 course on Quality Control and Improvement with Minitab, I am Professor Indrajit Pokerjee from Shailesh J. Mehta School of Management, Taiti Bombay. So, we are discussing about measurement system analysis and within that we are discussing about gauge R and R study, repeatability and reproducibility. So, we are taking some examples to understand and then we have seen that percentage contribution is one of the measures that needs to be considered over here and study variability can also be considered with respect to that how much is the instrument variation with respect to study variability that also we have seen that how we interpret that one. So, let me just go back to that and analysis part of that and so what we have seen is that we have taken a specific example where 10 parts are measured like that and there are 3 operators and each operator is measuring the same part 3 times, but randomly. So, the operator does not know which part is measuring and the master information of the values is not known to the operator like that what is the and 1 to 10 parts are covering the process variations basically or tolerance we can think of like that ok. So, this is as per the AIG guidelines I am discussing over here, these are the basic guidelines and Minitab adds on to that sound of measures that can be used for measurement system analysis. So, gauge R and F studies. So, over here what we have done is that we have seen when we implemented Minitab in the as a two factor factor two factor experimentation. So, in that case part variation is expected what what we see over here and what is what is what is not basically should not come out to be significant, but in this case operator to operator variation is quite significant that is shown and interaction term is also significant that should not should not happen basically if it is a very good instrument like that ok. However, we have calculated the percentage contribution over here this is around 3.6 and this is much less as compared to 10 percent criteria that we are using over here. And this repeatability what we have seen is a this is the error variation mean square error variations the other measures are also calculated like for operator what we have seen is that this is 0.56 and this can be calculated by this subtraction and divide by a multiplied by n that that gives you the measures and out of 100 percent if this is the total variations over here and we can get what is the contribution of total instrument over here that consists of repeatability and reproducibility like that ok. And interaction effects and also operator visibility this reproducibility within that we are getting these two components over here and and these two summation of this repeatability and reproducibility gives you the measures of total gauge repeatability. And then what we have seen is that we can also get the study variability and we have historic information of the variance if it is given and then process standard deviation can also be used and in that case we are getting some percentage over here study variability as compared to 42 what is the study variation and also percentage process also we have discussed in our last session that and the criteria what I told is that if it is less than equals to 30 percent we we can we can go ahead with the instrument but only thing is that we need to see which is creating problem over here repeatability, reproducibility which which percentage is contributing. So, repeatability is around 80 percent reproducibility about 18 percent over here every is less than 10 percent that is the best best we can get ok. So, overall it is 30 percent so every is less than so best instrument should be less than 10 percent over here, but 10 to 30 percent we can we can keep a within this if if it is within this in that case we can we can use the instrument. But if it is more than 30 percent what we can do is that we have to reject the instrument for use in production flow it has to go to calibration and figure out what is going wrong basically in the instrument what is going on in the instrument and they will make some corrections over there either they will send back the instrument to us or they will say that this cannot be used. So, you have to use a new instrument which they will provide to the operator or the production flow. So, ok. So, this study will reflect that one and when when you do this gauge and RNA study also what we will see is that this whatever we have calculated percentage study variation process variations like this this will be represented over here component of variability over here percentage contribution and percentage study variations over here this are the measures that is given. So, part to part it is expected that this will be very high over here and then we will get gauge R and R contribution for this study variations over here and percentage contribution also will be reflected over here. Similarly, repeat reliability and reproducibility this will be graphically represented. So, what it says is that most of the contribution is due to percentage is this is the favorable situation. Now, if this graph this increases and this goes down that is not expected over here. So, part to part variation should be the maximum contributor and others will have negligible contributions like that. So, this graph will tell you how much contribution is that in percentage how much is the contribution and how much is the study variation that by Caucasian of repeatability a gauge R and R repeatability reproducibility like that, ok. Then there is a control chart aspects also you will see over here one is monitoring the mean of the observations and one in monitoring the variability observations within operated to operator. So, operator 1, operator 2 and operator 3 how they are measuring the part that is given the variability within is reflected over here like R chart interpretation we have to use this one. And if all the points are within the control limit line that is given over here then there is that that seems variability within control. So, that there is no problem in this graph over here. So, there is not nothing unusual that we have to do over here. So, operator 1, operator 2 internal variability or within variability is not so significant like that. And the second one is x bar R chart that you will find that this is operator 1 is measuring operator 2 and operator 3 and the control limit lines will be narrow over here. So, it is expected like that because parts are different parts are from different ranges over here. So, what is expected is that the values of this mean values over here what do you see will fall outside the specification outside the control limit line basically. So, this is expected. So, whenever you are measuring the parts and you have a control you have calculated the control limit line using this R bar information over here and use the control chart. So, part to part variation. So, part to part variation will be there over here. So, 10 parts will be outside the specification most of the time we will find points outside. So, this is not unnatural in case of measurement system analysis it is expected if it is not then there is a problem. So, I have not selected the part which is having a different range like that within the within the within the specification. So, I have to create a range. So, I cannot select all parts within a single range like that. So, it is so a part should be distinct and should have measurements which are somewhat different from the other one like that. So, there should be a difference within the parts that we have selected like that measurements of the parts like that. So, if that is so if the parts are different in that case I have 10 observations 10 parts over here. So, all parts are differently measured. So, in that case it is expected point will fall out the specification limits over here. And these are the 10 parts that is measured like that. So, this is measurement one measure for the part 2 part 3 these are the points measured over here. So, measurement of parts this variability is shown over here. So, what is the range of that? So, this is measured at this range you this is the value that this part is having. So, this is the second part like that. And so measurements are quite scattered within the operating within the maybe process variability or the total specification. So, parts are selected randomly throughout the space. So, is overall. So, it cannot happen that all the parts are in this range like that. So, all the parts. So, I cannot have like that. So, I have selected a range on the higher side on the middle side and also on the lower side like that. So, that is the way we should do this engage R&R studies like that ok. Then what is required is that we want to see that whether operate to operator variation how is the median value is moving over here. So, more or less you see that operator to operator not much variation in box plot what we are seeing is that not much slope what we are expecting over here and we are not seeing that also not so prominent over here ok. And part and operator although the interaction is significant what we have observed ok operator to operator there is a significant, but statistical significance and actual significance means practical significance of that we have to consider over here and and we have to see that whether to take action or not to take action over here. And here what you see is that operator to part and operator interaction information is there. So, when when the points more or less all the three operators that is shown over here and these are the parts and these are the operators over here and more or less if they are parallel like this. So, we expect that there is little interaction although the significant interaction is shown over here which is significant that is shown over here in the previous one when we have said that part and operator interaction is significant, but statistically, but practically also we have to consider like that. So, either you go by percentage contribution over here and if this is very high then we will look into the operator and part and operator interaction otherwise we will we may ignore this one and we will only go by percentage contribution and based on that we make a decision out of that ok. So, over here what we are seeing is that this is the interaction plot over here although statistically it is significant, but more or less we can see that there is a there is more or less they are going parallel more or less they are going parallel. Now the data set says that it is somewhat significant statistically, but we have to see practical aspects of that and percentage contribution if it is less, but we can always look back to that and send it to metrology and try to figure out what is going wrong why interaction is happening like that. So, that has to be considered over here so that is one aspects over here and there are another aspects also even mind when so this how this graph is generated. So, this graph will be generated in Minitab also. So, when we do the analysis over here and let us say we have taken the same experimental trials over here and Gage studies and we have done this Gage R and R cross studies over here. So, part A let us let us consider this first part this one and then we have operator and then we have measuring over here and options what we have given is that this is this I am removing at this current position. So, we are not concerned about this we want to see the graphical interpretation of this and we will have this graph information over here what do you see. So, this when you plot this one this is the graph that I have just copy pasted in that our PPT what I am showing over here. So, this is the interpretation that we have discussed and there will be another important aspects over here number of distinct category over here I have 10 parts. So, the instrument should be able to differentiate between the 10 parts differentiate between the 10 parts and if the measurements are quite in the same range it may not be possible, but what is important is that number of distinct category should be more than 5 should be greater than equals to 5 it is 5 and more. So, I have selected 10 parts over here. So, it is expected that and when we select the range of the parts we need operating range of the CTQs like that or CTQ we get the values throughout the tolerance like that. So, we expect that at least instrument should be able to distinguish in 5 different categories at least 5 different categories because all are different categories parts are in different categories. Some parts may be very closely taken like that. So, here it is not 10 classification because some of the parts are in the same range observation is in same range like that. So, but this is calculated based on the part variation or standard deviation of the parts and when we divide it by standard deviation of the gauge or instruments like that variation of the instruments like that. So, that gives you the formula is given in Minitab or anywhere you can see like that in manuals also it is given. So, we will get a number of distinct categories. So, it is recommended that greater than equals to 5 will be considered as a good instrument like that. So, this is another important aspect. So, let us take one more example where the instrument is not so perfect. So, this is 14, 15, 16 I am considering over here. So, let us let us do this second one. So, before that one let me see what is the process variability C16. So, we can just see variability of this we can just display the statistics. So, we can say C16 we want to see what is the variations of this and it is around 2.5, 2.6 we can say the standard deviation is 2.6. So, what we will do is that we will take this and consider an 2.6. So, gauge studies crossed gauge and this is part B. So, this will be operator B and this will be measurement B over here and what we have got is 2.58. So, options what we can do is that we can write 2.58 over here or use the parts in the study to estimate the process variability. So, this is okay with us and ANOVA analysis we have mentioned that one and we click okay what happens is that in this case what we see is that part to part variation is there that is expected operator to operator variation is not there. So, if you if you want to see this image in image form. So, what we can do is that we can paste this one and we can show it like this. So, part to part variation is prominent. So, 0.013 operator to operator is not prominent and interaction is all that this is a favorable situation all these aspects are placed. So, this is the most suitable scenario over here. So, but we have to see the percentage contribution. So, we will go back to the results over here and let us do the ANOVA analysis. So, so ANOVA when we do the ANOVA and interactions is not prominent over here and is more than 0.25 what happens is that we need to have automatically combines and gives you a table where only part that p value will be reported and operator will be reported over here. So, that interaction will be taken out. So, without interaction it is without interaction will report and percentage contribution what you can see over here if I copy this one it is around 30 percent over here. So, if I paste this one so, this is quite high 30 percent I told if it is less than 10 percent we should accept that one here it is not. So, in that case instrument is having a big problem when I am considering total gauge R and R variability as compared to the total variation. So, part to part variation should be maximum 90 percent or above and gauge should be less than 10 percent, but here it is gauge variability is 33 percent as compared to part variability which is around 66 percent. So, that means, instrument has a problem over here and most of the problem is due to repeatability of the instrument. Instrument is not measuring the same part measurement is changing basically. So, that is very something is loose in the instrument like what we told that some screws or something is loose over here something is going wrong with this repeatability is not correct. So, we have to send it to meteorology to look into this what is going wrong basically. If it is due to reproducibility what happens is that operator to operator operators are measuring it differently that is not the case repeatability is a problem over here and that represents that instrument is having a problem over here not the operator that are used for measuring this doing these studies over here they are not measuring differently, but instrument is measuring differently over here. So, that is an important aspect it has to go to meteorology and we have to check that one percentage contribution 10 percent less we that is the favorable scenario and then another information what we have is that gauge evaluation. So, this is another information that we are getting over here and if we place that in excel what will happen is that we can enlarge that one and see. So, here what you are seeing is that study variability will be close to process variability because we have taken the information from the sample observations that we are having that is the parts information that we are having. So, here also 58 percent 61 percent that is quite high even 30 percent more than that one over here. So, it is a big problem like that instrument is having a big problem over here. So, we have to send it to meteorology and also what you can see is that when I am when I am doing this diagrammatically what you observe over here is that this is a bad bad instrument. So, in this case percentage contribution this is high here also you see gauge R and R percentage this is also quite high. So, component of variation what you see is this should be minimum over here, but this is also quite significant over here and operator to operator that there are two operators D and E over here. So, there is no within operator variation is not so high that is ok, but when you see part selection over here. So, the measurements is within this is not expected all the part should be most of the part should be outside the control limit line. So, that is not happening over here and here also measurements there is some difference, but that is not significant what we have seen that operator to operator variation is not significant D and E are measuring more or less in same pattern interaction is also not prominent that is also ok over here and the parts of measurement are shown over here. So, in this case what is a problem is the contribution component of variation over here that is that is the main aspects we are seeing and that is why this this is also not coming prominent over here. What is the number of distinct category let us try to see whether what is the calculation. So, number of distinct category is 1 which is less than 5 and that is a concern for also this is not acceptable instrument is not able to distinguish between the parts like that. So, that is not acceptable like that ok. We can take a from QS manual this example is taken quality standards that is standards for automobile industries. So, in this case this was the example that is given for measurement system analysis. So, C 7, C 8 and C 9. So, in this case also we can see what how interpretation. So, one more examples we can before we go to different topics like that. So, gauge RNR studies. So, cross gauge RNR studies over here. So, part QS operator QS and measurement QS we are taking over here only thing is that this variation we can calculate. So, QS we can calculate the standard deviation of this. So, let me try to calculate this standard deviation of this and let me try to see what is the value. So, point to approximately point to we can take. So, point to we can take over here. So, quality and then gauge studies and then gauge RNR and we have taken part as QS operator measurement as QS option is we are getting point 2 over here that is the estimation, but it can estimate for process variations over here and I will click ok and I will click ok. So, in this case what we are seeing is that part to part variation is there that is required. Operator to operator variation is also happening this is less than equals to 0.05 and part and operator interaction is also prominent. Percentage contribution if you see this one less than 10 percent. So, somewhat satisfactory over here. So, this is not a concern for us. So, this is favorable situation for us over here and if you see process variation it has just touched 30 percent and here it is just about 10 percent like that 9.25 and somebody can take 9 as a criteria also. So, in this case somewhat we are at the borderline over here. So, we have to see how to reduce this one total variability over here and the main contributor is reproducibility that means, that is happening from operator to operator. Operator to operator measuring it differently why it is happening that we have to see. We want it to be insignificant because operators are highly skilled. So, there must be some skill difference that is happening over here that is why reproducibility is giving you a higher values over here. So, you have to take measurement you have to take measures over here. So, that it does not happen like that operate to operator variation maybe this 10 percent that we are we are getting around 9 more than 9 percent will reduce over here. So, we have to take actions where it is necessary like that. So, reproducibility is a problem over here we can reduce repeatability. So, that will reduce the overall 30 percent criteria that we are having. So, what action to take whether to send to metrology or it is to operator to operator variation we have to we have to take action because operator to operator variation is also contributing to the overall variations of the measurements that you are getting. So, if operator every operator is measuring differently that is not acceptable basically in production or operations flow because somebody will reject the variation somebody will accept that this is ok like that. So, capability analysis will be different. So, everything goes wrong if one thing goes wrong everything goes long like that. So, we do not want that scenarios to happen. So, this is what I wanted to emphasize and number of distinct category also is 4. So, I have to I have to see the because it should be it should be more than greater than equals to 5. So, at least equals to 5 like that then only that instrument is or the. So, we have to concentrate why this is happening maybe operator to operator is contributing over here mostly. So, then it is and the part selection is also there is there is we have to be very precautious about selecting the parts over here. So, it should cover the operating range basically operating range of the CTQs basically or the specification range of the CTQs like that. So, this is all what we have to discuss in measurement system analysis. Let us go to another important topic over here which is known as which we will discuss now of improvement. So, what we have what we have said is that instrument should be correct instrument should be correct. So, that we we get the exact information of process variation and now we will enter into an important topic which is known as factorial experimentation which is known as factorial experimentation and we have already entered into that asymmetric factorial experimentation that is two way analysis of variance we have done. So, if we if we have already covered that one. So, this part becomes easier to understand this part becomes easier to understand and we assure that measurement systems are also ok. So, there is no problem. So, we can now interpret and select the factors factor screening basically what we are doing in factorial experimentation ok. So, what we will discuss is how how factorial interval factorial experiment is done how it is done in how results are generated and based on that in Minitab. So, based on that what conclusions to make ok. So, we have to explain factorial experimentation first. So, these are factors A and factor B this is the general expression that we are having over here there will be factor A factor B over here there will be observations this is replicates that we are having n number of replicates what we are having at each combination one with one over here. So, this is the combination and n number of replicates are happening over here like this the data will be. So, all factors will be combined with all factors over here and we will get the total experimentation and the contribution of these factors over here are given over here and the interaction contribution is given over here and the overall what is unexplained is error variability over here and in any factorial experimentation also we have to take care the error assumptions or residual assumption for aggression also it is true for factorial experimentation also it is true. So, this is the mathematical model statistical effect model that is considered over here and that is what we want to understand in hypothesis testing when we are doing the experimentation and ANOVO analysis will reflect which factor is important and which interaction is important or not. So, there can be A level and B level it can be asymmetric and it can be symmetric also. So, we will discuss about symmetric. So, what is important is that whenever we have done the experimentation we have the sources of variation. So, total variability is known as SST that can be we can have if it is two factor over here we will have effect of A what is that contribution of that effect of B what is the contribution of that interaction effects what is the contribution of that. So, degree of freedom can be calculated this we have already discussed mean square errors can be calculated and f 0 values can be calculated and based on that P values criteria can be used to see whether the A when I change A whether it is impacting the CDQ when I change B whether it is impacting the CDQ and when I change when interaction effect is prominent or not that also we can check over here. So, those P values will indicate what is happening in the. So, this is favorite this is this is an approach which is taken in screening experimentation and also maybe we want to suboptimal solution we want to see what is the combination of factor A and B and but this is not the final optimization what we do generally in screening experimentation factorial design is used and later on we will have we have a technique which is known as response surface methodology which which talks about optimization of the of the system or process like that. So, in that case sequentially we move towards optimal scenarios like that. So, here is maybe at a snapshot like that what is the optimal combination at this at this scenario if this is a operating range like and these are the two factors can you tell me which which is optimal over here that may be suboptimal solutions like that. Anyway, so we are talking about the factor A and B over here and nano analysis will tell me which factor is important and when we are talking about factorial experimentation it is basically a symmetric experimentation that we are doing. It is maybe a two factor at two levels like that ok. So, this is known as symmetric experimentation. So, this is let us say factor A and factor B. So, in this case we have four corner points that we are experimenting over here four corner points that we are experimenting over here and this is factor A and factor B factor A has same number of levels as factor B over here. So, levels can be defined over here let us say level over here is defined in some arbitrary definition what we are saying as low level and high level like that because there is only two levels. So, two factor at two levels. So, this is two square design basically we talk it as in terms of two square design over here. So, two levels and k factors that is a two k design basically that is a general expression when we have two levels experimentation and that is factorial design that symmetric factorial design what we are doing. So, that is known as this is known as two square design where we have two factors at two levels and levels are arbitrarily defined as low level and high level over here. So, it can have values or it can be like color or something like that categorical variables also because in experimentation we may have categorical variables we may have continuous variables like that. If there is both are continuous variable in that case we can have contoured plots and all these options are there response optimization that is possible like that what we have seen earlier also, but sometimes it is categorical whether the factor is important and based on that also we can develop equations and we can optimize the systems like that that is also possible. So, over here what we are saying is that we are starting with a simple experimentation and this is a two square design basically where two factors are there and both are at two levels over here both the factors are at two levels over here. So, a low and low combination is giving you a reading CTQ value of 20 over here and high and low combination factor B is at low level and factor A is at high level over here. So, this is giving you a reading of 40 like this. So, whenever both the both the factors are kept at high level this is the readings that we are getting over here and when the A factor is kept at low level and this is at high level the reading that we are getting is 30 like that all combination is tested over here. So, all combinations two square means four number of trials are required all combinations is four. So, all the four combination reading what you see over here all four combination. So, one is minus minus information that is if I write low as minus over here and over here also minus. So, that combination we have run so and then may be factor. So, this is factor A and factor B. So, minus minus means low level of A and low level of B like that. So, then we can have a combination of this minus plus then we can have a combination of plus minus over here and the final one may be plus plus like that that way also you can we can think of the experimental and this is the matrix that design matrix what we are using over here this is the design matrix they say this is the design matrix and we will run the experimental trial and we will measure the CTQ values and we will measure what what is the if I run this combination and if I run this combination this is let us say this is B combination over here and this is A combination over here is AB combination over here. So, in this case we will we will measure the value. So, this is minus minus combination. So, value is 20 over here. So, this is A at minus level over here A at minus and B at plus A at minus and B at plus. So, in this case the value is 30 over here. So, this is 30 observation and the this is 52 observation and then then then this is 40 observation. So, these are the observations that we have when we have run the trial like this so this is the symbolic notation that I am using over here. So, one means both at low level B means only B is at high level and A is at low level and then A means A is at high level and B is at low level like that and A B means both A and B at high level that we are experimenting over here and these are the results that we have gone we have got from the experimentation and this is randomized. So, which trial will run this is not the first trial that will run this will be randomized like that ok. We can also have a replicates over here that means, this is one one measurement set that we are getting we can have a second measurement set like that. So, N N will be the replicates number of replicates that we do and more and more we replicate that is the best scenario accuracy level of the model increases and the interpretation and the final conclusion becomes more accurate as compared to if we are only using one one replicates or no replicates basically ok. So, what is suggested is that you replicate experiments ok and here what we are doing is that at every level of A every level of A we are having all combinations of A. So, if it is A is at minus level over here A is at minus level over here ok and we are experimenting at B also at minus and plus the combination is with one set of minus over here we are having all combinations of B over here we are running. When A is at positive we are also running B at minus level and also at plus level like that this is known as balanced experimentation that we are doing ok. This is also important what what is what we considered in experimentation like that when we are talking about factorial experimentation it is a balanced experimentation it is very scientifically designed like that and it gives you information of interactions like that. So, what is the advantage of that that we will see up in our next session. So, this is what we are doing factorial experimentation it is symmetric design you can think of like two way analysis of annuals and factors are at k number of factors at two levels three levels like that. So, this is known as 2k design 3k design like that we can there is a general symbolic way we represent factorial experimentation like that. So, these are arbitrary low level and high level arbitrary. So, this can be of numbers this can be of categories like that and these are the observations that we have and we have covered all the points all the extreme corners over here. So, the surface that is covered over here basically this is the experimental zone that we are covering over here for factor a and factor b and a third dimension you can think of z dimension is basically CTQs like that. If we are talking about response surface so, in that case a and b are in x y axis and z is the basically response that we are seeing over here. In case it is continuous then we can develop the surface contour plot and everything is possible like that ok. We will continue from here. Thank you for listening.