 Welcome to session 31 on Quality Control and Improvement with Minitab, I am Professor Indrajit Mukherjee from Shailesh Yameta School of Management, IIT Bombay. So, in previous session what we have studied is that when two factors ah we are experimenting with two factors. So, in that case how to make conclusion and make a judgment which factor is important which factor is not and whether interaction is prominent or not like that and ah and overall judgment about what should be the optimal settings ah for a given ah given experimentation that we have conducted ah considering those are the only factors which influences the overall CTQs and we are making a conclusion ah based on the readings that we have generated by experimentation like that. Now, the authentication means this readings that we have taken whether that is accurate or not depends on the instrument that we are using for measurement like that. So, it is always preferable to ensure that the instrument that we are using to ah to get the measurements or overall variability of the process or CTQs like that should be correct and that will be minimum error in the instrument and if the instrumental error is minimized in that case we can ensure that whatever conclusion that we are drawing even in control chart ah that process is going out of control in control scenarios like that. So, ah that conclusion will be correct based on the instrument that if the instrument is correct everything will be correct otherwise process capability and this design of experiments ah have no meaning if the instrument is incorrect and gives you some reading which is which is not to ah not closer to the true readings like that ok. So, ah all this to ensure that the instrument is correct we need to understand one important topic which is known as measurement system analysis measurement system analysis. So, whatever CPK values or or ah variability analysis is a ANOVO ANOVO analysis that we are representing we are assuming that the ah overall variability is correct that overall variability total variability that we are measuring is correct, but in this case what you have to consider also that the actual variability and ah this overall variability consist of actual variability product variability and also some measurement variations that is happening ah because the instrument accuracy also impacts the overall reading like that ok. So, ah any distribution overall overall total variability distribution will be influenced by ah ah distribution of the measurement variability and the actual product variability over here. So, this is the overall variability so, ah so also ah we have to understand that overall process mean that we are generating over here ah will include the summation of the mean that we are getting based on the product variability actual actual variability and also the measurement system variability over here. So, that is written over here total variability of the total mean of the process will be equals to actual mean and also measurement mean that will influence also the overall means like that ok. Similarly, total variability if I am assuming normal distribution assumptions over here so, there are two parameters mean and standard deviation. So, in this case total standard deviation of the process will be I am using additive model over here. So, that will depends on the actual variability and also the measurement variability over here. Our our ah objective is to minimize the measurement of variability that instrument is quite correct variations and also to minimize the ah mean shift due to or biasness because of this instrument over here. So, this ah also has to has to be very ah we have to deduce it to ah we have to deduce it to ah such a way so, that the overall variability true means does not shift two means does not shift like that ok. So, error has to be minimized so, biasness of the instrument should be deduced and also the variability in measurements has to be reduced like that. So, ah that is the overall idea that we we are adopting over here that total variability is influenced by measurement of variability and it is influencing the mean and variance of the overall distribution of the measurements that we are getting for the CTQs ok. We can also draw a a cause and effect diagram for this because it will be influenced by some of the parameters like ah man over here that percent to percent variability over here the types of material that is used to develop this measurement systems like that and the environmental condition can also impact like that and the way we are taking measurements that can also have an influence over here and what type of instrument that we are using that that also can influence the measurement system like that ok. So, ah this cause and effect diagram can also be drawn in case ah in case we want to analyze further that what is going wrong in the measurement system like that ok. So, those things can be ah can be ah can be ah we can we can take those initiatives to find out what is going wrong basically in the instrument measurement system. So, cause and effect diagram can be used ok ah. So, overall source of variability if we see that one is process variation that is ah what is actually if we if we consider that one and the measuremental variation. So, measuremental variation is an important aspects which is also influencing ah my overall observations overall overall variation of the CTQs ok. And this can be due to two aspects over here one is known as variation due to gauge that means instrument gauge is the instrument that we are using over here ah. So, measuremental variation they the that can be contributed by the gauge variation variation due to gauge or instrument or variation due to operator because if you go to a process ah one person is operating the machine he is measuring ah the outcomes of CTQs and ah second day you go to a second ship somebody else is measuring that one. So, ah percent to percent variation will be there you see ah skilled workforce ah they have different even if if you use different operators we highly skilled operator even the measurements will differ a person working in tool room will have more precise estimation where more precise ah accurate ah readings he can take as compared to the person who is in production flow like that and the person like engineers they are unskilled workforce. So, they will measure something different. So, variation due to operators can also go into the ah overall variability measuremental variations over here. So, that can also contribute the variability of the overall measuremental variability it can impact over here ok. So, ah variation due to gauge ah or instrument ah we have ah we have some kind of studies that we ensure that how much is the variability due to gauge or instrument like that one is known as bias studies one is known as linearity studies over here one is known as stability studies over here ok and repeatability that that talks about sigma. So, this is talking about the mean of the observation this is also talking about mean shifting over here this is also mean shifting over here, but this is sigma that is variability of the ah variability of the instrument that is happening and ah variation due to operator also contributes to the sigma part. So, one is contributing to the mean part that that studies which is relevant to mean ah which is known as bias study ah linearity study and stability study over here and when we are talking about the ah variability of the instrument sigma over here we have two measures one is known as repeatability and one is known as reproducibility ok which is known as gauge repeatability and reproducibility studies like that ok. So, ah that is ah g R and R studies like that. So, we have to understand each important aspects over here one is known as bias aspects which is basically talking about the ah location of the instrument average values like that. So, there will be some reference based on which we will make a conclusion based on that how much is the bias whether it is acceptable not acceptable like that. Similarly, linearity studies and stability studies. So, so, first we will talk about location aspects and then we will talk about the ah precision aspects of that. So, location aspects when we are talking about location we have to remember we are talking about bias linearity and stability when we are talking about precision aspects we are we are just talking about these two aspects one is known as repeatability and one is known as reproducibility over here ok. So, ah this is what what we have seen earlier also in the diagrams for when we are talking about accuracy and precision. So, when we are talking about precision we are talking about sigma aspects of this when we are talking about accuracy we are talking about the mean of this over here measurement of system mean whether it is shifting like that. So, in this case ah two aspects accuracy and precision what we know earlier also. So, I need the instrument to be very accurate and also precise like that. So, no bias no bias in the instrument and also the variability in measurements that we are getting also should be minimized that means repeatability of the instrument should be very high ah. So, that that two aspects we have to ensure like that. So, we are talking about mean of the instrument measuring instruments like that that should have minimum bias or bias should be near to 0 like that and variability also should be near to 0 like that. So, so that is the thing. So, ah bias is equals to 0 means from reference point to the average that we are getting from the measurement instrument should be should be near to 0 like that. So, ah so mean and variance both are important in case of measurement variation when we are talking about reducing measurement variations. So, these two things are to be minimized. So, that their contribution to the overall variation or CTQs variation is minimal. So, that means, the overall variation is actually presenting the two variation of the process like that ok. So, ah so one aspects over here is the measurement system bias over here. So, bias is one of the term that we are concerned about linearity is another important study that is that is also we need to do ah. So, and another one is stability study. So, each of them we have to understand what is the meaning of this. So, one is bias, one is linearity and one is stability over here ok. So, ah and if there is any error. So, what will happen is that the mean ah will shift from the two true measurements. So, there will be bias. So, we want the bias to be near to 0 like that ok ah and linearity is the total scale of measurement that we have for this instrument like that and everywhere the bias should be close to 0 like that. So, there will be no as such will not be significant at different range of measurements that we are taking from the instrument like that ok. We will go into the details of that. So, let us go step by step what we want to understand is bias first then linearity and then stability like that which is talking about the location or mean of the ah measurement system over here. So, one we one is influencing the ah mean and one is influencing the variability. We are talking about the mean ah those studies which which basically says ah how much there is a shift in bias how much is a shift in how much is the overall bias and how much is a trend of the bias like that whether it is acceptable or whether we we need to ah send it to calibration that the instrument needs to be sent to calibration and do some rectification on that. So, ah and and you may have also observed that when you when you go to a shop floor and you see some operator is measuring something some before they measure the CTQ what they does is that they have a reference reference ah ah dimension kept in the shop floor and what they will do is that that instrument they will see that they knows what is the correct reading of that and they will measure with the instrument and recheck that everything is fine with the instrument. So, there is no variation of the true reading from the measurements that they are getting with the instrument. Let us say Vanya Kaliper what reading they are getting there should not be any difference like that. So, they will do that before they they will they take the reading of CTQs like that. So, those are ah some of the things you can observe ah if you if you go to a shop floor like that ok. So, ah first we will explain bias of a reading that we are talking over here ah and then we will talk about linearity and stability studies like that. So, bias is the difference between the observed. So, I will have a part over here I will have a part reference part let us say and maybe that dimension is given as 2 millimeter like that and then I have a measurement instrument which I will use to measure this part several times. I will use this part and there is only one single part. Let us say only one part we are having over here and that I am measuring same operator operator will be same and that operator will measure it several times. Operator will measure it several times and and you can do it blind studies like that you will not say the operator this is the same part that you are measuring over here you can you can just ah you can you can just say that these are the parts you have to measure over here and he does not know whether the same part is given or not. So, to ah to ensure that there is no biasness in the observation that he is mentioning like that he or she is mentioning like that. So, you will have a single operator over here and you will have a single instrument over here and the part will be thrown randomly like that he will not know which means the part is same or not he will not tell that this is a bias study like that. So, we will we will give the same parts time and again, but the operator will not know this is the same parts like that and the measurement will be taken. So, you will have a average observations of the because operator will say this is 2.2.01 something like that if the list count of this instrument is 2 plus of decimal. So, he may also say that this is 005 like that if it is 3 plus of decimal like that we can measure like that and this can be he can also say this is 2.1 like that. So, the measurements will differ every time you are giving ah the part and he does not know that the part is the same part like that. So, there will be ah variation in the observation there will be variation in the observation and the overall observation mean you can measure over here. So, that is sample observations and the master observation which is 2 that is also we have information that there are 2 millimeter dimension and how how do I get this master value over here this is sent to ah calibration or ah this instrumentation that lab that ah that rectifies if there is any problem with the instrument or metrology lab we can think of. So, in that case what happens is that that they they gives you some master value of a of a particular specimen. So, you send it to the ah master this specimen or one of the one of the ah ah product that is being that that that you have produced and the CDQ also mentioned that what is the what is the width of the width dimension I want of this and tell me accurate reading of that. So, they have a precise instrument to measure that one and they will say that this is 2 mm. So, master piece is the value is with you which is 2 mm and the then you ask the operator to measure it several times like that. So, on an average whatever average that you are getting and from the reference value. So, bias is equals to observed average from the reference value. So, this is 2 and observed average let us say 0.1. So, in this case bias will be equals to 0.01 like that. So, this is the positive bias on these aspects you can say that this is the positive bias that is defined over here and if it is 1.98 then in that case it will be negative bias like that. So, bias can be on the positive side it can also be on the negative side. So, what you have to remember over here when you are doing a bias study it is the same instrument same operator same parts and you are making you are you are asking the operator to measure it several times like that. When you measure it several times there will be variation in the readings like that what the operator says because operator does not know the same part is given to that person like time and again like that. And this is a cross sectional test study that means you have you have done the study at a specific time point and based on that you can calculate what is the bias of the instrument like that what is the bias because on an average the operator is measuring something and the master value is different that means that means some amount of bias already exist between the actual observation and the master value that is given by the meteorology lab to you. So, this measurements we can we can we can we can we can get what is the bias of the instrument and Minitab does it automatically for you if you get if you say the master observation and give the actual observation it will give you what is the bias and what is percentage bias and all this information we can get and we will see it in Minitab how it is done ok. This is one one important aspects the second important aspects which talks about location is linearity over here throughout the operating range throughout the operating range of the instrument. So, if an instrument can measure from 2 to 10 mm dimensions like that. So, in that case this is operating range of the instrument like that. So, within this operating range we have to select parts at different locations in the operating range over here. Let us say this is one of the part which we have selected over here 2.1 over here this is 2.9 over here and this is 2.1 this is approximately. So, this is 2 mm 2.1 like this. So, this is let us say 9.9 over here and this is 10 mm I have to measure like that. So, I will select a part which is I will select a master which is equals to 2.1 I will also select a master which is equals to 9.9 like this may be 10 15 masters we have to collect and we have to keep it for this linearity studies like that and each of these masters has to be measured by the operator. So, there will be operator and instrument will be same instrument will be same only we have different plots let us say 10 parts within this operating range of the instrument and each of the parts will be measured by the same operator and with the same instrument like that. So, at every point what we will have is that at every point we will have a observations number of observations let us say we are measuring it 5 times. So, I will have 5 observations at a given at a given reference value. Similarly, I will have a number of observations at different reference value over here ok. And this trials will be conducted its trials will be conducted. So, in that case what will happen is that at every location we will have a bias at every location we will have a bias and based on those bias information at every location throughout the operating instrument and we will get different biases like that and we can also calculate an average bias and then what is expected is that what is expected is that if this is the bias over here and this is the single point over here and you have taken a reference value from 2 to 10 let us say and it is expected that all the values should be close to 0 over here. And if you draw a line over here through this so you will not get any trend you do not expect this. So, expected value of the bias if you and if what we have discussed in regression over here for a given value of x which is from a reference value 2 to 10 what is expected is that the slope should be we do not expect any slope over here which is significant like that. So, but if the bias changes and we have a slope in the bias like that on the positive side or negative side and the slope is significant or beta 1 is significant over here and not equals to 0. So, in that case that is a that is a concern for us. So, we do not want that linearity that linearity measures that we are using over here which is represented by slope over here slope should not be significant. That means, we should not get a regression significant regression equation out of this ok. So, what is expected is that slope is near to 0. So, we are testing a hypothesis where beta 1 equals to 0 and we are making a regression equation of the bias over here. So, bias is the regress with the value reference value that is x over here which is changing we are changing the reference point. So, this is starting from some values and it will let us say from 10 to 50 over here. So, 10 to 50 something like that 30 40 50. So, 5 reference values we have taken over here and every point we have measured some observations over here we have 5 set of observations over here and we want this slope to be 10 theta or theta values over here should be equals to 0. So, we do not want. So, we have to test that one using the observations like that. So, when it does it automatically for you and tells you what is the percentage linearity what is linearity over here and that we can see with an examples like that ok. So, linearity is change of bias throughout the operating range linearity is a change of bias throughout the operating range and we need to ensure that the slope is near to 0 like that. So, or the beta coefficient beta 1 coefficient of slope is equals to 0 that that hypothesis testing we are doing over here ok. And if slope is significant then we have to see why this is happening basically in the instrument then again cause and effect diagram and based on that we take some corrective action we send it to metrology and they does the corrective action and send you back the instrument always they recommends that to change the instrument use something new ok. Because at different operating range we are getting a different mean slope like I mean mean values like that which is which is not expected because bias if bias is changing throughout the operating range and in that case when I am measuring on the lower side let us say low bias if I am measuring on the higher side higher bias like that if it is high bias in that case that is not expected bias should be insignificant throughout the operating range like that. So, this talks about bias over the operating range like that. So, this is linearity study what we have discussed and the third important another aspects which talks about location is the average value which is changing over a period of time. So, here time is given a dimension. So, longitudinal study. So, in this case time period 1 and time period 2 like that we have a reference value. So, we have a single part we have a single operator we have the same measuring instrument like that and the same part will measured will be measured at different time points and the reading how it is changing over time. So, that can be monitored using control chart techniques like that ok. Sometimes what happens is the viscosity changes with respect to time like that. So, when I am measuring the instrument at an even time point viscosity is showing something and different time points it will show. So, instrument should measure the same same same CTQ and same samples time and again time and again measurement should be same it should not change like that. So, instrument should be precise. So, time does not have any influence over the readings that you are generating like that. So, maybe a different operating range or temperature that is environmental temperature should not influence like that. So, in winter the measurement should be same as in summer also. So, measurement should be same for a given piece observations like that. So, this is what is known as stability study so that we can see that throughout the time period that we are measuring and the instrument measure the same dimension every time it gives you the same observation same measurement trading like that. It does not change with the environmental conditions like that. So, that has to be ensured which is known as stability study which is known as stability study over here. And this is monitored based on this bias how the bias is changing it can be monitored using a control chart mechanism what we have discussed earlier how the bias is moving whether some abnormalities observed with respect to time that can be seen like that. So, all is talking about locations over here one is talking about at a single sample and the bias of that bias of the measurements that we are getting or whether the average readings is different from the reference trading like that. And if you and the change of bias throughout the operating range that is studied in linearity and the change in bias with respect to time when we are studying that is known as stability studies that we are doing over here. And these are the three aspects that that needs to be we need to study initially to understand and we will do the bias and linearity study using an example over here. So, we may have certain we can take certain examples over here. And what we are doing over here is that we will we will take an example of linearity study linearity bias linearity study like that. So, we are going to an example over here where part observation is given in C 1 and the master piece reading is given in C 2 and C 3 is the response over here. So, initially what we are doing is that. So, we have different parts. So, part 1, 2, 3, 4, 5. So, different 5 parts are selected over here. And in this case each part is having a master value over here. So, first part is having a master value of 2 and second part is having a master value of let us say 2 mm, 4 mm like that. And like this 5 parts has a master information. So, master value of this part 5 is 10 mm let us assume over here ok. So, each of these parts are measured by the same operator over here, measured by the same operator. And each of these parts is measured by the same operator and first part is first part is measured over here and there are 12 observations you can see. So, 12 measurements are taken and the response is given. So, every time some values the operator is saying. So, master value is 2 and for the first part and we are randomly throwing the parts like that operator does not know which part is being delivered to this person. And the same operator, same operator I am giving 5 parts randomly and the person does not know which part I am giving and it will he will give you some response what is the value of that. So, master value was 2 he reported 2.7 like that. Similarly, the master value was let us say last one 10 and the he was delivering the observation is 9.4 like that based on the instrument that he is using ok. So, I am doing the bias and linearity study together. So, there is the and MINITAB gives you overall readings like that and we can make conclusions based on that ok. So, one part is over here is that every part is measured you have to remember every part is measured there is a master value for these parts and the response is collected from a specific operator we are not changing the operator over here. So, same operator we are using and we are changing the parts and the master value of the parts are different over here ok. So, I want to see bias and linearity study together over here and the results can be seen and when we when I go to STAT what you have to do is that I go to quality tools over here and when then gauge studies are there over here. So, if you go to gauge studies over here and go to gauge linearity and bias study over here. So, in this case what you have to do is that you have to mention that now what is the observations that you have got. So, part numbering. So, this is the first column C 1 I am giving reference value is given master value is given over here and the measurement value is given as response over here like that ok. These are the observations. So, in this case they will ask for process variation over here. This is optional we have to find out the process variability like that and based on that we can make certain conclusions and those are the reference that many companies uses like that. So, if I know the process variability percentage of that based on that I can make a judgment whether the instrument needs modification needs correction or instrument is not suitable to be used in the manufacturing flow like that ok. So, then in options you have to check that the method of estimating repeatability standard deviation over here which will influence the T value calculations like that what options I will click. So, I will click sample standard deviation over here which will say that whether the bias is significantly different or not. So, that P value interpretation that will come based on this sample standard deviation that we are using ok. So, if you have done this one and process variation I have not mentioned over here let us let us at present do not give that one. If you click ok over here what will happen is that you will get some values over here you will get some values that that is represented over here. So, in this case what you see is that you will get a those. So, this is plotted. So, all observations so, reference value is 2 and in that case 2 was the reference value 2 mm 4 mm 6 mm 8 mm 10 mm and I have taken 12 readings or something like that and this red spot that you see is the average average of these values that you have got all the average values are given over here and this is the bias line on this side bias bias on these aspects. So, what what is plotted over here is the bias that is for the 12 observation that we have get and the average bias is the red spot that you see over here at at any given reference point what is the average bias from the observed readings that we are getting over here. So, this is on the positive side this is on the positive average bias this is near to 0 and then again negative bias we are observing on the other 2 observations over here 8 and 10 ok. So, this will be shown over here. So, you see for a reference value of 2 the bias is shown as the observed minus reference and that is coming out to be 0.49 and similarly the average average values difference from the reference value is given over here. So, last 2 8 and 10th observation you see negative bias what we are observing others are positive 2 4 and 6, but 8 and 10th observation is negative bias over here. Then this bias observation with the standard deviation I have a t statistics and that confirms whether the significant bias is observed or not and p value interpretation the same p value interpretation we are we are observing over here. So, at a reference value of 2 what the p value is significant over here what we are observing and then at reference value of 8 and 10 we are observing a significant p values is observed over here. So, what is important over here is that at the lower side of the reference when I am measuring parts which are at the lower end of the overall overall process variation that we are measuring over here. So, at the lower end also we are getting a significant bias on the higher end also we are getting a significant bias only at the middle range of observations that we are measuring we are not getting biasness in the instrument like that. So, the overall average of the bias will be reported over here 0.05 that is the average of all these bias over here and it is showing a negative bias over here whether it is significant or not overall average bias whether it is significant or not that is shown over here as 0.089 we can ignore this one that means gauge biasness is overall bias average bias is not so significant over here that, but individually if you see this at reference 2 and reference 8 and 10 this is significant the bias is significant and this will be reflected. So, this study when I plot this one I am seeing a slope over here and the slope will be. So, a regression equation will be fitted by the Minitab software and it will say that what is the constant value beta 0 and beta 1 estimation. So, slope estimation is minus 0.13 like regression it will use a interpretation of p value and p value is coming out to be significant over here to b value is coming out to be significant over here and the regression model is having r square value of 71 percent like that and as the slope is significant that means the instrument has linearity instrument has linearity and whether to accept that one or that we will see in our next session like that, but 71 percent r square value that means a fitted regression model is prominent over here and if it is not what is expected is that we should have expected something slope and it should have gone through like this it should have gone like flat. So, we do not expect any slope over here. So, what you if the slope is not significant. So, what is expected is that you may have you may have got a flat line from the 0 bias condition like that. So, whenever this slope is prominent and theta is prominent over here. So, in that case what will happen is that that regression equation beta 1 coefficient will be significant like that beta 0, beta 1 over here will be significant and that is what is reflected in the studies over here is that the beta 1 is significant over here and that is shown over here and the r square value is prominent. And now overall average bias is not significant, but individually it is coming out significant. So, slope is coming out about 0.13 that is the minus negative of 0.13. Now, what is the criteria? So, then then to get the criteria whether to accept the instrument or send it to laboratories like that we need some information on process variability like that process variability some information from historic data or process variability because this is measuring a values within a range of 2 to 10. So, this is basically the overall range of the instrument that or the output CTQ that we are getting should be within this mostly within this operating range that we are. So, whenever we are taking the samples we are taking the samples of the CTQ from the lower range measurement and also on the high end measurement and one single instrument is used to measure the complete information of CTQ and that instrument linearity we are just checking over here. So, that we have to keep in mind and in next session what we will do is that we will continue discussion of this only thing is that we will incorporate a process variation over here and estimation of process variation over here so that we understand whether the linearity is acceptable bias is acceptable or not and then we will go ahead with the other aspects which is known as gauge repeatability and reproducibility which talks about sigma aspects of that ok. So, here we are talking about bias or accuracy part over here and whether to accept or not and later on we will study about the variance of that whether to accept the gauge or not based on variability over here. So, if there is any problem we have to send it to meteorology lab and they will do the corrective actions or they will replace the instrument like that if it is not correctable like that. So, bias can be changed and can be adjusted in the instrument like screw we can we can just see whether any screw is loose or not if it is a mechanical instrument like that and those things can be done in the meteorology lab and or it can be sent to the instrument manufacturer and they can do that adjustment and if it is possible if it is not possible we have to displace the instrument like that. So, we will continue discussion from here on linearity and bias and what is the reference point or reference values we should check to say that this bias is acceptable this linearity is acceptable like that we will continue our discussion in our next session. Thank you for listening.