GAUGES LIMITS, FITS, Meteorology Quality Control. T.E. Mechanical SEM - II. Chapter 4 INTERCHANGEABILITY

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1 Dhanvantari College Meteorology Quality Control T.E. Mechanical SEM - II of Engineering, Nashik Chapter 4 LIMITS, FITS, GAUGES INTERCHANGEABILITY When only a few assemblies are to be made, the correct fits between the parts are made by controlling the sizes while machining the parts by matching them with their mating parts. The actual sizes of parts may vary from assembly to assembly to such an extent that a given part can fit only in its own assembly. Such a method of manufacture takes more time and will therefore increase the cost. There will also be problems when parts need to be replaced. Modern production therefore is based on the concept of interchangeability. When one component will assemble properly with any mating component, both being chosen at random, then this is interchangeable manufacture. It is the uniformity of size of the components produced which ensures interchangeability. TOLERANCE Uniformity of size is needed to ensure inerhangeability. The question now is uniformity to what degree of accuracy? The answer is found by examining the fact that a given pair of mating parts functions quite satisfactorily even when the allowance is changed from a certain minimum value to other maximum value. This flexibility can be utillised for economizing the production by allowing the component sizes to very to such an extent that the allowance limits are not crossed. Thus each component is specified with minimum and maximum limits. The difference between the minimum and maximumm limits is termed as Tolerance. Fig. 4.1: Limits, tolerance and allowance Tolerance may be specified on one side of the size e.g. 25 mm which is called as unilateral tolerance. Alternatively the 0.01 Page 1

2 tolerance can be specified on both sides of the size e.g. 25 mm which is called bilateral tolerance. Fig. 4.1 shows tolerances on hole and shaft and its effect on the allowance. HOLE BASIS AND SHAFT BASIS The limit system covered in IS 919 is a general system convering wide variety of holes and shafts. Manufacturing organization may adopt their own systems. The various fits may be obtained by keeping the hole constant and varying the shaft sizes; or by keeping the shaft size constant and varying the hole sizes. When the hole size is kept constant it is termed as Hole basis system; and likewise if shaft size is kept constantt it is termed as shaft basis system. All modern limit systems employ the hole bases because in production of holes fixed sized tools like reamers, drills etc. are used and varying sizes of holes is not as easy as varying the sizes of shafts. LIMIT GAUGES In quantity production a by using limit simple, yet effective method for checking the size of components is Fig. 4.5 : Limit gauges gauge. Figure 4.5 shows two gauges. A plug gauge is used for checking holes. The Go end of the plug gauge is made of the size of lower limit of hole; and the No-Go end of the size of upper limit of the hole. It can be easily seen that if the Go end goes into a hole but the No-Go end does not go, then the hole lies within limits. For gauging of shafts rings of limiting sizes may be used; these are called as ring gauges. Snap gauges also can be used for shafts. A snap gauge is shown in Fig Apart from sizes of holes and shafts, limit gauges can be designed for checking gaps, widths of groves, lengths of jobs and in fact any dimension of a component which is specified with a tolerance. No-go ends of plug gauges most of the times will not enter the holes and thus wear less and hence are made shorter than the go ends. TAYLOR S PRINCIPLE OF LIMIT GAUGING This well known principle states that Go gauges should be of full from whereas the No go gauges should check only one dimension at a time. Page 2

3 Fig. 4.6: Illustration for Taylor s principle Fig. 4.6 (a) showss a rectangular recess with its tolerance zone. The full form go gauge is shown at (b) which will be as per Taylor s principle. It will ensuree fitting. If the right angles at the corners are in error, the go gauge will not enter even if the length and width are within limits; rightly rejecting the component. For the no go gauge two separate pin gauges need to be used as shown at (c). If a full form no go gauge is used the gauge will not enter a recess which is within limits for width but way outside limits for length; giving false conclusion that the recesss is within its upper limits. TYPES OF FITS By specifying limits of sizes for holes and shafts it is possible to obtain any desired fit between the two. To obtain a clearance fit the lower limit of hold is made larger than or equal to the upper limit of the shaft. To obtain the Interference fit the lower limit of shaft is made larger than or equal to the upper limit of the hole. In between these two classes lies a group of fits called as Transition fits. In this the smallest shaft will fit with a clearance into the largest hole, whereas the largest shaft will fit with an interference into the smallest hole. These three classes of fits are shown in Fig Fig. 4.2: Types of fits Fundamental tolerance unit : This quantity is denoted by i and its value is calculated using the imperical formula i = D. This gives the value of i in microns. D is the geometric mean of the end values of a diameter step. Value of D in mm. is to be used in Page 3

4 the formula. Thus to get the value of i for 25 mm, D = = 23.2 mm. and i = = 1.3 microns. The various grades of tolerance are multiples of this fundamental tolerance unit. Chapter - 5 COMPARATORS COMPARATORS Comparators are instruments for indicating the difference in size between the work piece and standard. This difference is magnified and indicated by a display system such as a pointer moving on a scale or a digital readout. A comparator should be able to record variations of one micron. Comparators may be vertical or horizontal, the vertical types being common. MECHANICAL COMPARATORS 1. Sigma Comparator : Fig. 5.2 shows schematically the arrangement in a Sigma mechanical comparator. A vertical bar A, carrying the measuring plunger B is mounted on two flat steel springs C and D, the form of the spring can be seen at (b). The portions E and F are fixed to supports and G is fixed to the bar A. These springs provide a frictionless straight line movement for the bar A. Such a mounting Fig. 5.2 : Schematic sketch of Sigma comparator system becomes possible as the total movement required is only about 0.5 mm. The bar carries a knife edge contact piece H. J and K are pivoted light metal arms pivoted by a crossed stripped hinge as shown at (c). Distance of the contact piece H from the pivot of J and K can be adjusted to obtain varied magnification, making possible the use of same basic units for making comparators of different magnifications. J and K carry between their extremeties a thin metal strip L wound around the spindle of the pointer M. In addition, the pointer spindle carries an aluminium disc which rotates in the field of a magnet and provides damping for movement. Standard models of this comparator are available with magnifications from 300 to 5000 in six choices with scale ranges from to 0.5 mm. Page 4

5 Merits and demerits of mechanical comparators: Merits: 1. Mechanical comparators do not require any external sources of energy and as such they are unaffected by variations in such external energy sources. 2. These are of robust construction and compact designs. 3. As they are independent of power supply they are portable. 4. The simple linear scales are easy to read. Demerits: 1. There are too many moving parts which create problems due to friction. 2. Wear of moving parts affects accuracy. 3. Inertia of moving part makes the instruments sensitive to vibrations. 4. Range is limited as the pointer moves over a fixed scale. 5. The pointer-scale system used can cause parallax errors. Merits / Demerits of Optical Comparators: Merits: 1. There are very few moving parts and as such problems of friction and wear are reduced. 2. Higher range even at high magnification is possible as the scale moves past the index. 3. The beam of light provides a weightless optical lever and hence the inertia of the system is considerably reduced. Demerits: 1. Heat from the source of light may cause change in setting of the zero position. 2. Electrical supply is required. 3. The eye-piece type instruments cause strain on the operator. 4. The projection type instruments occupy large space. PNEUMATIC COMPARATORS (SOLEX GAUGE) The pneumatic gauging system are based on the principle that if air under constant pressure escapes by passing through two orifices, the air pressure in the space between them is dependent on the cross sectional area of the orifices. If one of them is kept uniform then the pressure will vary according to the size of the other. Fig. 5.5 shows the essentials of the well known solex air gauging Page 5

6 Fig. 5.5: Solex pneumatic comparator system. Compressed air entering at D expands in E and maintains a constant pressure equal to the water head H; excess air escaping as bubbles. Air from E passes through control jet A, along the tube connecting to the instrument and finally escapes through the jet B. The pressure between A and B will depend on the orifice at B i.e. on the gap d. This pressure maintains a head h between liquid in the manometer tube C and the mainn chamber, so that the scale on this tube may be calibrated to indicate differences in gap d. change in d of mm changes h, 3 to 20 mm. The method may be used for gauging parts such as bores when a loosely fitting plug having two or more nozzles is inserted in the bore. In process gauging for operations like grinding is also done using these principles. When a high pressure system is used the water manometer is not suitable as a measuring device. Pressures may be 200 to 300 kn/m 2 and a pressure gauge with a pointer moving on a calibrated scale may be used. Merits / Demerits of Pneumatic Gauging Merits : 1. The gauging member is not in direct contact with the work. 2. There are almost no moving parts. 3. The measuring pressure is small. 4. Indicating and measuring can be at different places. 5. Taper and ovality of bores can be easily detected. 6. The method is self-cleaning due to the continuous flow of air through the jets and this makes the method ideal to be used on shop floor for on line controls. 7. The gauging head is self-aligning in the bores. 8. Cost is low. 9. There is no wear as the gauging member is not in direct contact with w the work. Page 6

7 Demerits: Dhanvantari College of Engineering, Nashik 1. Elaborate auxiliary equipment such as air filters, pressure gauges,, regulators needed. 2. Non uniformity of scale is a peculiar aspect of air gauging as the t variation of back pressure is linear over only a small range of the orifice size variation. 3. Water column manometers are not very clear to read and meniscus errors are caused. 4. The water manometer type is not easily portable. 5. Different gaugingg heads are needed for different jobs. The LVDT : The linear variable differential transformer (LVDT) is a for converting very popular device Fig. 5.7: LVDT a very popular device for converting a mechanical displacement into electrical signal which can be magnified to obtain readings. It consists of three coils (Fig. 5.7) ) P, S 1 and S 2 wound around the insulated body. The primary coil P is connected to the mains.. The secondary coils S 1 and S 2 are connected together in series but in opposition to each other. Thus when the core is centered in the centre, the voltage induced in each secondary coil willl be identical and 180 degrees out of phase and the net output will be zero. As the core is i moved the mutual inductance of the two secondary coils is changed upsetting the balance and this gives signal which is further magnified. LVDT probes are pen like probes, come in various v sizes and with suitable circuitary. The magnifications can be changed. Digital readouts are commonly provided with LVDT probes and readings to 0.1 micron are quite common. Merits / Demerits of electrical comparators Merits: 1. Measuring units can be remote from indicating units. 2. Several magnifications are easily possible. 3. Compact sizes of the probes are available. Demerits: 1. External source of energy is needed. 2. Heating of coils can cause zero drifts. Page 7

8 GAUGE LENGTH INTERFEROMETER Dhanvantari College of Engineering, Nashik Fig. 6.9: Gauge length Interferometer This is an instrument for the absolute measurement of slip gauges. The T optical system is shown in Fig The light source is mercury of cadmium lamp. Each of these lamps gives four wavelengths. Cadmium gives red, green, blue and violet whereass mercury gives two yellows, green and violet. The pivoted constant deviation prism can be rotated to preset positions to bring each wavelength in to operation. The condensing lens focuses the light and sends it through a slit which is further converted into a parallel beam byy the collimating lens. This beam is split into a parallel beam by the collimating lens. This beam is split into beams of constituent wavelengths by the prism; one of which is selected to be sent s almost vertically on the gauge and base of the instrument. Light reflected from the top of o the gauge and base returns along a path slightly inclined to the incident path so that it is focused not on the slit but on a prism and then into the eye-piece. The optical flat is adjustable for f inclination in two planes, so that the pitch and direction of the interference fringes may be set to the best position. The gauge coming to this instrument will be absolutely flat and parallel and hence the bands on the gauge top and the base will be of the same pitch and direction, but relatively displaced from each other. It is this displacement which is recorded for each colour ; as a surface by applying pressure on the optical flat at various points and observing the change in the pattern of bands. COMPARISON OF END GAUGES BY OPTICAL FLATS: An experimental method of comparing two end gauges more of academic a interest than of any practical value is shown in figure 6.4. The master gauge and the gauge under test having their ends perfectly flat and parallel, differ in length by the amount H shown, which may be a few microns. The experiment aims at finding the value of H.. The master and the gauge are wrung on to a perfectly flat lapped base. The optical flat is placed in good contact but not wrung to the gauge tops. The orientation of the flat is adjustedd till pattern of bands parallel to the sides of the gauges is obtained. The distance L is noted down and Page 8

9 Fig. 6.4: Comparison of end gauges The pitch / of the bands is found by counting the total number of o bands on the gauge faces. As each band represents a air gap change of, the value of H will be. Whether the length of the gauge is more or less than the master can be found by observing o the change in the pitch of the bands on the two gauges when a little pressure is applied at the centre of the flat. In the situation shown in the figure, such pressure will decrease the t wedge angle with master and increase it with the gauge, thereby making the bands on the master wider and those on the gauge narrower. FLATNESS INTERFEROMETER Fig. 5 shows the optical system of a flatness interferometer. Mercury vapour lamp is used as the source of light. The light passes through a condensing lens which focuses it and sends it through a pin hole. Before the pin hole a colour filter is used to obtain o pure Fig. 6.5: Flatness Interferometer Monochromatic light Further a collimation lens sends a parallel beam through an optical flat on the base. Light reflected from the base is reflected by thee semireflector and is viewed by the eye- piece. The optical flat is adjustable for inclination in i two planes so that the pitch and direction of the interference fringes may be set to the best position. The base is rotatable. With mercury vapour lamp fringes can be obtained over a distance of up to 25 mm and hence for gauges up to this length fringes from the lapped base as well w as from the top of the gauge can be viewed simultaneously. The gauge is wrung to the basee and the flatness and Page 9

10 parallelism of the faces of the gauge can be judged by comparing the relative pitch and inclination of the fringes on top of the gauge and those on the base. Figure 6.6 shows interference Fig. 6.6: Fringe patterns by flatness interferometer band patterns for four gauges. At (a) the pitch and direction of the bands on the base and gauge are same indicating a perfectly flat and parallel gauge. At (b) through the direction of bands is same, the pitch is different indicating a taper along the longer edge e of the gauge. At (c) Chapter 6 INTERFEROMETRY Fig. 6.3: Interference band patterns Fig. 6.3 shows interference band patterns on various surfaces. the spherical surface can be concave or convex and a little pressure on the optical flat at the centre c will spread the bands outwards in a convex surface. If can readily be seen from Fig that if the angle of the wedge decreases, the distance between the bands increases. Page 10

11 Chapter 8 Dhanvantari College of Engineering, Nashik GEAR MEASUREMENT SOURCES OF ERRORS IN MANUFACTURING GEARS The teeth of gears are produced either by a reproduction method or by a generating method. With the first method the cutting tool is a formed involute cutter which forms the gear teeth profiles by reproducing the shape of the cutter itself. Each tooth space of the gear is cut independently of the other tooth spaces. In gear generation, the cutting tool, e.g. a hob, forms the profiles of several teeth simultaneously during constant relative motion of the tool and blank. The main sources of errors when gears are machined by reproduction method are incorrect profile of the cutting tool : incorrect positioning of the tool in relation to the work ; incorrect indexing of the bank. Sources of error when gears are generated are 1. errors in the manufacturing of the cutting tool. 2. errors in positioning the tool in relation to the work. 3. Errors in relative motion of the tool and bank during generating operation. Tool maker s microscope The tool maker s microscope may be used for: a) Measuring the distance between two points on work, by measuring the table travel necessary to bring the second point to the position previously occupied by the first. b) Comparison of thread forms with master profiles enlarged in the eyepiece and measurement of pitch and effective diameter. c) Measurement of angles using the protractor eye piece. d) Comparison of an enlarged projected image with a magnified scaled tracing fixed to the screen i.e. using it like a profile projector. Optical Profile Projector By using lenses and beams of light, profiles of small shapes can be magnified. The enlarged image can be compared with accurate drawings made to the scale of magnification. Such a comparison can reveal any deviations in the sizes and contours of the objects and to get a numerical assessment of such deviations, measurements can be made on the enlarged shadow. The measured dimensions on the shadow will then have to be divided by the multiplication factor. The projection apparatus used for this purpose is termed as an optical profile projector. The essential features of a profile projector are that it should not distort the features in the process of magnification, the magnification should be accurately as stated and that there Page 11

12 should be maximum latitude in holding and adjusting the work piece and examining the projected shadow. QUALITY CONTROL Once the design of quality has been specified the actual manufacturing process will start as per the specification. The term quality control can be defined as the control of various factors that affect the quality. It mainly depends on working conditions, type of labour, measuring instruments, material, tools, machines and skill required. Quality control denotes all those activities which are directed to maintain and improve quality such as 1. Setting of quality targets. 2. Appraisal of conformance. 3. Taking corrective action where any deviation is noticed. 4. Planning for improvements in quality. 5. Functional efficiency. 6. Ease of installation and operation. 7. Reliability and maintainability. 8. Appearance and safety. OBJECTIVES OF QUALITY CONTROL 1. To produce optimum quality at economic rate. 2. To ensure satisfaction of customers with products and services of higher quality. 3. Develop a procedure for good vendor and vendee relations. 4. To improve quality and productivity. 5. Evaluation of quality standards of incoming material, product, WIP and outgoing product. 6. Judging the conformity of the process. 7. Developing quality consciousness within the organization. 8. Reduction in scrap and work. 9. Few customer complaints. 10. Reduction in inspection. Page 12

13 PART II Dhanvantari College of Engineering, Nashik QUALITY CONTROL Chapter 1 CONCEPT OF QUALITY WHAT IS QUALITY Quality is a relative term and used with reference to the end use of the product. Quality generally signifies the Degree of its excellence. The quality of a product can be defined as Fitness for the purpose. The component is said to possess good quality, if it works well for which it is designed. The quality is also defined as Grade. The distinguish features of the product are appearance, test, maintainability, performance and reliability. In any organization, quality involves all department and all groups of personnel. The idea can be represented as shown in figure. Producer Deisgn Manufacturing Cutomer Requirement Testing Fig. 1.1 TOTAL QUALITY CONTROL It is an effective system for integrating the quality development, quality maintenance and quality improvement efforts of various groups in an organization, so as to enable production and service at most economical rates which allow for full customer satisfaction. The two basic responsibilities of total control functions may be stated as : 1. To assist and assure optimum quality costs for the products. 2. To provide quality assurance for the products. The quality control function fulfills these responsibilities through its sub functions such as quality control engineering, process control engineering and quality information equipment engineering. The quality control engineering does the quality planning which establishes the basic framework of the entire quality control system. The process control engineering mainly includes inspection, testing and shop floor control. The quality information equipment engineering designs and develops the inspection and testing equipments for obtaining these process control measurement: Page 13

14 Quality manager Quality cost analysis Market quality research Quality engineering Quality control Quality Standards Test Planning & specification equipment design Inward material Process Inspection quality control control & testing PLANNING THROUGH TRIAL LOTS Whenever a manufacture may desire to introduce a new product in the market, this activity involve new design, new functional features, cost, manufacturing process, skill required, demand, tools required and work holding devices. In such a case it is necessary to plan for trial lots before going for mass production. Trial lot is used to ensure following purposes. 1. To locate deficiencies in the manufacturing process. 2. Performance of all the functions of the product for which it is designed. 3. Assess overall product performance 4. It should be easy to operate and handle. 5. It should be safe. 6. Cost should be economical. QUALITY MINDNESS It is a state of mind in which the awareness of quality is constantly present. It will give the desired result with less risk and minimum time. Quality awareness should be present with the upper management, intermediate levels, supervisory stage and the workers. This will help the company to achieve the required results and will get good reputation in the market. To get good results, the company should give training to all the employees either (1) on job training (2) classroom training (3) conferences (4) seminars (5) and make available the latest industrial journals. Page 14

15 The principle force for meeting the quality lies not in the gauges, instruments or other facilities for inspection i.e. it lies in the state of mind of persons working in the organization from top executive to the down worker. Quality awareness can be developed only when employees have got job satisfaction and the top management is committed to quality. Motivating people to work for quality is an important aspect of quality mindness. The various factors necessary for quality mindness are (1) Recognition (2) Advancement (3) Achievement (4) Responsibility (5) Work for the company. QUALITY AUDIT Quality audit is an independent evaluation of various aspects of quality performance. It is a survey of the quality system of an entire plant. OR It is an appraisal of the whole quality control. Quality audit may be conducted periodically or only when occasion demands, due to existence of quality problem. Purpose of Audit 1. Corrective action is taken with respect to deviation. 2. Opportunities for improvement. 3. There is conformance to specification. 4. Preparations for attaining quality system. 5. Customer quality complaints. 6. Adequacy of gauges and test equipments used. 7. Rejection rate of the product. 8. Procedure for vendors capacity verification. 9. Completeness and clarity of the manufacturing drawings and specifications and procedure for their updating. 10. To evaluate own quality performance. The quality audit must be independent of the established inspection and process control. Audit result should be properly documented and forwarded to the quality manager as well as to the concerned divisions and sections of the company. Any discrepancies revealed in the audit should be rectified within a reasonable period. Quality audit should be treated as a tool to help in improving the quality of a product and not for witch-hunting and punitive action. Effective quality audit requires active co-operation of all departments and sections concerned with quality of product. The audit team consists Company President as a chairman outside consultants and members of the section. POLICES TO BE OBSERVED DURING AUDITING 1. Discovery of causes Auditor should investigate major deficiencies in order to determine the cause. 2. Recommendation and remedies. 3. Avoid atmosphere of blame. 4. Verification of facts. 5. Audit should be done on scheduled basis. QUALITY BUDGET Budget is a tool used by the management for planning programming and control of business activities. Budget represents the financial requirements of different sections of the business during a given period. Quality budget may be defined as an estimate of future expenditure required to meet the quality requirements. Page 15

16 The various phases involved are: 1. Planning phase : Forecast the expenditure such as distribution cost, production cost, material requirement availability of resources. 2. Cost reduction phase : In this phase all the planned activities are critically examined. By observing the last years budget, some changes can be done in the planned activities. It is possible to reduce the cost. 3. Cost control phase : In this phase there is a comparison done on the budget estimate and the actual expenditure. RELATIONSHIP BETWEEN VALUE OF QUALITY AND COST OF O QUALITY It can be seen from the coast curve, that as the quality of a product is improved, the cost ends to rise at an increasing rate. On the other hand, the value curve shows as opposite tendency, in that, the value of the price which the customer is willing to pay for improved quality increases at a decreasing rate. The difference between the value and the cost of product at any particular quality level, represents quality contribution. Fig. Page 16

17 Chapter 3 Dhanvantari College of Engineering, Nashik QUALITY MANAGEMENT Total quality management The modern concept The basic aim is maximum user satisfaction at minimum cost. It has been realized that inspection alone cannot build quality into a product unless quality has been designed and manufactured into it. Therefore awareness must begin at the very conception of the product and continue during the various stages of it s development and and manufacture and even during its usage, to provide feedback from the users which is very essential for quality improvement. The quality of products in a company is determined by the philosophy, commitment and the quality policy of the top management and the extent to which this policy can be put into actual practice. The effectiveness of TQM concept requires proper organizational frame work through which quality programmes are implemented. TQM is basically a management function, involving direction by top management and co-ordination of all quality related activities throughout the company. TQM deals with the product in its totality. Quality is determined by the combined efforts of various departments such as design, engineering, purchase, production and inspection. Objective of quality circle 1. To improve quality and productivity of products. 2. To promote consciousness among workers about quality, safety and cost of production. 3. To give opportunity to the employees to learn new techniques of identifying technical problems. 4. To improve employee motivation. 5. To allow employees to solve problems in their work area, thereby giving job satisfaction. 6. To inspire more effective team work and develop leadership among some potential employees. 7. To develop a proper problem solving methodology within the company. 8. To develop healthy relationship between supervisors and subordinates. 9. To increase employees loyalty and commitment towards the company. 10. Recognition for proper achievements. Limitations of quality circles 1. Quality circle is not an agency for diverting its own problems by the management. 2. A large investment of money and time is required. 3. Employees who mainly depends on their supervisors for direction who lost their initiative and feel uncomfortable. 4. Over expectation of some employees who are excited initially may turn to disappointment afterwards. 5. Control of quality circle activities is difficult. 6. There should be positive attitude from all the members to solve quality related problems. Page 17

18 7. Quality circle is not a substitute for the main tasks of the management. Chapter 4 FUNDAMENTALS OF STATISTICAL CONCEPTS TYPE OF VARIATION The various reasons for variations are i. Poor raw material. ii. Machine vibrations. iii. Tool wear. iv. Faulty work holding devices. v. Carelessness and attitude of operator. vi. Measurement errors. vii. Working conditions. viii. Weather conditions. ix. Skill required. The difference between the chance cause and assignable cause is as follows. Chance cause Assignable cause 1. This cause occurs by chance. 1. This occur due to individual errors. 2. In this there is minute amount of variation. 2. In this there is small and large amount of variation. 3. These variations are difficult to 3. These can be easily traced trace and uneconomical to and economical to eliminate. eliminate. 4. Within random variation process is stable to use sampling procedures. 5. Examples such as slight vibrations in machine hardness variation in material variation in raw material. 6. Follow statistical law of variation. 4. Variation process is not stable to use sampling procedure. 5. Examples such as faulty setup careless, poorly trained workers, faulty figs and fixture different working conditions, difference of skill among worker. 6. Do not follow any statistical Law of variation. Page 18

19 GRAPHICAL REPRESENTATION OF FREQUENCY DISTRIBUTION Histogram : It is a vertical bar chart of frequency distribution values of varying characteristic are shown on horizontal or X axis and the frequency of occurrence on vertical or Y axis. Y Resistance Fig. 4.1 : Histogram of resistance Frequency polygon: It consists of a series of straight lines joining small circles which are plotted at cell midpoints with a height proportional to frequency. The frequency polygon can generally be used to better advantage if two or more distributions are plotted on the same diagram. X Frequency Frequency polygon Fig. 4.3 Page 19

20 Chapter 5 Dhanvantari College of Engineering, Nashik STATISTICAL QUALITY CONTROL BENEFIT OF SQC a) Better quality level b) Uniformity in quality c) Better utilization of resources like man, machines and manpower. d) Less scrap and rework e) Better inspection f) Improved producer and consumer relations g) Improvement in employees morale h) Easy detection of faults i) Increased productivity j) Creating quality awareness in employees. Process capability : It is defined as the minimum tolerance which must be provided for a process in statistical control in order to ensure that variation in size within the permissible limits. The data of process control is very much useful for quality control department. a) To decide specification limit. b) Selection of alternate machines and process. c) To find out rejection areas. d) Selection of machine to use for a specific process. e) To determine shift in the process tendency. The procedure to calculate process capability. 1) Calculate the average X and Range R of each sample. 2) Calculate the grand average X. This measures the centring of the process. 3) Calculate the control limits and Plot X and R charts. 4) Calculate the process capability 66 = 6. CHARACTERISTICS OF A GOOD SAMPLING PLAN 1. Simplicity of operation 2. Economy of inspection 3. Easy to draw samples 4. Testing effort and duration for test. 5. The plan should be flexible enough to reflect changes in size, quality of product submitted and any other factor. 6. The plan should protect both the supplier and consumer. 7. The availability of inspection and personnel and facilities. 8. Administrative expenses 9. Difficulty in training inspectors to use sampling plans. Page 20