STATISTICAL PROCESS CONTROL

Statistical Process Control (SPC)
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ACKNOWLEDGEMENT
What has been far a flung dream has now achieved its physical dimensions and is
present before me in all its glory. But I myself feel that.
“What I have done is just a drop in the ocean, but the ocean would be less
Because of this missing drop’’
It would not be fair, if I would take all the glow of success because hadn’t the
support of my friends with me, I would not be able to taste success.
I am very much thankful to my Mentors, Colleagues and all the friends of for their
motivation and help & who give me all important suggestions and help which brought a
new life and dimensions to this report.
Mr. Thorve Vivek Baban.
Quality Engineer
D.M.E.(Govt.Polytechnic Ahmednagar)
. B.E. Mechanical (Pune University)

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ABSTRACT
To prosper in today’s economic climate, manufacturers, suppliers and dealer
organizations – must be dedicated to continual improvement. We must constantly seek
more efficient ways to produce products and services. These products and services must
continue to improve in value. We must focus upon our customers, both internal and
external, and make customer satisfaction a primary business goal.
To accomplish this, everyone in organizations must be committed to improvement
and to the use of effective methods. This technique describes several basic statistical
methods that can be used to make our efforts at improvement more effective. Different
levels of understanding are needed to perform different tasks. This technique is aimed at
practitioners and managers beginning the application of statistical methods. It will also
serve as a refresher on these basic methods for those who are now using more advanced
techniques.

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INDEX
NO. CONTENT PAGE
NO.
1.0 INTRODUCTION 1
1.1 Terms 1
1.2 What Is SPC? 2
1.3 Then & Now 2
1.4 Why Use SPC? 4
1.5 For Success 4
2.0 PROCESS CONTROL SYSTEM 5
2.1 The Process 6
2.2 Information About Performance 6
2.3 Action On The Process 6
2.4 Action On The Output 7
3.0 VARIATION & CAUSES 8
3.1 Local Actions & Actions On The System 11
4.0 STATISTICS 12
4.1 Central Tendency-Mean 12
4.2 Dispersion- Range &Standard Deviation 12
4.3 Control Charts 13
4.3.1 Building The X Bar-R Chart 14
4.3.2 Drawing Conclusions From The Charts 15
5.0 PROCESS CONTROL & PROCESS CAPABILITY 17
6.0 ADVANTAGES OF SPC 20
7.0 LIMITATIONS OF SPC 21
8.0 APPLICATIONS OF SPC 22
9.0 CONCLUSION 23
10.0 REFERENCES 24

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LIST OF FIGURES
FIG. NO. PARTICULARS PAGE NO.
1.1 CLASSIC CONTROL CYCLE 3
1.2 SPC CYCLE 3
3.1 VARIATION: COMMON CAUSE & SPECIAL CAUSE 8
4.1 EXAMPLE OF CONTROL CHART(X BAR-R
CHART)
13
4.2 GRAPHICAL EXAMPLES 16

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1. INTRODUCTION
The biggest problem most people have with using today’s methods of quality
control is the fear that statistics are too difficult for the average person to understand.
True, Statistical Process Control, or SPC, is based on some very powerful and complex
math. But SPC improves quality, productivity and profits because it can be used, and
used easily, by everyone in industry - from management offices to the production line.
Statistical process control (SPC) is a method of quality control which uses statistical
methods. SPC is applied in order to monitor and control a process. Monitoring and
controlling the process ensures that it operates at its full potential. At its full potential, the
process can make as much conforming product as possible with a minimum (if not an
elimination) of waste (rework or scrap). SPC can be applied to any process where the
"conforming product" (product meeting specifications) output can be measured. Key
tools used in SPC include control charts; a focus on continuous improvement; and the
design of experiments. An example of a process where SPC is applied is manufacturing
lines.
1.1 TERMS:
Assignable Cause – Something that brings about a change in population from which
measurements are being made and is due to changes in the equipment, material or a
change of operators.
Common Variation – Something which brings about a change in population and is due
to the natural variation of the system.
Control Chart – Graphic means for detecting assignable variations from common
variations that is the variation greater than the random fluctuation.
Lower Control Limit (LCL) – The line below the centerline on a control chart.
Upper Control Limit (UCL) – The line above the centerline on a control chart.
Mean – Average of sample data.
Natural Variability – Variability common to the process, generally cannot be reduced or
eliminated without changes to the process itself.

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Range – The difference between the highest and lowest values in the sample.
Population – The total number of objects or units with a particular characteristic.
Sample – Part of the population selected according to some rule or plan.
Representative Sample – The items from the population are selected in such a waythat
the properties of the sample correspond to the properties of the population.
Random Sample - Each item in the population has an equal chance of being selected.
1.2 What Is SPC?
Let’s look at the three words which form SPC – Statistics, Process, and Control:
Statistics - A way to collect, classify, present and interpret numerical data (information
expressed in numbers).
Process - A combination of machines, equipment, people, raw materials, methods and
environment that produces a product. A process is how something gets done.
Control - Directing or regulating a process so that it behaves the way it is meant to
behave.
So SPC is the use of numerical data to direct or regulate the methods used to produce a
finished product.
1.3 Then and Now
In the past, American quality control has been by inspection. After products were
produced, the good was sorted from the bad, and the bad products either reworked or
scraped. This has led to higher cost and lower quality. This inspection method is called
the Classic Control Cycle, shown in Figure 1.1.
Using the classic control method, bad products go through the entire production
process before they are caught during inspection. As much time and material is spent
producing a defective product as making a good one. Because inspection can never be
perfect, some bad products are going to get shipped to the customer - and that's bad
business.

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The SPC Control Cycle (Figure 1.2) is different. In SPC, the process is monitored
during production. Records are kept on how the process is working. Based on these
records, action is taken to make sure the process is always producing good products, not
bad. This reduces scrap and production costs, and improves quality.
FIG1.1 CLASSIC CONTROL CYCLE
FIG 1.2SPC CYCLE

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1.4 Why Use SPC?
SPC has become the new standard for quality control because it:
 Increases customer satisfaction.
 Decreases scrap, rework, and inspection costs.
 Decreases operating costs.
 Improves productivity.
 Sets a predictable and consistent level of quality.
 Eliminates or reduces the need for inspection by the customer.
1.5 For Success.
SPC is not an overnight cure for production problems. It must be used as an
ongoing program by all levels of personnel. The goal is to improve quality.
Remember: The key concept in SPC is that if the effect each cause has on a process
isknown, and if a certain level of process performance can be expected, then corrective
action can be taken when performance does not meet expectations.

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2. PROCESS CONTROL SYSTEM
A process control system can be described as a feedback system. SPC is one type
of feedback system. Other such systems, which are not statistical, also exist. Four
elements of that system are important to the discussions that will follow:
Prevention Versus Detection
In the past, Manufacturing often depended on Production to make the product and
on Quality Control to inspect the final product and screen out items not meeting
specifications. In administrative situations, work is often checked and rechecked in
efforts to catch errors. Both cases involve a strategy of detection, which is wasteful,
because it allows time and materials to be invested in products or services that are not
always usable. It is much more effective to avoid waste by not producing unusable output
in the first place – a strategy of prevention.
A prevention strategy sounds sensible – even obvious – to most people. It is easily
captured in such slogans as, “Do it right the first time”. However, slogans are not enough.
What is required is an understanding of the elements of a statistical process control
system. The remaining seven subsections of this introduction cover these elements and
can be viewed as answers to the following questions:
 What is meant by a process control system?
 How does variation affect process output?
 How can statistical techniques tell whether a problem is local in nature or involves
broader systems?
 What is meant by a process being in statistical control? What is meant by a process
being capable?
 What is a continual improvement cycle, and what part can process control play in
it?
 What are control charts, and how are they used?
 What benefits can be expected from using control charts?

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2.1 The Process – By the process, we mean the whole combination of suppliers,
producers, people, equipment, input materials, methods, and environment that work
together to produce output, and the customers who use that output (see Figure I.1).
The total performance of the process depends upon communication between supplier
and customer, the way the process is designed and implemented, and on the way it is
operated and managed. The rest of the process control system is useful only if it
contributes either to maintaining a level of excellence or to improving the total
performance of the process.
2.2 Information About Performance – Much information about the actual performance
of the process can be learned by studying the process output. The most helpful
information about the performance of a process comes, however, from understanding
the process itself and its internal variability. Process characteristics (such as
temperatures, cycle times, feed rates, absenteeism, turnover, tardiness, or number of
interruptions) should be the ultimate focus of our efforts. We need to determine the
target values for those characteristics that result in the most productive operation of
the process, and then monitor how near to or far from those target values we are. If
this information is gathered and interpreted correctly, it can show whether the process
is acting in a usual or unusual manner. Proper actions can then be taken, if needed, to
correct the process or the just-produced output. When action is needed it must be
timely and appropriate, or the information-gathering effort is wasted.
2.3 Action on the Process – Action on the process is frequently most economical when
taken to prevent the important characteristics (process or output) from varying too far
from their target values. This ensures the stability and the variation of the process
output is maintained within acceptable limits. Such action might consist of:
 Changes in the operations
 Operator training
 Changes to the incoming materials
 Changes in the more basic elements of the process itself

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 The equipment
 How people communicate and relate
 The design of the process as a whole – which may be vulnerable to changes in
shop temperature or humidity.
2.4 Action on the Output – Action on the output is frequently least economical when it
is restricted to detecting and correcting out-ofspecification product without
addressing the underlying process problem. Unfortunately, if current output does not
consistently meet customer requirements, it may be necessary to sort all products and
to scrap or rework any nonconforming items. This must continue until the necessary
corrective action on the process has been taken and verified.
It is obvious that inspection followed by action on only the output is a poor
substitute for effective process management. Action on only the output should be
used strictly as an interim measure for unstable or incapable processes. Therefore,
the discussions that follow focus on gathering process information and analyzing it so
that action can be taken to correct the process itself. Our focus should be on
prevention not detection.

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3. VARIATIONS AND CAUSES
Understanding variability is the key to SPC – which is probably becoming more clear
already. Variability simply means that no two things are exactly alike.
FIG3.1VARIATION: Common Cause & Special Cause

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In order to effectively use process control measurement data, it is important to
understand the concept of variation, as illustrated in Figure 3.1.
No two products or characteristics are exactly alike, because any process contains
many sources of variability. The differences among products may be large, or they may
be immeasurably small, but they are always present. The diameter of a machined shaft,
for instance, would be susceptible to potential variation from the machine (clearances,
bearing wear), tool (strength, rate of wear), material (diameter, hardness), operator (part
feed, accuracy of centering), maintenance (lubrication, replacement of worn parts),
environment (temperature, constancy of power supply) and measurement system.
Another example is the time required to process an invoice could vary according to the
people performing various steps, the reliability of any equipment they were using, the
accuracy and legibility of the invoice itself, the procedures followed, and the volume of
other work in the office.
Some sources of variation in the process cause short-term, piece-to-piece
differences, e.g., backlash and clearances within a machine and its fixturing, or the
accuracy of a bookkeeper’s work. Other sources of variation tend to cause changes in the
output only over a longer period of time. These changes may occur either gradually as
with tool or machine wear, stepwise as with procedural changes, or irregularly as with
environmental changes such as power surges. Therefore, the time period and conditions
over which measurements are made are critical since they will affect the amount of the
total variation that will be observed.
While individual measured values may all be different, as a group they tend to
form a pattern that can be described as a distribution (see Figure I.2). This distribution
can be characterized by:
 Location (typical or “central” value)
 Spread (span or “width” of values from smallest to largest)
 Shape (the pattern of variation – whether it is symmetrical, skewed, etc.)
From the standpoint of minimum requirements, the issue of variation is often simplified:
parts within specification tolerances are acceptable, parts beyond specification tolerances
are not acceptable; reports on time are acceptable, late reports are not acceptable.

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However, the goal should be to maintain the location to a target value with minimal
variability. To manage any process and reduce variation, the variation should be traced
back to its sources. The first step is to make the distinction between common and special
causes of variation. Common causes refer to the many sources of variation that
consistently acting on the process. Common causes within a process produce a stable and
repeatable distribution over time. This is called “in a state of statistical control,” “in
statistical control,” or sometimes just “in control.” Common causes yield a stable system
of chance causes. If only common causes of variation are present and do not change, the
output of a process is predictable.
Special causes (often called assignable causes) refer to any factors causing
variation that affect only some of the process output. They are often intermittent and
unpredictable. Special causes are signaled by one or more points beyond the control
limits or non-random patterns of points within the control limits. Unless all the special
causes of variation are identified and acted upon, they may continue to affect the process
output in unpredictable ways. If special causes of variation are present, the process
output will not be stable over time.
The changes in the process distribution due to special causes can be either
detrimental or beneficial. When detrimental, they need to be understood and removed.
When beneficial, they should be understood and made a permanent part of the process.
With some mature processes, the customer may give special allowance to run a process
with a consistently occurring special cause. Such allowances will usually require that the
process control plans can assure conformance to customer requirements and protect the
process from other special causes (see Chapter I, Section E).

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3.1Local Actions and Actions on the System
Local Actions
 Are usually required to eliminate special causes of variation
 Can usually be taken by people close to the process
 Can correct typically about 15% of process problems
Actions on the System
 Are usually required to reduce the variation due to common causes
 Almost always require management action for correction
 Are needed to correct typically about 85% of process problems

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4. STATISTICS
There are several basic SPC tools that are useful in an industrial environment.
One of the most useful is the control chart.
A control chart is a very powerful way to check the stability of a process over
time. These charts show the difference between normal and abnormal operating
conditions and determine whether or not corrective action is needed. They help determine
if variation is inherent or assignable.
Only two statistical concepts must be learned in order to build a control chart.
These two concepts are called “central tendency” and “dispersion”.
4.1Central Tendency – Mean
Measures of central tendency show where the data is clustered or grouped
together near a central point. The measure of central tendency we will use is the mean
(average).The mean is calculated by adding all the observations and dividing by the
number of observations.
4.2 Dispersion – Range, Standard Deviation
Not only is it important to know the central tendency of data, but also to know the
amountof scatter about the central point. It is possible that the data may be closely
grouped nearthe central point, it may be uniform, or there may be large numbers of
extreme values.
Some description of spread is needed. The two most common measures of dispersion are
Range and standard deviation.The range is calculated by subtracting the smallest
observation from the largest.Sigma (σ) is the standard deviation. The advantage of usingit
is that it is a very efficient estimator of dispersion. Unfortunately, it is very difficult
tocalculate. Because statistical calculators are available, calculators will generally be used
toobtain the standard deviation.The types of control charts for variables used in this
manualare X-bar (X) control charts and range (R) control charts. Although each chart is
separate,they usually appear as one, which is called an X-R chart.

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4.3CONTROL CHARTS
A control chart (Figure 1-3) is a statistical tool used to check the stability of a process
over time. Its basic functions are:
 To describe what control there is.
 To help get control.
 To help judge whether control has been attained.
 To detect change in process performance.
 To estimate the process capability.
 To signal when corrective action is needed.
The types of control charts for variables used in this manual are X-bar (X)
controlcharts and range (R) control charts. Although each chart is separate, they
usuallyappear as one (an X chart and an R chart.) The (X) chart measures and monitors
FIG4.1EXAMPLE OF CONTROL CHART(X BAR-R CHART)

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the average performance of the process over time. The range (R) control charts measure
and monitor the process variability within a sample.
4.3.1 Building the X BAR-RChart
4.3.1.1. Choose a variable (characteristic):
The characteristic chosen should be a measurable quantity, which can be
expressed in numbers (size, length, weight, etc.).
The characteristic should have a direct effect on the process or product and provide the
Prospect of reducing or preventing costs such as waste.
4.3.1.2. Choose sample groups:
There are two main criteria for choosing a good sample group. First, the
properties of the sample should be like the properties of the population. Secondly, the
sample should represent the population.
Choosing items that were produced one after another is often a good way to select a
quality sample group.
4.3.1.3. Choose sample size and frequency of sampling:
Four or five is a good sample size. It is relatively quick and easy, and tends to
lower variation within a sample. The sample size should be the same each time the
process is sampled.
Large samples of 20-25 are sensitive to changes in the process average. Also, the
larger the sample size, the tighter the control limits.
The frequency to use in collecting the sample data must bedecided on an individual basis.
Sometimes, hourly checksare needed, sometimes weekly.
4.3.1.4. Secure control chart paper:
The chart form is handy and easy to use. Fill in the spaces at the top of the form
with the needed information. Remember that the more completely filled out the form is,
the more the control chart can be used as a communication tool.
4.3.1.5. Plot data on control chart:

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The sample data is then plotted on the control chart as shown in Figure 4.1.
Calculate the range and mean to establish graph points on the chart. The upper and lower
control limits and center line will be determined by other personnel.

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4.3.2 Drawing Conclusions fromthe chart
Conclusions from the control charts can be made after the central tendency lines
and the upper and lower control limits are drawn.As a guideline, early estimates of the
control limits can be made after about ten sample groups have been collected. It is better
to wait until at least 25 sample groups have been collected. Firm control limits can then
be established.Points outside the control limits mean that the process is not in control. It
also means that assignable causes of variation are present.Points within the control limits
are a first indication that the process is in control. Even though all points are within the
control
Limits, lack of control may still be indicated. For example, seven points in a row between
the center line and a control line may indicate lack of control. Normally, points should
fall randomly above and below the center line.
Here are some factors (Figure 4.2) that indicate a lack of control:
1. A point outside the control limits.
2. Seven or more points on the same side of the center line.
3. A trend up or down.
4. A repetitive pattern in the chart indicating a cycle.

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FIG 4.2GRAPHICAL EXAMPLES

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5. PROCESS CONTROL AND PROCESS CAPABILITY
The process control system is an integral part of the overall business management
system. As such, the goal of the process control system is to make predictions about the
current and future state of the process. This leads to economically sound decisions about
actions affecting the process. These decisions require balancing the risk of taking action
when action is not necessary (over-control or “tampering”) versus failing to take action
when action is necessary (under-control). These risks should be handled, however, in the
context of the two sources of variation special causes and common causes (see Figure
5.1).
• A process is said to be operating in statistical control when the only sources of
variation are common causes. One function of a process control system, then, is to
provide a statistical signal when special causes of variation are present, and to avoid
giving false signals when they are not present. This allows appropriate action(s) to be
taken upon those special causes (either removing them or, if they are beneficial, making
them permanent).
• The process control system can be used as a one-time evaluation tool but the real
benefit of a process control system is realized when it is used as a continual learning tool
instead of a conformance tool (good/bad, stable/not stable, capable/not capable, etc.)

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When discussing process capability, two somewhat contrasting concepts need to be
considered:
• Process capability
• Process performance
FIG 5.1PROCESS CONTROL & PROCESS CAPABILITY

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Process capability is determined by the variation that comes from common
causes. It generally represents the best performance of the process itself. This is
demonstrated when the process is being operated in a state of statistical control regardless
of the specifications.
Customers, internal or external, are however more typically concerned with the
process performance; that is, the overall output of the process and how it relates to their
requirements (defined by specifications), irrespective of the process variation.
In general, since a process in statistical control can be described by a predictable
distribution, the proportion of in-specification parts can be estimated from this
distribution. As long as the process remains in statistical control and does not undergo a
change in location, spread or shape, it will continue to produce the same distribution of in
specification parts.
Once the process is in statistical control the first action on the process should be
to locate the process on the target. If the process spread is unacceptable, this strategy
allows the minimum number of out-of specification parts to be produced. Actions on the
system to reduce the variation from common causes are usually required to improve the
ability of the process (and its output) to meet specifications consistently. For a more
detailed discussion of process capability, process performance and the associated
assumptions.

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6. ADVANTAGES OF SPC
 Reduces waste
 Lead to a reduction in the time required to produce the product orservice from end
to enddue to a diminished likelihood that the final product will haveto be
reworked, identify bottlenecks, wait times, and other sources ofdelays within the
process.
 A distinct advantage over other quality methods, such as inspection -its emphasis
on early detection and prevention of problems
 Cost reduction
 Customer satisfaction

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7. LIMITATIONSOF SPC
SPC is applied to reduce or eliminate process waste. This in turn,
eliminates the need for the process step of post manufacture inspection. The
success of SPC relies not only on the skill with which it is applied, but also on
how suitable or amenable the process is to SPC. In some cases, it may be difficult
to judge when the application of SPC is appropriate.

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8. APPLICATIONS OF SPC
 In Automotive Industry it is used to reduce waste & improve in production
processes. Also in New product development of the part it is used to validate the
processes.
 Healthcare & Pharmaceutical Industry to Monitor the Quality of Medicine &
treatments.
 Software Engineering Processes in the Capability Maturity Model (CMM). The
level 4&5 of the Capability Maturity Model Integration use this concepts.
 It is using in Machine setup to study the Machine Capability.
 In food industry, to monitor the quality of product.

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9. CONCLUSION
Statistical process control (SPC) is a method of quality control which uses
statistical methods. SPC is applied in order to monitor and control a process. Monitoring
and controlling the process ensures that it operates at its full potential. At its full
potential, the process can make as much conforming product as possible with a minimum
(if not an elimination) of waste (rework or scrap). SPC can be applied to any process
where the "conforming product" (product meeting specifications) output can be
measured. Key tools used in SPC include control charts; a focus on continuous
improvement; and the design of experiments. An example of a process where SPC is
applied is manufacturing lines.

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10. REFERENCES
 www.wikipedia.com
 REFERENCE MANUAL _SPC_2nd_Edition of AIAG, Edition 2005
 Nelson, Loyd S. (1985), "Interpreting Shewhart X Control Charts", Journal of
Quality Technology, 17:114-16.
 Steel, R. G. D. and J. H. Torrie (1980), Principles and Procedures of Statistics.
New York:McGraw-Hill.
 Western Electric Company (1956), Statistical Quality Control Handbook,
available from ATT Technologies, Commercial Sales Clerk, Select Code 700 444,
P.O. Box 19901, Indianapolis, IN 46219, 1-800-432-6600.

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