQA, I just wanted to show you how these numbers are calculated. And based on this, you get these two numbers which are three and four. That means if the number of defectives in these 80 items are three or less, then you accept the whole lot.

And if the number of defectives in these 80 items which you sampled are four or more, in that case you reject the whole lot and send the truck back to supplier and say thank you very much. We have rejected the whole lot. So this is how you use acceptance sampling. Acceptance sampling always has a risk. Luckily, you might have picked all the bad items and everything else was fine and you rejected the whole truck. The truck went back and the supplier has incurred a lot of cost in making those items, transporting that item, and now the supplier has to suffer because luckily you picked all the bad items.