 Session 32 on Quality Control and Improvement with Minitabh and Professor Indrajit Mukherjee from Shailesh J. Mehta School of Management at Bombay. So, we are discussing in the last session about measurement system analysis and within that we have just stratified into two parts, one is for accuracy and one is for precision. So, we are discussing about accuracy and within accuracy what we have discussed is basically bias definition and linearity and stability that is the mu part that we are talking over here. So, this is the mu parts which is which gets affected. So, mean of the observations are if there is an instrumental bias it will it will deviate the actual observations somewhat and the mean will change the overall observation mean will change. So, in this case we do not want any basically biasness in the instrument there should not be any bias in the instrument like that. So, measurement of this bias can be in different way what we do is that one is known as basic bias that is what is the average observation and how far it is from the reference point like that ok. When I have only one reference information like that one part one instrument and one reference that I am measuring several times and we get the bias information like that ok. But sometimes what we are interested into the what we what we intend to do is that throughout the observation throughout the measurement range observation how much is the bias at each and every location like that because the instrument may be measuring different parts based on the process variability because the parts will be generated at different range like that. So, we do not expect that every parts will be in a specific zone like that. So, instrument should be flexible to measure throughout the throughout the tolerance zone of the of the parts like that ok. So, what is expected is that throughout the operating range the instrument should be able to measure accurately. So, bias let us say varnier caliper. So, bias at the any at the observation close to 0 should have minimum bias also and the observation at a high range of high range of measurement also should be having minimum bias or near to 0 like that. So, throughout the operating range of the instrument the bias should be minimal like that. So, that is known as linearity when we are talking about bias throughout the operating range of the instrument and that is what we consider as process variability total process variability and that should be having bias should be negligible like that. So, we then only the instrument is suitable like that and stability study what we have mentioned is that stability is with respect to time. So, the instrument is same and the sample is also same, but sample reading of the samples that we are getting at different time points in morning and evening we are going to say or at different time points throughout for a specific time period longitudinal study when we are doing like that. So, in that case what is expected is that every time it should measure the same same biasness should be same. So, that should not be any shift in the measurements that we are observing. So, that is measured by stability using control chart techniques that we are not discussing about stability. So, bias and linearity study we have immediate have an options to see the bias and linearity. So, in that case what we have done is that we have taken a specific example and we are doing that and we will continue from there. So, the examples that we have taken is that one simple example that we have taken one part measurement is given and master specimen observed that that is the master's value of the master's samples that is collected over here throughout the operating range. So, it can be from meteorology labs or tool rooms like that we have a master piece that we are measuring with this instrument like that. So, in this case so, how many parts are there in C 1 column like that. So, we can we can just see this one. So, number of observations is part bias over here. So, there are 5 parts over here and 5 will have different different specimen values like that. So, one so, the parts that we have taken over here. So, in this case we have parts which has a specification of 2 over here. So, that the first part is having a value of 2 basically the master value is 2 around and this is the operator who has measured that one. So, actual value is 2 or reference value is 2 and this is the observed value like that observer keeps on changing because even if I do not tell the operator what is the measurement of the parts that I have given him. So, in that case he will measure the parts and he will tell me what is the true values of that what he can measure using the instrument. So, we have to select the operator also very skilled operator over here. We cannot take the measurements let us say you are an engineer and you are trying to measure that one that is not feasible that way we do not do gauge and any measurement system analysis. It has to be done by skilled operator who knows the instrument who can handle the instrument like that those people will do the measurement system analysis ok. We will only record and we will only analyze and try to figure out whether the instrument needs calibration needs to go to metrology lab for further rectification like that or not that only we can we can just say about the instrument ok. So, and they will take care of the instrument what is going wrong we have to identify what is going wrong in the instrument then they will take care of that and they will send us either the old one after repairing or what you have to do is that they will change the instrument altogether they will say that this is not possible to rectify in that case you can use a new instrument like that. So, and due to warranty or some at a certain given time point we have to change the instrument also in production flow ok. So, that that is natural. So, in this case so, here we have five different parts and five different parts are different measurements. So, it varies from 2 to 10 and these are the observations that we are having over here these are the observations that we are having. So, simultaneously I want to see what is the bias at each of the operating zone that is what is the bias as reference value of 2, reference value of 4, reference value of 6 like this. And we want to see that overall biasness whether it is overall bias in the instrument whether it is throughout the operating range whether it is ok or not. So, for that what we have done is that statistics we have gone to quality tools and in that case gate studies and gate studies linearity and bias over here. So, then we have given the part bias over here master over here and response over here and here there is option of process variability over here. So, that I am not giving at present. So, and then how do I method of estimating standard deviation over here. So, this will be used for a t statistics that will be used for p value calculations. So, what I am doing is ok over here. So, what do you observe over here is the results that you are observing over here. So, in this case what happens this we have discussed earlier also. So, in this case what do you see is that these are the part observation at reference value of 2, these are the 5 observations that we have taken and the red points that you are seeing over here is the average value over here. So, bias average bias is given over here. So, out of this 4 measurement what is the average observation and what is the reference value that will give you the bias over here. So, bias is in y axis and reference value is in x axis. So, we can regress bias with reference value over here and that regression equation is fitted over here with the constant value of the intercept that is given over here, slope is given over here as minus 0.13167 and slope is coming out to be significant that that test statistics is used over here, hypothesis testing is done for the regression and in this case what is observed is a slope is significant. So, we do not want slope to be significant in a linearity studies like that. If that is so, that means, there is something going wrong at different operating range bias are drastically changing like that. So, this slope should be insignificant then only the instrument is ok in linearity aspects like that. So, but the r square fit that you are seeing over here r square value is about 0.71 like that and then we have a values over here what is the reference value and corresponding what is the bias whether add 2 reference value whether it is significant or not. So, it is significant at 2 and 4 and 6 it is not significant, but 8 and 10 it is significant. So, it is measuring at the lower range and higher range which is significantly bias is significantly having a statistical such skill importance over here that means, statistically significant basically. So, at the at the reference value of 2 and 8 and so, lower range it is having a high bias or significant bias and the higher range also it is measuring, but in the middle range what we are observing there is no as such bias is not so, significant over here. So, although overall the slope is linearity is significant over here that is because of at the lower range bias is high and the higher range also bias is high at the lower range what we are seeing a positive bias is reference over here and the lower range and the higher range higher range of observation what we are getting is that negative bias is observed over here. So, this is the basic interpretation. So, whenever there is a bias when bias is changing in the operating range we need to correct that one and slope should not be significant that is the overall interpretation that we can make out of this ok. Now, sometimes what happens is that they they calculate say linearity index also they calculate linearity index also over here. So, what you have to do is that quality tools over here you go to guess studies over here and you go to linearity over here only thing is that process variability you have to mention over here based on which this linearity values will be calculated and based on that whether to accept the instrument or not to accept the instrument that you have to do ok. This is mentioned as 6 multiplied by historic standard deviation of the of the process like that. So, what we can do is that this is response taken from the process only that means the range of values is taken from the process we can say that this is the part variation. So, what we can do is that we can just see what is the variability over here standard deviation of this. So, we can just take that one in statistics what we will do is that we do not want all information over here we need only the standard deviation information. So, we will eliminate all other options over here and then we will click ok and we will let us try to see that whether this information can be used it is around 6.7 6.775 let us say 6.75 over here. So, this is 6.75. So, in this case I can use the calculator. So, 6.75 over here if you multiply it with you have to multiply with 6 over here. So, this is around 40.5 this is around 40.5. So, what we will do is that here we will go to quality tools and then get studies and linearity and bias. So, in this process variability we will we will write 40.5 what we have got over here. So, in this case and in the options what we do is sample standard deviation. So, that is ok. So, I will click ok over here. So, when you do this you will get a different percentage linearity over here. So, we need to have calculates percentage linearity over here ok. So, based on this slope over here slope value multiplied by process variability that will give me a linearity percentage over linearity values over here that is mentioned at 5.33 over here and we can convert the percentage linearity and again multiplied by. So, again multiplied by process variability. So, one is slope divided by process variability and another is multiplication. So, overall it will be around 13.2. So, the standard that is followed in industry is that mostly if it is less than 30 percent like that they can they can, but it varies from industry to industry I am not saying there is specific like that ok. Somebody can say 10 percent we will allow linearity 10 percent more than that we will not allow, but overall what we see is that even if we do not go by this we see whether the slope is significant or not like that. Not sometimes statistical statistical significance does not imply it is very high highly significant means practically it may not be so much means so much critical like that, but that is why we are using process variability measures over here and we are finding out the percentage how much is the linearity or or this shift deviation with respect to the process deviation like that with respect to the process deviation like that. So, these measures can be taken based on the industry standards what you are following in your industry. So, so that way we can we can express linearity over here ok, but when we are doing this study what we are getting is that one linearity percentage we need to have also reports like that. So, and there can be criteria for different industries. So, somebody can take 10 percent somebody can say anything less than 30 is ok, but there needs to be some corrections over here. So, percentage linearity is a concern whenever it is more than 30 percent it is a concern whenever it is more than 30 percent that means it is highly significant. So, in that case we have to take some measure because bias is changing drastically over here in the operating range, but that information where it is changing we will get this information over here ok. So, this is one aspects of when we are talking about mean and that aspects we are covering over here and, but there can be also impact on variability that means impact on variability whether the now this is bias we are talking about the bias aspects of that or accuracy part of that we we have to shift to now variance we have to shift the variance information whether the variance of the instrument is quite large or not that we have to see. And that study what we do is known as repeatability and reproducibility R and R study ok, gauge R and R study also they call it a gauge R and R study. Here we are more concerned about this sigma measurement over here. So, we are concerned about this sigma over here and variation variation due to the measurement system over here can be contributed by two two aspects over here, one is known as repeatability of the instrument and one is known as reproducibility of the instrument over here. What is repeatability if you are measuring it same parts like that there will be some variation in the measurements like that. So, same operator is measuring repeated times like that and the instrument will have some variations like that that will contribute to the repeatability aspects of that that is known as error aspects of that in the instrument. So, that is repeatability. So, this is basically common common variability everywhere there is this types of variation will happen because same instrument if I am doing its second time sometimes readings may somewhat deviates in that and that variability that amounts to that amount of variability is represented by this measure which is known as repeatability over here ok. And what is reproducibility because we are measuring by because in in in short flow what happens is that there are different operators. So, there are different operators over here. So, and in every shift there can be a different operator. So, what is expected is that all the operator should measure the measure the same parts with same accuracy like that that does not happen operator to operator variation can happen. So, operator may measure somewhere over here, operator B is measuring somewhere over here, operator C is measuring somewhere over here. So, overall mean of location over here for operator A is different from the second one and third one like that. So, this this variation that is happening due to operator is known as reproducibility. So, this is reproducibility and this is known as repeatability like that. So, a specific kind of study is recommended over here which is known as gauge R and R study which is the repeatability and reproducibly measure and that we have to. So, in this case what happens is that in this study what happens is that I have a measuring instrument which is which is the same instrument that I am doing and there will be different parts like in linearity study what we have taken throughout the operating range we will select the parts like that and then there will be different operators. So, here we are having a change rather than linearity where single operator was used here there are multiple operators over here. So, in this case they these are three operators that is selected over here and based on that we will do the study. And this study will be done by using we can use two types of methods over here. I will discuss only one method which is known as two way analysis of variance method which we have already studied like that ok. So, this is two way analysis of variance method that we will explain over here and the way study is conducted over here that we will explain and how to analyze the data that we will explain and what is to be seen that is to be that is will be elaborated in this in this in this session over here ok. So, here what you have to do is that they have selected different parts like that in the operating range. So, this is the 10 parts that is selected over here and these are the observations for a specific part from a specific operators like that. So, this is basically repeatability of the observations that we are happening. So, same sample is measured by the same operator several times over here this is three times that is measured n equals to 3 over here. So, this is nothing, but we can think about repeated measurements what we are taking over here ok. So, similarly operator 2 will measure the same parts part 1 like that and the third operator will also measure the same parts like that. Now, this total experiment that you are seeing over here is randomized over here and the operator does not know which part he is measuring basically which part he is measuring. So, part number will be randomly generated over here and it will be given to some operator and measurements will be taken like that. So, this is randomization is ensured so that no biasness no there is no bias as far as operator is concerned like that. So, operator does not know next part what is the measurement of that which part it is coming like that. So, randomly we will generate and this data will be generated like that. So, 10 multiplied by 30 30 multiplied by 3 is 90 observations we have. So, it is like design of experiment. So, what is the factor over here? So, one is the parts that is the one one aspects 1 to 10 number of parts over here and there are three different operators. So, operators operator 1 operator 2 so, level 3. So, this is at level 3 and there are 10 parts over here. So, this is part and operator that is that is the factor that we have considered over here. So, it will be a two way analysis of variance that we have already studied like that. So, we will fit this data into MINITAB and the results we will just try to see over here. So, these parts that we have selected is within the process variability like that. So, this is we can think of that overall process variation is covered over here. So, generally when parts are selected that will be from from the process and it covers more or less the outcome of the process like that CTQ outcomes like that. So, we want to ensure that that part variation will be there because intentionally we have selected different parts like that which is having different measurements like that. We cannot select parts which are very similar in observations like that. So, one to 10 parts are at different range like that and there is some difference between the observations. So, they are basically unique observations that we are having over here. So, this covers the overall variation tolerance zone of the CTQ basically what we are covering over here. So, this is taken from the process these 10 parts will be selected like that this data will be fit into MINITAB and then we have to see what is to be done. So, when this is the data set and it is taken from Montgomery's book Introduction to Statistical Quality Control is another another very good books that you can and the way that we are doing over here is basically following a guideline that is measurement system analysis reference manual which is developed by Chrysler for General Motors Supply Quality Equipment Task Force over here. So, this is AIG standard AIG standards that we are following and there are manuals you can you can see manuals of AIG for measurement system analysis and we are going by the manual and we will somewhat deviate if required otherwise more or less what manual says we are going by that and MINITAB also does what is given in the manual basically ok. So, and also you can see QS 9000 that is earlier earlier when people quality systems in automobile industries like that that is the certification like ISO 9000 certification there is a QS certification which is changed recently. So, anyway anyway so, then that there you can get the standards of measurement system analysis. So, two way analysis you already understand. So, we are doing this experiment experiment setup I have told parts are different operators are different and we are taking repeated observations. So, why we are doing repeated observation because we will go by the average value we will be more accurate more number of. So, we have taken n equals to 3 over here if we have increased this one more accuracy we can we can assure out of the study. So, this is basically design of experiments what we are doing and this is two factor experimentation that we are doing over here. So, this measurements is there in my MINITAB file and that is given at the at the last part of this. So, this part Montgomery operator Montgomery and measurement Montgomery because this is a Montgomery's example. So, I have taken from there. So, what I am doing is that these are the three observations 90 observations is given over here. So, all these 90 observations we are just going to analyze using Gage RNA study like that whenever you have fit the data what happens is that then you have to go to quality tools and then you have to go to Gage studies and then you have to take Gage RNA study crossed you have to see this one that we are selecting this one cross studies over here. So, in this case what will happen is that it will it will ask for this where is the parts measurement where is the operator measurements like that. So, you have to mention which column is what. So, part is given in this one operator is given in basically operator is given in this second one. So, this is this is not the correct one. So, we have selected this is part over here this is and the measurement that we have taken at the end this is the measurement of Montgomery that we have taken over here. And our analysis we have clicked not this one we are analyzing this one. So, in this Gage information you have to provide all details over here and in options what you have to do is that the standard deviation study variation is taken as 6 over here. So, and then what you can do is that you can later on we will come back to this historic standard deviation. So, that needs to be calculated and put over here so that we can also calculate study variability like that. So, we will not do it as at this time point. So, in this case what we will do is that we will click ok over here whenever we have clicked ok what will happen is that you will get. So, we will make an excel we will open an excel sheet over here so that we understand and see it clearly what are the results. So, two way analysis variance is prepared over here with interactions that minute I have automatically does it for you and it indicates some important things over here. So, what we will do is that we will just click this one and we will copy paste the information that is given over here. So, I am copying this as a picture and I will paste it in excel sheet so that it is visible for everyone. So, what you see is that source of variation. So, part to part variation. So, part is one of the factor. So, in this case that is significant and it is expected that part variability is will be part to parts are different. So, this will be significant we are not bothered about this one. We are bothered about the second part which is operator to operator variation that whether this factor is significant or not that means when operator A is measuring easy measuring differently as compared to operator B and C like that. Now, what you observe over here in the analysis or what it signifies is that operator is basically significantly different because p value is less than 0.05 over here. So, operator to operator measurements are differing over here then is there any interaction between part and operator over here that is also significant over here that means operator A measures part A differently, but that same operator measures part 2 differently that means the method there is there is some interaction over here. So, depending on the part measurements also comes depending on the part. So, operator measures part based on the there is a dependency between parts and operator. So, there is a interaction between part and operator that is also not required whenever it is less than 0.05 we are concerned about that, but if it is more than 0.05 that is a favorable situation. Similarly, operator p value is more than 0.05 is a favorable situation. So, we want part variation to be significant, but these two operator variation and interaction effect to be not significant like that. So, that is expected, but that is not so over here. So, let us see the next part of that. So, next what we have is this variance variance component and percentage contribution over here. So, this calculation we have to explain by using a diagram over. So, this is the PPT we have gone. So, this is the observation that you see the first part over here. So, this is the first part that you see p value of parts is significant and that that is expected, but these two are significant that means we are concerned about this, but this is statistical significance over here. So, and this value is what you see repeatability or error we can think of error over here that measure is basically repeatability that means that is the measure of repeatability and mean square of this is considered as repeatability over here. So, when when I say source of variation that MINITAB provides in the variance component that you will see the next result what it shows. So, in this case repeatability is nothing, but this mean square is represented over here. So, this is same as this one what you see over here is same as this one over here repeatability. Similarly, we can calculate that what is the operator contribution of this source of variation over here. So, this is the operator contribution of this. So, in this case the formula is given. So, you have to take mean square of operator which is given as this one and then we have to calculate mean square of interaction between operators and parts like that. So, this is the operator part interaction. So, you subtract this from this and divide it by a multiplied by n. So, what is a is the number of parts and number of replicates over here number of parts is 10 over here and the number of replicates is basically 3 over here that we are taking. So, if you do that one what you will get is that you will get operator variation over here which is the variance component over here. Similarly, there are formulas to calculate reproducibility and interaction part of this and part to part variations also you can calculate and overall total variation is given as 50.0963. So, and this total gauge and R and R values that you are getting 1.88037 is nothing but summation of this two repeatability and reproducibility that comes as a total gauge R and R variance component over here which is 1.8 like this. Now, summation of this, this, this, this and this and this part variability. So, part variability is expected to be very high. So, this is expected because parts are different. So, most of the variation contributed. So, in this study most of the variation is contributed due to change in parts. So, this is expected over here and then percentage of that we can also calculate. So, if I convert this 48 out of 50 this is around 96. Similarly, we can calculate the percentage contribution over here and the overall contribution will be 100 percent over here. So, the overall is 50. So, with respect to 50 what is coming we have we are just mentioning over here. So, whenever we have mentioned this, this percentage contribution percentage contribution is an important measure to accept or reject the instrument like that. So, generally what is taken is that less than 9 to 10 percent we can think of. So, standard says 9 to 10 percent. So, I have just written 10 percent over here it depends from industry to industry it will differ like that. So, generally it is taken as percentage contribution whenever it is less than 10 percent we will go by that measures as a acceptability of the instrument as when the variance component is concerned over here. So, total gauge RNR study this variance component should be less than 10 percent that we are recommending over here. So, if it is less than 10 percent then we are we are ok with the instrument like that. But what is our concern over here although it is less than 10 percent there is some interaction between the parts and operators and operator to operator different differentiation is happening over here we need to see what is going wrong over here. So, if we can minimize that that variability will also reduce although the significant we are not getting high values over here because this is 3.6. So, you have to be judgmental over here you cannot be statistically significant. So, we will reject that one no we have another criteria of acceptance there are various criterias in measurement system analysis which needs to be considered before we take a decision whether to use the instrument or not to use the instrument like that ok. This is one of the major percentage contribution like this we can also find out we can also find out the with respect to process variation there is another measure which is which percentage variability. So, we we can also go to that PPT is over here. So, this is calculated over here there is there is another important component over here that you see standard deviation study variations over here. So, if I copy this we will copy a picture over here and we can paste it over here. So, we can we can paste this information over here and we can just enlarge this image over here. So, what do you observe is that this standard deviation 1.34 is nothing, but what you are seeing. So, this is the variance repeatability that that you are observing. So, it is sigma square if you take a square root of this you will get. So, if I if I can see this one. So, if you see this one. So, this is the variance component that we have calculated that this is the variance component 1.8037. So, and then standard deviation we can also calculate. So, if you take the square root of this it will be 1.34. Similarly, all these values are calculated. So, this this is basically represented this is variance component what we have collected total gauge R and R. So, standard deviation is the square root of this and if you take the square root of this and then you get all the components over here. Similarly, if you want to see the study variability you multiply it with 6 and 6 multiplied by standard deviation gives you all this measure over here. And based on this we can calculate also study variation percentage study variation. So, 8.051 this is the study variation with respect to total how much it is it is around 18 percent over here ok. In addition to this what we can do is that we can also add process variability historic process variability over here that can that is also possible to be incorporated over here and that gives you a different percentage over here which is 22 how this is coming. So, that we can see. So, this is how the calculation happens in unit have interface is that. So, after this what you can do is that you can you can just mention. So, study variations of this. So, something we we have over here let us try to see whether we have given this one gauge R and R cross to over here. So, this is options over here. So, in this case 6 standard deviation with respect to percentage standard deviation and this is calculated from the historic information or this is calculated from the sample. So, here what we can do is that we can we can provide information over here. So, percentage study variation. So, this is this is done over here. So, once again. So, this is the slide let me go back to the slide. So, process variation we have given information of the process variability over here that is why this percentage is calculated percentage process variation is calculated over here. So, let me go back what what we can give over here as process variability. So, what what is required is that I will go to Minitab and then let me try to see what is the variation of this process there is the last one. So, we can calculate the basic statistics display basic statistics I want to see the Montgomery's measurement and I want to see the standard deviation we we only want standard deviation information over here and this is around standard deviation is 6.75 6.75 no. So, 6.75. So, we can just calculate 6 point we can calculate 6.75 multiplied by 6 is around 40.5 that we have done also 40.5. So, what we have to do is that stat quality tools and gauge R&R studies. So, gauge crossed over here. So, in this case options what we provide is that 6.75 we can write 6.75 what we are getting over here and we can also say that use parts to estimate the process variability over here. So, I will click observations historic we can we can replace that one with the ah measurement of variations what we have, but we can also say use parts in the study to estimate process variability that is the overall process variability we can indicate that one when you click this one and it will go by the ah that measure only. So, when I have click this one. So, it will estimate process variability of standard deviation based on the observation that is given in this experimentation that we have ah we have considered. So, if you click ok then ah then you will get this information which is percentage process variability over here. So, if I copy this one and we can paste this over here and then we will have another information over here that is 19 point what what we observe over here. So, percentage process variability. So, study variation is measured over here in respect to so, more or less study variation if it covers the overall process it will be more or less near to this one study variation and percentage process variation over here. So, the criteria that is used for the study variation process variation is that ah whenever it is less than 30 percent we we try to accept that instrument. So, if it is less than 10 percent very good instrument 10 to 30 percent what what what is recommended is that ah you need to be very precautious and see whether we can reduce that one ah variability that is happening process variation ah with respect to process variation study variation if study variation is contributing more ah with respect to process variation then that is a concern for us operative this part to part variability will be high and this summation of this what will happen is that it will not turn up to be 100 over here. So, this is 100 over here, but this this is with respect to ratio that we are taking over here and study variation and process variation and then percentage we are converting. So, it will not be equals to 100 when we sum this up. So, ah the criteria over here is that ah when we go by that contribution it should be less than 10 percent when I going by study variability or process variations over here then the criteria may be 30 and it depends on the industry to industry what what is the standard. But overall concern over here is that now we have operator operator to operator variations is happening and also part to operator there is a interactions that is observed. So, we can correct that one and try to see more more into the instrument and figure out what is going wrong ah, but the instrument can be ah suggested for use for the time being and we figure out how to reduce this one interaction between parts and operators and operator to operator how we can reduce that one further. So, that it becomes insignificant basically. So, we will stop here what we will do is that we will continue with some more examples on this which which is taken from the manual QS manuals like that ok. And some more examples where we have bad ah bad instruments like that. So, how to understand that one and graphical display that we are having. So, we want to explain that one also because when we when you get the mini type information we also get a graphical interpretation also over here. So, what what is this graph meaning of this graph that we will explain after this before we entered into design of experiment basically. So, thank you for listening.