1. UNIT -9
STATISTICAL QUALITY CONTROL
SQC was started during the world war-2, on account of the pressure of production in the U.S.A. In
India after the independence, Indian statistical institution, National physical Laboratory, have contributed
much to the development of S Q C. The S Q C units were started by the institute in 1953.
The primary aim of these institutions is to ensure quality, uniformity and inter – changeability of
consumer goods and engineering items. The I S I certification marks – scheme has made steady and
significant progress for the protection of consumer interest, these institutions play a pivotal role in
development and maintenance of the national standards at the highest level of accuracy.
The National physical Laboratory supplies standards to several quality control organizations and ahs
introduced SQC Concepts in Indian standards.
Meaning and definition
SQC refers to the statistical techniques employed for the maintenance of uniform quality in a
continuous flow of manufactured products.
SQC is simply a 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.
SQC has been defined as the art and science of ensuring the optimum use of material and human
resources so as to meet the human needs to their entire satisfaction.
The word quality in SQC refers to the property of a product that conforms to a desired standard.
Therefore, in broad sense SQC means- “ the employment of various statistical principles in quality control
A.V. FEIGENBOUM has defined SQC as- “an effective system for co-ordinating the quality
maintenance and quality improvement efforts of the various groups in an organisation so as to enable
production at the most economical levels which allow for a full customer satisfaction.”
The quality control programmes involve extensive use of statistical techniques like control charts and
sampling Table. Both these tools are based on principles of statistical inferences and are designed to help in
decision on the quality of a product.
The quality standards are normally set by the makers of the product. The quality consciousness
amongst producers is always more when there is competition from rival producers. The continuing patronage
of customers depends a great deal on maintenance of quality control. The SQC is only diagnostic. It can only
indicates whether the standard is being maintained. The remedial action rests with the techniques.
Govt. is also keen on quality standards. Only quality products are given AGMARK and ISI labels.
For marketing goods abroad there is compulsory inspection for quality.
Walter A Shewhart and Harold.F.Dodge of the BELL Laborites (USA), have used probability theory
to develop methods for predicting the quality of the products.
Today the methods of SQC are used widely in production. The tests being confined to only a part of
the whole lot and at times only at suitable intervals. These methods have saved lot of time and expenditure
otherwise involved in full inspection.
PURPOSE OR USES OF SQC
SQC is aimed at planned collection and effective use of data for studying causes of variations in
quality either as between processes, procedures materials, machines etc or over periods of time. This cause
effect analysis is then fed back into the system with a view to continuous action on the process of handling,
manufacturing, packaging transporting and delivery at end – use.
The following are the advantages of SQC:-
1. An objective check is maintained on the quality of the product.
2. It has a healthy influence on the workers. They know that quality is being checked.
3. If producers have strict quality control, the users may relay on it and may not resort to a thorough
4. The quality can be defended before any governmental inquiry on the basis of statistical quality
5. The degree of check can be related with the precision required in each process and the part
performance thus economising cost of inspection.
6. Good deal of data are available. The data on average level of performance and the average rouge of
variability can be used by the management for choice of plant and machinery as well as the technical
7. The continued market is ensured for a product.
8. The efficiency working life of machinery can be determined.
BASIS OF QUALITY CONTROL
The basis of SQC is the degree of variability in the size or the magnitude of a given characteristics of
the product some amount of variability is bound is there, however, scientific and accurate the production
process is the various causes of variation may be classified into
1. Specific and identifiable
2. Random and Chance.
1. These causes include those arising on account of inexperienced worker, fault in the tool or the design
2. These causes have nothing to do with any patent defect in the production process. These arise in the
process of taking out samples and drawing inferences. It is difficult to assign any specific cause for
The purpose of SQC is to separate these assignable causes from the chance or random causes. The
statistical process of achieving this objective is to lay down the limits of chance variations, any variation
beyond those limits must be due to assignable causes within samples. If it is found that the process is out of
control, the specific causes may be looked into through technical examination of the production process in its
Thus, the whole basis of SQC is the degree of variability, whether it is within the tolerable limits due
to chance only and the product is acceptable.
TYPES OF CONTROL
There are two broad ways of statistically controlling the quality of product VIZ
1. PROCESS CONTROL
2. PRODUCT CONTROL
1. PROCESS CONTROL
This is concerned with controlling the quality of goods manufactured in the process of production,
process control detects whether the production process is going on in the desired fashion. In other words it
controls quality of the goods to be produced. It ensures that the machines are turning out the product of a
requisite standard. This is achieved largely through control chart devices. The process control provides
means to discover assignable causes of quality variations when they began affect a process. If a process goes
out of control, this fact can be observed at an early stage, obviously it helps substantially in reducing the
waste, delay and the percentage of scrap.
2. PRODUCT CONTROL
This is concerned with the classification of raw materials or finished goods into any acceptable, non –
acceptable, or whether another sample has to be tested. It is concerned with the inspection of the goods
already produced, whether there are fit to be dispatched.
It is necessary to note even when the process is under control individual products may turn out to be
non –acceptable. Certainly a good process control will not require a strict product control.
3. PRODUCT UNDER CONTROL
The process is said to be under control if the means of sample lots are within the control limits around
the grand mean or any originally established standard based on population survey. This is revealed more
easily and clearly by control charts.
The control charts are the graphic devices developed by SHEWART for detecting un natural pattern
of variations in data resulting from repetitive processes. There are three horizontal lines on the Graph. There
are three horizontal lines on the Graph. There are:-
1. Control lines to indicate the desired standard.
2. An upper control limit indicating the upper limit of tolerance.
3. A lower control limit indicating the lower limit of tolerance.
The control line as well as the upper and lower limits are established by computations.
The following chart shows the various techniques used for SQC
Process control by control charts Product control
By acceptance plan
Variable Attributes Attributes Variable
0 - Chart R – Chart C-Chart p-chart np-chart
MAJOR PARTS OF CONTROL CHART
out of control.
------------------------------------------------------U.C.L. Upper Control Line
-------------------------------------------------------central line = 0
------------------------------------------------------ L C L Lower Control line
out of control.
0 1 2 3 4 5 6 7 8 9 10
The central line represents the average quality of the samples plotted on the chart.
The upper control limit, which is commonly obtained by adding 3 sigma to the average.
The lower control line which is obtained by subtracting 3 sigma from the average. The upper and lower
control limits are usually drawn as dotted lines.
UCL = 0 + 3 SD
LCL = 0 – 3 SD
4. Types of control charts
Broadly speaking control charts can be grouped under two categories
1. For variables.
2. For attributes
1. Many quality characteristics of a product are measurable and can be expressed in specific units of
measurement such as diameter of a screw. Tensil strength of steel pipe, life of an electric bulb etc.
For purpose of control data, two types of control charts are used. Mean chart [0 - chart] and range
2. Some times the quality characteristics of the product are not amenable to measurement. Such
characteristics can only be identified by their presence or absence from the product. Also the
produced item may be classified as good or bad. In such a case to assess quality, it is only possible to
determine the proportion of bad or the defective item in a sample. In such a case control chart for
proportion of defective is used – i.e. p - chart.
c-chart is used to measure average number of defects per item.
USES OF THE CONTROL CHARTS
1. A control chart tells when to leave a process alone and when to take action to correct the trouble.
2. The quality control chart is used to detect shifts in the process average form the desired level. This
information can be help to management in taking appropriate steps.
3. Comparison of budgetary figures with actual performance may help to improve the actual
4. Since only a fraction of output is inspected, cost of inspection is greatly reduced and efficiency goes
5. With the help of control charts one can easily detect whether or not a change in the production process
results in a significant change in quality.
6. The SQC technique helps more economical inspection on the basis of samples.
7. With the help of control charts, we can also decide about the change in the method of production. And
sorting out good products from the bad ones.
8. Control charts find applications not only in the sphere of production, but also in areas in areas like
packing, scrap etc.
DRAWING OF CHARTS
Mean chart – 0 chart
The chart is constructed on the basis of a series of samples drawn frequently during a production
process, which are called sub-groups. Usually smaller sub-groups of size 4 or 5 units are preferred and at
least 25 such – groups are used in the evaluation of control limits.
The procedure of constructing 0 chart
1. The mean of each sample 0 = ∑x
2. The mean of sample means = 0, 0 = ∑0
3. Control limits – Calculation
UCL = 0 +3°0 Where 3°0 = 3(σ/√n)
LCL =0 – 3°0
This procedure can be further simplified if the number of samples and size of each sample is large by
taking the control limits as follows.
UCL = 0 + A2R
LCL = 0 - A2R
Where A2 is the control limit factor, its value can be obtained from a table.
Range –chart R-Chart
Though standard Deviation is the best measure of variation, Range is commonly used in SQC to study
the pattern of variation in quality. This is due to the fact that for small samples of size say 15 or less range
provides a good estimate.
5. The range chart is used to show the variability or dispersion of the quality produced by a given
process. The process of constructing R-chart is similar to that for the 0-chart.
1. The range of each sample is R
2. The mean of sample ranger is R
3. Control limits
UCLR= R + 3σ/R
LCLR= R – 3 σ/R
Where σ/R is the standard error of the Range or SD of the ranges of all possible samples of the same
In practice the UCL and LCL can be conveniently computed by using the range Factors D4 and D3.
In that case
LCLR= D3 - /R .
EXERCISE QUESTIONS (5, 10 & 15 Marks)
1. Define the term SQC.
2. Define SQC Briefly explain the need and utility of SQC in industry.
3. What is a control chart? Explain how a control chart is constructed?
4. How does SQC help in industry.
5. What are the advantages of SQC
6. Briefly explain the basis of SQC
7. Briefly explain Types of Control
8. Briefly explain types of control charts. 0 – Chart and R- Chart
9. State the uses of control charts.