MCom I Semester Analysis Statistical Quality Control Study Material Notes
Table of Contents
MCom I Semester Analysis Statistical Quality Control Study Material Notes: Causes of Variation Test of Variations Statistical Quality Control Main Requisites of Statistical Quality COntrol Origin of SQC Techniquew Objects of Statistical Quality ControlProcess COntol Charts Techniquest of Statistical Quality Control Advantages or Importance of Statistical Quality ControlConstruction Technique of Control Chats Types of Control Charts for Variables :
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Statistical Quality Control
of ever-growing competition, it has become absolutely necessary ucer to keep a continuous watch over the quality of the goods produced consumers are not satisfied with the quality of the product and the complaints are not given proper attention, it shall be impossible for the manufacturer to continue in the market.
The need for quality control arises because of the fact that even after the quality standards have been specified, some variation in quality is unavoidable. For example, a machine is producing 1,00,000 bolts per day of 2 cm length. It is very unlikely that all the screws are exactly 2 cm in length. If the measuring instrument is sufficiently precise we can detect some screws which are slightly less than 2 cm and some which are slightly more than 2 cm. If the difference is not much it can be ignored and the product can be passed off as OK. But if it is beyond certain limits, the article has to be rejected and the cause of such variations has to be investigated. If all the dimensions are measured with sufficient precision it can be determined that the objects differ in some degree. Manufacturing specifications take into account the variability of identical items and allow a tolerance range within which measurements must fall. Items falling within the tolerance limits are judged to be of acceptable quality, and those falling outside the tolerance limits must be scrapped or reworked. Statistical quality control is a very important technique which is used to assess the causes of variation in the quality of the manufactured product.
Causes of Variation
As it has been stated that the variation in a given characteristic is the basic feature of mass-produced items. These variations can be grouped into two classes on the basis of the causes of the variation:
(1) Chance or Random Causes : Variations due to chance factors are all natural to the process of manufacture and cannot be checked i.e., such causes will continue to cause variations but inspire of such variations the quality of the product is said to be controlled and is considered to be in conformity with the product specifications. Thus, natural variation is beyond the control of human hand and cannot be detected or prevented. Natural variation is also sometimes known as allowable variation’ as it cannot be eliminated and one has to allow for such variations in the process.
(2) Assignable Variations : Assignable causes are also known as non-random es and the variation due to these causes is termed as chaotic or erratic or antive variation. The assignable causes may creep in at any stage of the process arrival of the raw materials to the final delivery of goods. Some of plant factors of assignable causes of variation are substandard or defective rial, new techniques or operations, negligence of the operators, wrong on the important factors of assignable cause raw material, new techniques or Opera improper handling of the machines, faulty equipment, unskilled or inexperienced technical staff and so on.
Quality Control Study Material
Out of these two types of variation nothing can be done about the former type. However, assignable variation can be detected and corrected. The value of quality control lies in the fact that assignable variations in a process can be quickly detected. Infect, these variations are often discovered before the product becomes defective.
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Test of Variation
This being so, a manufacturer is faced with the problem of ensuring that his products are of requisite quality and the size of the characteristics in terms of which their quality is measured does not fall outside the maximum and minimum tolerances stipulated by the assembly plants.
There are two different ways of controlling the quality of a product :
(a) Cent-percent Inspection Method : One method usually employed to ensure that defective products are not passed into stock from the factory is to have a 100 percent inspection system that is to say that each unit of product is inspected to assess its quality.
The system of 100 percent inspection is not very satisfactory because of the following reasons :
(i) It is too expensive and the time-consuming.
(ii) 100 percent inspection does not always mean 100 percent assurance, neither men nor machines are infalliable. Persons inspecting each and every item, may pass defective items also.
(iii) 100 percent testing is simply out of question, when test of quality involves destroying the product. For example, if the breaking strength of each and every rod or quality of each and every match stick is tested, the products will be destroyed. Thus, we find that even 100 percent inspection is not infalliable.
(b) Sampling Inspection Method : This method is based on continuous testing of outputs by the use of randomly selected samples whether the units are according to the predetermined specifications or not. Though, it is possible to ensure that all manufactured items or parts meet specifications by inspecting each object for quality.
Today, sampling is almost universally used to control quality of products. Experience has taught that a quality of a product after 100 percent inspection is no better and may be worse) than the quality of the product subjected to inspection by sampling.
Statistical Quality Control
Statistical Quality Control (SQC) refers to the statistical techniques employed for the maintenance of uniform quality in a continuous flow of manufactured products. Some important definitions of SQC are as follows:
“SOC is a simple statistical method for determining the extent to which quality goals are being met without necessarily checking every item produced and for indicating whether or not the variations which occur are exceeding normal expectations. SOC enables us to decide whether to reject or accept a particular product.”
Main Requisites of Statistical Quality Control
(1) Fundamental Objective: The fundamental objective of SQC is to find out the extent to which the products fulfil the specifications, what are the limits ol Variations, why deviations are there, etc. On the basis of information obtained on these points, corrective actions for future are planned.
(2) Random Sample Inspection : SQC is based on continuous testing of outputs by the use of randomly selected samples whether the units are according to the predetermined specifications or not
(3) Use of Statistical Methods: In statistical quality control, various statistical methods, such as selection of random samples, normal distribution, standard deviation, mean, probability theory, etc. are used, that is why it is called statistical quality control
Quality Control Study Material
(4) Decision-making : With the help of control charts, it is ascertained whether the products are within the tolerance limits of the quality or not. If the plotted values fall within the control limits, then product is said to be within quality control.
(5) Co-ordination : SQC process involves specilication, production and inspection. For the successful application of this process, co-ordination in its all the three aspects is very essential.
In short, the SQC technique helps in separating the assignable causes from the chance causes and thereby helps in controlling the manufacturing process. Technically, this is known as process control the object of which is to maintain quality of products coming out of a given process. It should be noted that SOC techniques are diagnostic and not remedial.
Origin of S.Q.C. Technique
The origin of statistical quality control is only recent. It was introduced after The First World War by Walter A. Shewhart and llarold E Dodge of the Bell Laboratories (U.S.A.). They used probability theory to develop methods for predicting the quality of the products by conducting tests of the quality on samples of products turned out from the factory. During the Second World War these methods were used for testing war equipment. Its success for testing war equipment. Its success in the war was followed by its continued anded use in the post-war period. These days, the statistical quality contro some extent in virtually every kind of industry in existence. In fact, it has become as integral and permanent part of management
Objects of Statistical Quality Control
Statistical Quality Control is a very important technique which is used to variation in the quality of the manufactured product. It enables us to determine whether the quality standards are being met without inspecting every unit produced in the process. It primarily aims at the isolation of the chance and assignable causes of variation and consequently helps in the detection, identification and elimination of the assignable causes of erratic fluctuations whenever they are present. A production process is said to be in a state of statistical control if it is operating in the presence of chance causes only and is free from assignable causes of variation.
Advantages or importance of Statistical Quality Control
The following are the main advantages of statistical quality control technique :
(1) Reduction in Costs : Since only a fraction of output is inspected, costs of inspection are greatly reduced.
(2) Early Detection of Faults : SQC ensures an early detection of faults and hence there is a minimum waste of rejected production. The moment a sample point falls outside the control limits it is taken to be a danger signal and necessary corrective action is taken. Thus, SQC provides us timely warning so that improvement may be made.
(3) The Only Course in certain Cases : In certain cases 100 percent inspection cannot be carried out without destroying all the products inspected, for example, testing breaking strength of chalks, proofing of ammunition, etc. In such cases, if 100 percent inspection methods are followed then all the items inspected will be spoiled. In such a case, sampling must be resorted to and by the application of SQC techniques not only the quality is controlled but also valid inferences about the total output are drawn from the samples.
(4) Helpful in Determining the Effect of Changed Process : With the help of control charts one can easily detect whether or not a change in the production process results a significant change in quality.
(5) Healthy Influence on the Workers : The mere presence of an SQC scheme in any manufacturing concern has a very healthy effect as it creates quality consciousness among their personnel. Such a scheme keeps the staff and the workers alert thereby increasing their efficiency.
(6) Greater Efficiency: Not only there is reduction in costs but the efficiency also goes up because much of the boredom is avoided, the work of inspection being considerably reduced.
(7) Creates a Civic Consciousness : It creates a civic quality consciousness among the producers and consumers of the product.
(8) Helpful in Overall Coordination : Statistical quality control helps in resolving the differences arises among the various interests in an organization. It also helps in determining the best practical balance between the cost of quality and the sales value of the product.
SQC has a special role to play in a country like India because of the extraordinary variations encountered in raw materials and in machines. The importance of applying SQC has become greater in our industries in the context of the need for earning foreign exchange by supplying quality goods to successfully compete in the world markets.
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Techniques of Statistical Quality Control
The statistical quality control is done in two ways:
(1) Process Control and
(II) Products Control
A process is said to be in a state of statistical control if the variation is such as would occur in random sampling from some stable population. If this is the case. the variation among the items is attributable to chance and there is no point in seeking special causes for individual cases. But when the process is out of control, It should be possible to locate specific causes for the variation and by removing them to improve the future performance of the process. Statistical quality control may be applied to any repetitive process. Such processes are found not merely in machine production in a factory but also in many management problems. Statistical quality control methods have been used in connection with such diverse problems as the stamping out of bottle caps, errors in the work of accountants, the filling of cartons, complaints received from customers, and airline reservations.
Control Charts
As stated above the main tool of process control is the control chart. Contro: charts developed by Walter A. Shewhart, are the graphic devices for detecting unnatural pattern of variations in data resulting from repetitive processes. Usually the standards of products are specified to which the quality must confirm. These standards also specify limits within which the quality of a product must lie. Thus, there are two control limits viz., the upper control limit (UCL) and the lower control limit (LCL). These limits are termed as tolerance or specification limits. At regular periodical intervals, samples are taken and the data plotted on the graph. if the sample points are within control limits (though they all may not be on the control or the standard line) then it does not call for any corrective action and the process is said to be under control and whatever variations are seen in respect to the standard line, they are all attributed to chance factor. But if the sample points deviate considerably from the control limits, then the process is said to have gone out of control and in such a situation the concerning man must inspect, examine and correct the process.
In short, a control chart is characterised by three horizontal parallel lines. The central line’ represents the average value of the plotted statistic for a large number of samples. In a perfect and ideal manufacturing process the measurements of all the samples will lie on this line. The lower and upper lines, called the lower and upper control limits respectively, are located three standard deviations (of the statistic) away from the centre line. The upper and lower limits are determined on the basis of area-properties of the normal distribution. According to sampling theory, the distribution of statistics of randomly selected large number of samples form a normal distribution. The upper and lower limits, taking mean (w) of the sample mean as the central line, can be determined as follows:
Quality Control Study Material
Construction Technique of Control Charts
The construction of a control chart involves the following steps:
(1) Selection of Sample: The produced units of a product are divided into sub-groups. From different sub-groups, random samples of pre-determined size (n.) are taken.
(2) Measurement of Characteristic: Various statistical measures like mean. range, standard deviation, proportion of defectives etc., are taken for the quality characteristic under study.
(3) Calculation of Statistics : For all the samples, the statistic pertaining to the control charts are calculated. For example, for preparing X-Chart, the mean of all the samples will be calculated.
(4) Grand Average- Parameter : This is obtained by dividing the sum of the sample means by the number of samples included in the chart. This forms the central line.
(5) Scale : Take sample number against X-axis and the measurement of the quality on Y-axis.
(6) Determination of Control Limits : The upper and lower control limits are determined by adding thrice of standard error and deducting thrice of standard error respectively,
(7) Plotting of Lines and Points : Plot the CL, UCL and LCL. The central line is a solid line, while control limits are customarily plotted as broken lines. The sample statistic is plotted as point, thus there will be as many points as there are samples, which may or may not be connected by a line.
A process is considered out of control and and action to Check and Correct the process is taken when :
(1) a plotted point falls outside the control limits:
(11) several points lie close to the control limits; and
(III) the plotted points are randomly scattered, but form a systematic array.
Types of Control Charts
Broadly, the control charts can be grouped under the following two heads :
(1) Control Charts for variables
(2) Control Charts for attributes
(1) Control Charts for Variables
Control charts for variables are designed to achieve and maintain a satisfactory quality level for a process whose product is amenable to quantitative measurements like the thickness, length or diameter of a screw or nur, the weight of the bolts, tensile strength of yarn or steel pipes, resistance of a wire, etc. The observations on such units can be expressed in specific units of measurements. In such cases, quality control involves the control of variation both in measures of central tendency and dispersion of the characteristic. The variables under consideration are of continuous character and are assumed to be distributed normally. Control charts for variables are :
(i) Control chart for mean (X).
(ii) Control chart for range (R).
(iii) Control chart for standard deviation (o).
(i) Control Chart for Mean (X Chart)
The mean chart is used to show the quality average of the samples drawn from a given process. This is primarily designed to control the variation in the process average. In other words, the X-chart is prepared to show the fluctuations of the means of samples about the mean of the process and can be used to determine whether or not the fluctuations are due to random causes or to assignable causes. The construction of X-chart involves the following steps :
(1) Obtain the mean of each sample i.e., X1, X2, X3, etc. This is done by dividing the sum of the values included in a sample (XX) by the number of items in the sample (1 or sample size).
Range Control Chart (R-Chart)
Though standard deviation is the best measure of variation, range is commonly used in statistical quality control to study the pattern of variations in quality. The range of a sample is the difference between the largest and smallest measurement the sample and thus, it gives a picture of the variability within the process. In Tact R-chart is designed to ensure that the variability within samples does not exceed specified limits i.e., the R-chart is used to show the fluctuations of the ranges of the samples about the average range (R). R-chart is the companion chart to the X chart and both are usually required for adequate analysis of the production process under study. The R-chart is generally presented along with the X chart. The general procedure for constructing the R-chart is similar to that of the X chart. Briefly, it is constructed as follows:
(4) Construction of R-chart : As in case of X chart, the sample number is taken along the horizontal scale and the statistic (range) is taken along the vertical scale. The sample points R1, R2, …,R are then plotted as points (dots) against the corresponding sample numbers.
The central line is taken as a bold horizontal line at R and UCLA and LCLR plotted as dotted horizontal lines at the computed values given.
If the points fall within limits, then everything is okay so far as the given process is concerned but if a point falls outside the limits then there is reason to think that something is wrong with the process under consideration and this calls for direct investigation of the process along with the remediate action.
Even when all the points are within control limits but if there appears some concentration near the upper or the lower control limits or there is a clear upward or downward trend of points in the control chart, then the process should be checked to find whether the machine requires adjustment.
