 Hello friends, I am Mr. Sanjeev B. Naik working in a Mechanical Engineering Department of Walshian Institute of Technology, Shalapa. In this video, I am explaining about the statistical techniques which are used in deciding the tolerances in engineering practices. So at the end of the session, learners will be able to know the statistical techniques used in analyzing the tolerances in engineering practices. We know that in any manufacturing process, all the identical parts which are produced cannot be produced with identical measurements. So no two parts are alike in their dimensions. They vary in the dimensions or the characteristics, dimensional characteristics. So whatever may be the process well designed or how careful it is operated in spite of taking all the precautions in operating the process, a certain amount of inherent natural variability always exists in the dimensions of the parts produced of the specified parameters. So inherent variations are there in any of the manufacturing process. These variations may be due to various reasons. A number of reasons can be listed out. However, the reasons which are common are tool wear, tool or machine vibrations, misalignments, faulty fixtures, poor maintenance, measuring errors, measuring errors because of the human errors or sometimes instrument errors. It depends. Poor quality of raw materials, carelessness of labour, unskilled operators, voltage fluctuations, etc. So these are number of reasons which have been there because of that natural variability exists. Now these variations are being considered as a tolerance. So tolerance can be defined as the magnitude of permissible variation of a dimension or other specific measured value which is of interest. It can be also defined as the total variation permitted in the size of a dimension and it is the algebraic difference between the upper and lower acceptable dimensions. So it is the difference between a minimum accepted dimension and a maximum accepted dimension of a product, of a part. Hence it is an absolute value. It is a difference between upper and lower limit. The basic purpose of providing tolerances is to permit dimensional variations in the manufacture of components. Provided it should satisfactory perform its intended function and it has been established by the designer. So as per the need of the function the tolerance is to be permitted as a dimensional variations in the manufacturing of components. The difference between the upper and lower limits is termed as permissive tolerance. So we know that whatever variation is expected which has been rewarded on particular manufacturing as a process capability, it should be within certain acceptable limit called the permissive limit and that is called the permissive tolerance. For example, a shaft has to be manufactured to a basic dimension of 40 mm. We know that it cannot be produced exactly at 40 mm for all the shafts. There is a variation and that variation which has been allowed as a tolerance is referred as 40 plus or minus 0.02 mm. Means what? The maximum dimension of the shaft having basic size 40 mm, its maximum acceptable diameter is with upper limit and that is 40 plus 0.02 mm that is 40.02 mm and the lower limit is naturally 40 minus 0.02 mm and that is why it is 39.98 mm. So that becomes something. The setting arbitrary the values of lower limit and upper limit once we decide the tolerance and that difference is called as permissive tolerance and that is why upper limit is 40.02 minus 39.98 that results in the absolute tolerance of 0.04 mm that is the way we can consider the permissive tolerance. Now we have seen that the variations in the dimensions of specified parameters in any production process mainly occur due to two causes. One is called as a chance cause or chance causes which are random in phenomenon. They occur randomly and they are inbuilt in the process. These are common causes many times which occur with the process itself naturally. Whereas another causes are assignable which are detectable causes which can be identified and which can be removed from the system or they can be if not totally eliminated they can be kept under control of some variation and these are special causes. These are not random non-random causes. Now the various chance causes are once again with the causes those are what you have seen now tool wear or vibrations or other number of minor causes are there that behave in random all those are considered to be chance causes and the variation due to these causes is beyond the control that we cannot control them at all. These are inherent and natural with the process and that is why they are going to be there to be accepted whereas they cannot be prevented as I said or eliminated under any circumstances. There are many in number but their contribution is very very less each contributed very little to the variation. So causes are large but their individual contribution to total variation is very very small and these are continuously been there active with the process and are inbuilt as such we can call as a part of process. So they are unavoidable in general or in short they are unavoidable they are there naturally inherently with the process and one has to accept it because they are beyond control and that we call as a variation of dimension due to chance causes. Whereas as I said assignable causes are few normally because these are due to errors. So these are eliminated by identifying proper reason and the errors and one can eliminate it but they add variation a lot. So we have to control their variation so one should try to eliminate totally or at least they should be controlled. Such variations are termed as preventable variations because they can be prevented. So either we eliminate it totally or one can keep them under control that is what something assignable causes. Now total whatever tolerance or variation is observed because of now two reasons chance causes plus assignable causes. So chance causes are always there. So minimum variation is according to chance cause variation. However that is added with assignable cause variation if they cannot be made 0 because sometimes it is un-economical or it is related to cost and process improvement itself and that is why they can be kept under controlled value. So chance causes variation plus assignable causes either 0 variation because of that or it can be under control. That total called variation will be well within certain prescribed limits which is called as natural tolerance. So natural tolerance is some permissive limit which includes both that is chance causes plus assignable causes but normally assignable causes are tending towards 0 or they will have some controlled value. That is what we call natural tolerance. So understanding of natural tolerance is that all the variations due to chance causes must be inherently considered along with some of the assignable causes if at all going to exist with controlled value that we call natural tolerance. Now it is observed that these natural tolerances as a variation they occur with normal distribution over the range. So whatever the range of tolerance from lower value to upper limit value this distribution is normal distribution. So variability follows normally the normal distribution over the range and we know that this normal distribution curve is definitely characterized by its mean value and standard deviation. It will have certain value mean about which we observe the deviation and that is the standard deviation. Once again the standard statistical curve which is used as a normal distribution curve for which the total dispersion is between plus 3 sigma limit minus 3 sigma limit and that dispersion is a tolerance value lower limit and upper limit over here and that is having characteristics as a mean value and certain standard deviation. So by making use of this curve we can analyze the quality manufactured whether accepted or rejected that analysis we can do under statistical quality control method. So now recall and classify the tolerances. So the various types of tolerances are there many lateral or bilateral or any other way you want to decide you can classify that tolerance. This is my reference. Thank you.