 Welcome to session 12 of our course on Quality Control and Improvement using Minitab. I am Professor Indrajit Mukherjee from Shailesh J Mehta School of Management, Diety Bombay. So, we are discussing in last session about attribute control chart. So, two charts we have discussed like C chart and U chart which is used for monitoring the defects and C is used when constant sample size are used to monitor defects and U is used when sample size varies at different time points like that. So, we will move on with other attribute control chart. So, beyond this what is there is that we have a P types of P type of control chart over here. P is basically P chart and NP chart we will discuss both the charts over here. So, a P is proportion defective which is monitored, earlier case was defect this is defective over here and defective means 0 1 condition either it is useful or it cannot be used like that. So, in this case either useful or scrap we can think of. So, in this case one of the example that is showing over here is a number of defective cans when every time I am inspecting 50 samples subgroup size we can think of. So, number of samples at a given time point what we have at time point E 1. So, these are the 12 cans which was found defective and 50 cans were inspected basically. So, over here formulation is also this assumption was taken as binomial distribution assumption and based on that formulation is given over here. What you can see is that UCL will be P average P average will be calculated based on individual proportions over here. So, proportions can be calculated for a specific values over here. So, if I take this value P 1 it will be 12 by 50 basically. So, then I can calculate what is the value proportion over here P 2 similarly P n like that. So, P i is given over here which will be a number of defective items divided by sample size that we have taken as respect to 1. So, P i and then we can get we will get 30 P i's and then average of this 30 P i's will give me P bar or average defectives of the process like that. So, that will be the central line over here and then we can calculate UCL P bar 3 multiplied by and this will be constant in case we are taking constant sample size and it will be different if I am taking a different sample size at every time point like that. So, we can vary the sample size also if you have varied sample size also we can plot that one. So, this is for scenarios where we are we are interested in plotting the defectives like that. So, somebody may be number of rejections in number of rejections of may be engine assembly in that case how many engines are rejected like that. I produce this many engines in a shift and how many produced are defective like that. So, that scenarios also can be monitored which is abnormal which is normal which is abnormal like that. So, this is one example and we have some other example also on this. So, this is also another example where 20 samples of size 100. So, every time I take 100 samples and this is taken from the book Amitav Amitav both the case we will solve and try to see how P charts can we can use P charts for interpretation of the data. So, what we will do is that we will take some examples over here. So, I will open P charts and then I will illustrate how this can be done in Minitab. So, this is the two examples that we are talking about non-confirming CANS first one and then the sample fraction defective what you see is that 12 by 50 was done and this is 0.24. Like this we divided by 50 I get proportion defectives and that can be monitored like that. So, what we can do is that we can calculate this one. So, we can use calculators over here to calculate this one. So, if we want to calculate this one. So, this store results in if I say C3 over here what I can do is that I will write down that C2 divided by 50 let us say. So, that is the expression I want to use over here and if you click that one automatically this values will be replaced and you will get all this observation that you see over here. So, these are the observations that is saved over here. So, this is same numbers what I can see over here. So, this is 12, 12, 15 like that. So, sample size or subgroup size was 50. So, that division was done. So, Minitab you do not need to divide this one. So, what you do is that stat you go to I know this is for defectives and I go to control charts attribute control chart I go to P chart directly. What I do is that which is the variable number of non-confirming cans over here. What is the subgroup size? I mentioned 50 over here and P chart option again the same thing I test I want to test anything beyond 3 sigma limits like that which is abnormal scenarios I click ok. What will happen is that you will get the P chart corresponding P chart. So, in this case what happens is that two points are going outside what you can see and these are the abnormal scenarios. So, proportion defectives goes outside. So, proportion defective what you see is that upper limit line is 0.41, average is 0.23 and lower control is 0.05. So, two points gone outside. So, we have to find out figure out what has gone wrong at this time point when proportion non-confirming are very high in these two points like that ok. Now, the problem with this is that in this case. So, this is proportion defectives and if this proportion defectives changes and when the sample size changes in that case also we can we can figure out what can. So, this is a P chart over here if the sample size changes in that case only what will happen is that I will have a variable UCL and variable LCL like that ok. So, that is one aspect. So, what happens is that in production flow what generally happens is that proportion defectives people understand defectives one defect one defective two defectives like that when you say in fraction they do not understand because engine fraction defective does not make any sense. So, what they does is that they multiply is the N with P. So, they call it as N P charts like that that makes an impression that number of defectives then we can we can immediately understand over here ok. So, in this case what you see is fraction in the central limit UCL and LCL like that. So, operator may not understand what is fraction that you are saying average defective is 0.04, but I understand that it should be more than 1 like that. So, it should be more than 0 or on the higher side or on the positive side we want to we do not understand means how this average is 0.04 like that proportion I do not understand make it much simpler like that. So, in that case what they does is that they will multiply it with N nothing else they are doing over here. So, in this case what they will do is that they will have a different limit lines. So, in this case N P charts are recommended over here. So, this N is multiplied over here with P and this is N multiplied by P formula somewhat changed. So, this will be the central line and this will be the lower control limit line. So, in this case what you will observe is that the numbers are in whole number with some fractions like that. So, now 2011 this is understood. So, this is 2. So, this is understood by the operator lower control is 2 defectives like that. So, we expect out of 50 this 2 is the lower control limit line. So, we should be above this one and the upper is around 20 or something like that. So, that is what is the upper limit. So, number of defectives out of 50 inspection should not go beyond 20 like that, that is the feeling of the operator like that. So, that becomes easier to monitor for the operator like that. So, we have a chart which is not as N P chart which is just a variance of P chart. So, what we can do is that we can we can we can same charts like that. So, we can we can also see N P charts and where we can. So, number of cans like this over here same examples we are taking. So, stat I go to stat control chart attribute chart I click on N P charts like that. So, I do not want to see proportion and their upper limit lower limit like that. I want to see number of non confirming one and I will say subgroup size is 50 because and other conditions remain same and then what I do is that I click ok. And then I get the control limit lines this is the N P chart which is which is done by Minitab and here you see the numbers are 20. So, this is easily understood by the operator that 20 defectives if it is going beyond that then I should be very very much cautious like that out of 50 more than 20 is defective then that means something unnatural is happening if the average is average should be around 11. So, out of 50 my process is like that. So, on an average I am getting 11 types of 11 number of defective items like that and the lower limit is around 2. So, and here we can see two abnormal scenarios which is coming up like that. So, it becomes easier for the operator to understand this type of representation of the data otherwise P and N P are both used for defective. So, any of the one you can use like that ok. So, only one thing is that there can be variable sample numbers like that. So, it can it can also vary. So, maybe some example this is variable subgroup size what you see C 9 and C 10. So, defective number of defective sample size changes and in that case also if you if you plot this one. So, control chart and attribute chart N P charts like that and I mentioned that I want to see defectives and instead of 50 I say that this is in column C 10 and I want to see what happens like that. So, then what you get is that this type of control chart you will get. So, this is N P charts where N is varying. So, number every time I am inspecting is changing. So, in this case limit lines are also changing like that. So, central line is changing because it is multiplied by N. So, N is changing. So, central line is changing upper limit is also changing and lower line what you see is that this is taken as 0. So, minute I was considering this as 0 because every calculation is negative coming out to be. So, whenever you see attribute charts and this is coming out to be negative what happens is that I freeze that point to 0 because negative defects or defectives does not make any sense in this case. So, that is why you do not see uniform uniformity in central line and the upper control limit line and lower control limit line. So, that will always happen. So, when we are talking about defects and defectives it cannot be less than 0. So, that is the constraint that we have. So, and underlying distribution I told that this is binomial based on which this control chart is developed. So, this is a prominent chart which is used nowadays in any quality control aspect. So, these are the main control charts. So, when we talk about control chart generally we try to understand X bar R, X bar S, individual moving range and C chart, P chart, NP charts like that. So, these are the common types of control chart that is used to monitor any CTQs like that. CTQs if it is in continuous variable. So, that can be otherwise if it is attribute like the defects and defectives like that we can use this type. But it is always preferable to go to a CTQ which can be measured in continuous scale like that I have mentioned earlier also. So, with this information over here we will move on to a different topic which is also an important topic in quality because we are assessing the quality before we go into improvements. So, we are trying to control and we are trying to see that what are the measures that that will help us to go towards improvement like that. So, one of the measures that is used is known as process capability. So, earlier what we are talking about is the natural variability based on which I am giving upper UCL control limit line and LCL control limit line. So, but when we are talking about process capability we are talking with respect to customer specification basically. So, our natural behavior with respect to tolerance where we stand basically ok. So, what you see is the natural variation over here, what you see is the natural variation over here. So, this is the region of my natural variation of the process and then I compare it to the upper specification which is known as upper specification limit and this is known as lower specification limit which is the LCL over here. So, on an average my process average is around 25 let us say, but my specification given is between 20 and 30 like that. So, with respect to my tolerance how I am how I am basically performing. So, that comparison when I am doing that is known as process capability analysis or we will use some indices for this. So, that will be known as process capability index ok. Some index we will use to express this one process capability. So, that is known as process capability index So, it is basically how where is my process as compared to the specification width that is given by the designer ok. So, voice of the customer is what you see is that lower specification to upper specification. So, this is the voice of the customer we can say and if I consider this one the plus or minus 3 standard deviation this is voice of the process basically. So, I am just comparing voice of the process with voice of the customer ok. So, that will give me process capability measures like that ok. So, before I go into process capability we should have stability in the process. So, that is the primary condition. So, before we calculate the process capability my process should be stable. So, that is the basic criteria which is used ok. So, in this case how this calculation is done. So, every time process is moving. So, in this case with respect to time what you see over here. So, in control scenarios is taken to calculate the process capability and in that case this is upper specification, this is lower specification and how the process is behaving. So, where we stand with respect to my variation with respect to specification that is what is seen in process capability analysis like that ok. Based on which I will decide whether I need to improve and how much improvement is needed like that ok. So, this is graphical representation with respect to normal distribution what you see is that this is a just capable process. So, this is the tolerance that is given by the designer which is voice of the customer like that and we are performing exactly we are matching with the specification over here. My voice of the process is about using the same width like that because and if you are using that one I am just capable basically. So, I am just fitting into the specification like that my variation is there and if you see you on this side. So, my mean as if I am assuming mean equals to target over here. So, I am I am exactly on the target as far as accuracy is concerned, but precision voice I am using the total tolerance like that whatever whatever is given by the designer ok. Here what you can see is that variation is high, but I have shifted to the lower specification side this is also I have moved away from the target values. So, this is undesirable. So, we have variation we are also moving away from the target values like that. Similarly, what you see over here is that I am moving away to the other targets I am moving over towards the upper specification. So, I am moving to the one end of the customer given specification like that. So, which is known as upper specification limit and this is known as lower specification limit which is which designer this is defined from the upper control limit and lower control limit. So, lower control limits are defined by the process variability and process centering process process mean and this is defined this is defined by the designer over USL and NSL like that ok. So, and if we are producing if my variation is very high. So, in that case what you can expect is that there will be certain fallouts over here because if you remember normal distribution in that case some fallouts will happen over here and this is rejection basically. So, this is reject whenever some products are falling within this. So, normal distribution if you can think of a normal distribution graph you know that does not touch the axis over here there will be certain rejection. But in this case because we are centered and this scenario is much better this scenario is much better because the tail is much thinner as compared to this one. So, whenever it touches so there is some probability high probability over here which is greater than this one what you see over here. So, this scenario is what scenario this is also a what scenario. So, this is just capable and this will not be capability will be much less also as compared to this this will also be less capability over here ok. So, most suitable scenario is that I am hitting the target and my variability is also less like that. So, I have less variability like that. So, that is the scenario we were looking for over here ok. So, there are different index to measure the capabilities and we will talk about two index over here. So, what do you see if you want to visualize this one? So, if we divide this we call it as process capability index. So, process capability visualization is that if this is the scenario I am using the full tolerance and if this is the scenario I am using much less tolerance as compared to what is given by the designer like that ok. So, index CP is expressed as tolerance divided by so we can say that what is voice of the customer and this is the voice of the process which is known as 6 standard deviation and as standard deviation may be estimated over here. So, this is the expression for this so one is tolerance divided by so how much of the so this is the voice of the voice of the customer and this is the voice of the process. So, voice of the process means how much of the tolerance I am basically using my process is basically using that ratio is known as CP. So, earlier examples what you see is that total my voice of the process is this much and my variability plus or minus 3 standard deviation I am using the full tolerance I am using basically. So, in this case the ratio will be same. So, our ratio will be this voice of the customer will be exactly equals to voice of the process. So, this will be equals to 1 what what you see in the earlier diagram like that and in this case second scenario what you see is that my tolerance is just maybe double of the voice of the what we are using over here. So, in this case a voice of the process basically. So, voice of the process is just half of voice of the customer. So, this will be we can represent this as if I represent this one as 1 this will be half. So, CP index will come out to be equals to 2 what you see is shown over here. So, favorable scenario is that I am using less as compared to what is given by the designer and I want to reduce it further like that. So, it is like you are moving car in a tunnel like that and if I am if I am just fitting into that is not the best scenario if I can go into the tunnel with ease. So, that is the open that is the that is the best scenario what we can think about. More and more I reduce the variability more and more favorable situation assuming the target remains same like that. So, this CP index what it shows is that it shows how much of the variability my variability is with compared to the tolerance that is given by the designer or given by the customer like that. So, if you have one-sided scenarios. So, in this case you can calculate a CPU and CPL like that. So, MINIDAP does it automatically for you. So, just capable process we can think of CP is equals to 1 industry standard I am talking about. This may be scenario some of the industries follows that you should be CP should be exactly equals to 1.33 or more than that is acceptable scenario or somebody can say it should be greater than equals to 1.67 that is the most favorable scenarios over here. And if it is excellent means if it is more than 2 it is always excellent. So, process capability if it is 2 if it is greater than equals to 2. So, in that case that is the most favorable scenarios and excellent performance we can say for the process like that ok. So, this can be calculated and this will be done automatically like what do you see over here like philosophy of Six Sigma which we will discuss afterwards maybe in some of the sessions where it says that higher the capability better is the process condition like that and less variation. So, less rejection basically. So, if you see with respect to specification in that case lesser is the width of this. So, thinner is the proportion which is going outside over here or the probability of falling outside the specification like that that is the philosophy of Six Sigma. So, I hit the target and it reduces the variability like that generally CP equals to 2 indicates that is a Six Sigma process, but there are other conditions which needs to be satisfied for that ok. So, how do we calculate process capabilities that we need to see in Minitab. So, in this case for a given set of data I want to calculate the process capability like that and what is the option that we have. So, in this case we will take some example maybe and we will see how this capability index can be calculated. So, let us take some data set what is provided in this. So, this is one bursting strength of 100 containers like that. So, at a given time point it was taken some observation was taken container 1 to 5, 5 subgroups were taken over here and this is observation that we have and for this data set some specification is given customer specification lower specification limit is given over here and we want to calculate or we can take this piston ring which is both sided specification over here. So, this becomes easier to understand. So, this is 74 plus 0.035 like that and 74 minus 0.035 that will be the specification for this product over here. So, and we will place this into Minitab and try to figure out what is the CP index, what is the value of CP index. So, this is the data that was collected at a given time point. So, piston ring 74 and this is the data set that we have every time we have 5 subgroups. So, we will calculate the process capability index over here. So, if you go to the data set, so we will close this one and we will open capability analysis process capability analysis Minitab file which is already stored with me and this is the piston ring examples that we are taking over here and this example we are taking first. So, in this case, we have both sided specification what you have seen. So, plus or minus 74 plus or minus 0.035, this is taken from Montgomery's book example. So, we will try to illustrate that one. So, what you do is that stat quality tools and capability analysis over here. So, assuming normality over here, there are various options over here. I will take the simplest one assuming normality over here, normality can be checked. So, we are not doing that at present. So, are they in single column? No, they are in subgroups are in different one. So, this is ring 1 to ring 5, we will highlight this one and enter over here. Now, specification, lower specification we will enter like that. So, this is given us. So, let me just check this one. So, 73.965, 73.965 that I will put as lower specification 73.965 that is the specification mentioned by the designer. And the upper specification will be equals to 74.035. So, that will be 74.035, 74.03. So, now options over here. So, this transformation you ignore at present estimation over here. So, this is we can ignore at present. We will only see the CP index what is the value of that. So, this analysis is not required at present. So, these things we can ignore at present whatever value comes. So, I want to see only the CP values. So, from here we can see. So, if you click ok, what will happen is that it will do some analysis and it will come up with some diagram over here. At present we do not want to see all of that. So, what do you see is that just note that LSL is taken as 73.965, USL is taken as 74.035. I have not given the target over here. I have only given the width band that is given by the customer and then I will only see the CP index that you see over here. So, this CP value is 1.16 and that is the formula that we are using over here CP formulation will be this one. So, which I am using over here. So, this is the formulation which uses USL minus LSL that is the tolerance or delta values over here. So, that is plus or minus 0.034 that is the total width of that 2 times of that and divide by 6 into standard deviation over here. So, there is a method of calculation of standard deviation. So, that we have to discuss afterwards. So, at present we will assume that Minitab has calculated some standard deviation. So, this is taken and the output given over here is CP is 1.16. So, some way they have calculated the standard deviation which we will discuss in the next session how Minitab is calculating this one. And I also told that we do capability analysis whenever the process is stable like that. So, we will check that whether the process is stable and then if the process is stable how do I calculate the standard deviation which will be used in process capability analysis to calculate CP index that means delta divided by when I am doing the specification total tolerance that is given and divided by 6 process voice of the process. So, voice of the process this sigma is calculated based on certain assumptions like that that is process is under statistical control and then we can calculate sigma and there are ways to calculate sigma which is calculated from X bar R charts like that. So, R is used as a measure R bar is used as a measure and number of subgroups here it is 5. So, that ratio is used R bar by D2 is used to calculate the process standard deviation. So, that multiplied by 6 gives you the denominator and numerator is the tolerance that we are having like that. So, based on that we will discuss we will start discussing about how they calculate this CP indices like that. So, sigma calculation we will see and that sigma calculation is given over here what you see standard deviation within what you see over here and this is basically calculated based on control chart concept and R bar by D2 is the formulation that is used to calculate standard deviation within and many other calculations we will see. So, ignore all other information just see USL and LSL that is given and the difference between them will give you the voice of the process voice of the customer and 6 multiplied by the standard deviation within what is the way we will calculate next time and that will give you the voice of the process. So, ratio of this gives me 1.16 and we can say just capable it has not reached 1.33 which was the standard in many of the companies, but it has just crossed 1 we can think of. So, there is a need for improvement of this process we need to reach around 2 CP values like that. So, that is our objective we want to reduce the variability and more and more I reduce the variability more and more my CP index increases like that. So, that will be our point of discussion. So, we will see first how the sigma is calculated and based on the concept that whether they are under statistical control that we will also cross check with these examples like that and then we will see other measures which is used to check capabilities like that. So, we will stop over here and we will continue discussion of this capability analysis. So, these two example we will use to illustrate our many of the measures that we will see that MINITAB provides and what is the meaning of each of these outputs that you see that you see in MINITAB like that. Thank you for listening. This session we will continue in the next session from here. Thank you for listening.