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Statistical Process Control Page 1
Statistical Process
Control
Quality Management
Assignment
Submitted to: Submitted from:
Dr. Hima Gupta Juhi Chauhan
Shiven Sharma
Vandita Agarwal
Aishwarya Alagh
Shashank Kumar
Himanshu Sharma

Content
1. Definition and Importance of SPC
2. Advantages of Decreasing Process Variability
3. Statistical Control Charts – General
3.1 When to Use an effect Chart
3.2 Control Chart Basic Procedure
3.3 Out-of-control signals
4. Control Charts for Variables
5. Control Charts for Attributes
5.1 Types of attribute control charts
5.1.1 The p chart for attribute data
5.1.2 The u chart for attribute data
6. Process Capability Index (PCI)
7. Measuring Process Performance
7.1 Steps Involved In Using Statistical Process Control
8. SPC and Quality Improvement
9. Software for SPC
Summary

1. Definition and Importance of Statistical Process Control(SPC)
Statistical Process Control is an analytical decision making tool which
allows you to see when a process is working correctly and when it is not.
We define Statistical process control as the application of statistical
methods to the measurement and analysis of variation in a process.
Variation is present in any process, deciding when the variation is
natural and when it needs correction is the key to quality control.
Where did this idea originate? The foundation for Statistical Process
Control was laid by Dr. Walter Shewart working in the Bell Telephone
Laboratories in the 1920s conducting research on methods to improve
quality and lower costs. He developed the concept of control with regard
to variation, and came up with Statistical Process Control Charts which
provide a simple way to determine if the process is in control or not.
Dr. W. Edwards Deming built upon Shewart’s work and took the
concepts to Japan following WWII. There, Japanese industry adopted
the concepts whole-heartedly. The resulting high quality of Japanese
products is world-renowned. Dr. Deming is famous throughout Japan as
a "God of quality". Today, SPC is used in manufacturing facilities
around the world.
These fascinating techniques can make an important contribution to
achieving quality objectives. For many organizations, statistical process
control techniques are essential. To help ensure successful and continued
application of these concepts in the reality of lean operating budgets,
statistical process control techniques must not become an end in
themselves.

The Importance of SPC is –
Reduction in waste.
Lead to a reduction in the time required to produce the product or
service from end to end.
A distinct advantage over other quality methods, such as inspection, it
emphasis on early detection and prevention of problems.
Cost reduction.
Customer satisfaction.
2. Advantages of Decreasing Process Variability
Lower variability may result in improved product performance that is
discernible by the customer. Field experience revealed that product near
the specification limits generates complaints from customers. The higher
internal loss due to complaints would, of course, likely result in lower
future sales.
Lower variability of a component characteristic may be the only way to
compensate for high variability in other components and thereby meet
performance requirements in an assembly or system.
Lower variability results in less need for inspection. Lower variability
may command a premium price for a product. For some characteristics
such as weight, lower variability may provide the opportunity to change
the process average.
3. Statistical Control Charts – General
A statistical control chart compares process performance data to
computed “statistical control limits,” drawn as limit lines on the chart.
Control charts, additionally referred to as Shewhart charts (after Bruno
Walter A. Shewhart) or process-behavior charts, in applied math method

management are tools accustomed verify if a producing or business
method is in a very state of applied math management.
The management chart may be a graph accustomed study however a
method changes over time. Information is aforethought in time order. An
effect chart continually contains a central line for the common, associate
in nursing higher line for the higher management limit and a lower line
for the lower management limit. These lines are determined from
historical information. By examination current information to those
lines, you'll draw conclusions concerning whether or not the method
variation is consistent (in management) or is unpredictable (out of
control, full of special causes of variation).
Control charts for variable information are utilized in pairs. The highest
chart monitors the common, or the centering of the distribution of
information from the method. Rock bottom chart monitors the vary, or
the breadth of the distribution. If your information were shots in
practice, the common is wherever the shots are clump, and therefore the
vary is however tightly they're clustered. Management charts for
attribute information are used on an individual basis.
Control charting is one of a number of steps involved in Statistical
Process Control. The steps include discovery, analysis, prioritization,
clarification, and then charting. Before using Statit QC software,
appropriate data must be collected for analysis. Then, you need to begin
again and do it over and over and over. Remember, quality is a CYCLE
of continuous improvement.

3.1 When to Use Control Chart
Controlling ongoing processes by finding and correcting problems as
they occur. Prediction of the expected range of outcomes from a process.
Determination whether a process is stable (in statistical control).
Analyzing patterns of process variation from special causes (non-routine
events) or common causes (built into the process). Determination
whether the quality improvement project should aim to prevent specific
problems or to make fundamental changes to the process.
• When dominant current processes by finding and correcting issues as
they occur.
• When predicting the expected vary of outcomes from a method.
• When deciding whether or not a method is stable (in applied math
control).
• When analyzing patterns of method variation from special causes (non
routine events) or common causes (built into the process).
• When deciding whether or not your quality improvement project ought
to aim to stop specific issues or to form basic changes to the method.
3.2 Control Chart Basic Procedure
The purpose of drawing a control chart is to detect any changes in the
process that would be evident by any abnormal points listed on the graph
from the data collected. If these points are plotted in "real time", the
operator will immediately see that the point is exceeding one of the
control limits, or is heading in that direction, and can make an
immediate adjustment. The operator should also record on the chart the
cause of the drift, and what was done to correct the problem bringing the
process back into a "state of control".

1. Opt for the acceptable management chart for your information.
2. Verify the acceptable fundamental quantity for collection and plotting
information.
3. Collect information, construct your chart and analyze the info.
4. Rummage around for “out-of-control signals” on the management
chart. Once one is known, mark it on the chart and investigate the cause.
Document however you investigated, what you learned, the cause and
the way it absolutely was corrected.
3.3 Out-of-control signals
• A single purpose outside the management limits. In Figure one,
purpose sixteen is on top of the UCL (upper management limit).
• Two out of 3 serial points are on identical facet of the line and farther
than a pair of σ from it. In Figure one, purpose four sends that signal.
• Four out of 5 serial points’ are on identical facet of the line and farther
than one σ from it. In Figure one, purpose eleven sends that signal.
• A run of eight in a very row are on identical facet of the line. Or ten
out of eleven, twelve out of fourteen or sixteen out of twenty. In Figure
one, purpose twenty one is eighth in a very row on top of the line.
• Obvious consistent or persistent patterns that counsel one thing
uncommon concerning your information and your method.

Figure one management Chart: Out-of-Control Signals
Source: Control Chart; Published: 07 Jul 2010 01:04:18 PST
 Still plot information as they're generated. As every new information
is aforethought, check for brand new out-of-control signals.
 Once you begin a replacement management chart, the method could
also be out of management. If so, the management limits calculated
from the primary twenty points are conditional limits. Once you have
a minimum of twenty serial points from an amount once the method
is working au fait, cypher management limits.
4. Control Charts For Variables
During the 1920's, Dr. Walter A. Shewhart proposed a general model for
control charts as follows:
Shewhart Control Charts for variables
Let w be a sample statistic that measures some continuously varying
quality characteristic of interest (e.g., thickness), and suppose that the
mean of w is μw, with a standard deviation of σw. Then the center line,
the UCL, and the LCL are:

UCL=μw+kσw
Center Line = μw
LCL=μw−kσw
Where k is the distance of the control limits from the center line,
expressed in terms of standard deviation units. When k is set to 3, we
speak of 3-sigma control charts.
Historically, k=3 has become an accepted standard in industry.
The centerline is the process mean, which in general is unknown. We
replace it with a target or the average of all the data. The quantity that
we plot is the sample average, X. The chart is called the X chart.
We also have to deal with the fact that σ is, in general, unknown. Here
we replace σw with a given standard value, or we estimate it by a
function of the average standard deviation. This is obtained by averaging
the individual standard deviations that we calculated from each of m
preliminary (or present) samples, each of size n. This function will be
discussed shortly.
Figure 2: Type of control chart
Source: foundasoft (1990)

5. Control Charts For Attributes
The Shewhart control chart plots quality characteristics that can be
measured and expressed numerically. We measure weight, height,
position, thickness, etc. If we cannot represent a particular quality
characteristic numerically, or if it is impractical to do so, we then often
resort to using a quality characteristic to sort or classify an item that is
inspected into one of two "buckets".
An example of a common quality characteristic classification would be
designating units as "conforming units" or "nonconforming units".
Another quality characteristic criteria would be sorting units into "non
defective" and "defective" categories. Quality characteristics of that type
are called attributes.
Note that there is a difference between "nonconforming to an
engineering specification" and "defective" -- a nonconforming unit may
function just fine and be, in fact, not defective at all, while a part can be
"in spec" and not function as desired (i.e., be defective).
Examples of quality characteristics that are attributes are the number of
failures in a production run, the proportion of malfunctioning wafers in a
lot, the number of people eating in the cafeteria on a given day, etc.
5.1 Types of attribute control charts
Control charts dealing with the number of defects or nonconformities are
called c charts (for count). Control charts dealing with the proportion or
fraction of defective product are called p charts (for proportion).
There is another chart which handles defects per unit, called the u chart
(for unit). This applies when we wish to work with the average number
of nonconformities per unit of product.

With knowledge of only two attribute control charts, you can monitor
and control process characteristics that are made up of attribute data.
The two charts are the p (proportion nonconforming) and the u (non-
conformities per unit) charts. Like their continuous counterparts, these
attribute control charts help you make control decisions. With their
control limits, they can help you capture the true voice of the process.
Some attribute data for control charts is defect data — the number of
scratches on a car door, the number of fields missing information on an
application form, and so on. If you’re counting and keeping track of the
number of defects on an item, you’re using defect attribute data, and you
use a u chart to perform statistical process control.
Although the words sound almost identical, it’s critically important to
know what type of attribute data you have: defectives (pass/fail) data or
defect (count) data. If you get this distinction wrong, your subsequent
control chart will be completely invalid.
5.1.1 The p chart for attribute data
The p chart plots the proportion of measured units or process outputs
that are defective in each subgroup. The sequential subgroups for p
charts can be of equal or unequal size. When your subgroups are
different sizes, the upper and lower control limits aren’t constant,
horizontal values — they will look uneven. But the same rules for
interpreting the control chart remain — the control limits just move from
subgroup to subgroup.
You find the proportion of defectives for each subgroup by dividing the
number of defectives observed in the subgroup by the total number of
defectives measured in the subgroup.

Source: Quality Digest (1989)
A common application of a p chart is when you have percentage data,
and the subgroup size for each percentage calculation may be different
from one subgroup to the next — for example, the number of patients
that arrive late each day for their dental appointments or the number of
forms processed each day that have to be reworked due to mistakes or
oversights (defects).
In both of these examples, the total size of the subgroups measured may
vary from day to day. The p charts are generally used where the
probability of a defective is low -usually less than 10 percent. So to be
effective, the subgroup size needs to be large enough to register one or
more defectives. You also need to consider the length of time that a
subgroup represents: Long periods of time can make pinpointing a
specific cause difficult.
Remember, just as with continuous control charts, you need to be alert
for other indicators of special cause variation in addition to just
exceeding the control limits. The presence of unusual patterns, such as

runs or trends, even if all the points are within the control limits, can be
evidence of instability or an out-of-the-ordinary change in performance.
5.1.2 The u chart for attribute data
Like with the p chart, the u chart doesn’t require a constant subgroup
size. The control limits on the u chart vary with the subgroup size and
therefore may not be constant. Counting the number of distinct defects
on a form is a common use of the u chart. For example, errors and
missing information on insurance claim forms (defects) are a problem
for hospitals. As a result, every claim form has to be checked and
corrected before being sent to the insurance company.
One particular hospital measured its defects per unit performance by
calculating the found number of defects per unit for each day’s
processed forms. Each point on the chart represents the average defects
per claim form for that subgroup. Points higher on the chart represent a
greater number of defects per unit. The centerline, calculated at 1.870,
indicates an overall average process performance of 1.87 defects per
form.
6. Process Capability Index
In process improvement efforts, the process capability index or process
capability ratio is a statistical measure of process capability: the ability
of a process to produce output within specification limits. The concept
of process capability only holds meaning for processes that are in a state
of statistical control. Process capability indices measure how
much "natural variation" a process experiences relative to its
specification limits and allows different processes to be compared with
respect to how well an organization controls them.

If the upper and lower specification limits of the process are USL and
LSL, the target process mean is T, the estimated mean of the process
is and the estimated variability of the process (expressed as a standard
deviation) is , then commonly accepted process capability indices
include:
Index Description
Estimates what the process is capable of
producing if the process mean were to be
centered between the specification limits.
Assumes process output is approximately
normally distributed.
Estimates process capability for
specifications that consist of a lower limit
only (for example, strength). Assumes
process output is approximately normally
distributed.
Estimates process capability for
specifications that consist of an upper limit
only (for example, concentration). Assumes
process output is approximately normally
distributed.
Estimates what the process is capable of
producing, considering that the process
mean may not be centered between the
specifications limits. (If the process mean is
not centered, overestimates process
capability.) If the process mean
falls outside of the specification limits.

normally distributed.
Estimates process capability around a
target, T. is always greater than zero.
normally distributed. Is also known as
the Taguchi capability index.
Estimates process capability around a
target, T, and accounts for an off-center
process mean. Assumes process output is
approximately normally distributed.
Source: Wikipedia
is estimated using the sample standard deviation.
7. Measuring Process Performance
Performance measures are recognized as an important element of all
Total Quality Management programs. Managers and supervisors
directing the efforts of an organization or a group have a responsibility
to know how, when, and where to institute a wide range of changes. A
performance measure is composed of a number and a unit of measure.
The number gives us a magnitude (how much) and the unit gives the
number a meaning (what). Performance measures are always tied to a
goal or an objective (the target). Performance measures can be
represented by single dimensional units like hours, meters, nanoseconds,
dollars, number of reports, number of errors, number of CPR-certified
employees, length of time to design hardware, etc. They can show the
variation in a process or deviation from design specifications. A

performance measure is composed of a number and a unit of measure.
The number gives us a magnitude (how much) and the unit gives the
number a meaning (what). Performance measures are always tied to a
goal or an objective (the target). Performance measures can be
represented by single dimensional units like hours, meters, nanoseconds,
dollars, number of reports, number of errors, number of CPR-certified
employees, length of time to design hardware, etc. They can show the
variation in a process or deviation from design specifications.
7.1 Steps Involved In Using Statistical Process Control
Proper Statistical Process Control starts with planning and data
collection. Statistical analysis on the wrong or incorrect data is rubbish,
the analysis must be appropriate for the data collected. Be sure to PLAN,
and then constantly re-evaluate your situation to make sure the plan is
correct. The key to any process improvement program is the PDSA
cycle described by Walter Shewart.

Figure: PDSA CYCLE
Source: A Guide to service improvement, (2005)
PLAN - Identify the problem and the possible causes. The QC tools
described in this manual can help organizations identify problems and
possible causes, and to prioritize corrective actions.
DO - Make changes designed to correct or improve the situation.
STUDY- Study the effect of these changes on the situation. This is
where control charts are used – they show the effects of changes on a
process over time. Evaluate the results and then replicate the change or
abandon it and try something different.
ACT - If the result is successful, standardize the changes and then work
on further improvements or the next prioritized problem. If the outcome
is not yet successful, look for other ways to change the process or
identify different causes for the problem.
Proper Statistical Process Control starts with planning and data
collection. Statistical analysis on the wrong or incorrect data is rubbish,
the analysis must be appropriate for the data collected.
Be sure to PLAN, and then constantly re-evaluate your situation to make
sure the plan is correct. The key to any process improvement program is
the PDSA cycle described by Walter Shewart.

Control charting is one of a number of steps involved in Statistical
Process Control. The steps include discovery, analysis, prioritization,
clarification, and then charting. Before using Statit QC software,
appropriate data must be collected for analysis. Then, you need to begin
again and do it over and over and over. Remember, quality is a CYCLE
of continuous improvement.
8. SPC and Quality Improvement
SPC tools can be used in the following stages of process evaluation and
improvement:
1. Identify the Problem
 Flowcharts identify and communicate information about the flow
of a process, including constraints and gaps.
 Pareto analysis identifies the issues that are causing most of the
problems.
2. Identify the Reasons for the Problem
 Use Ishikawa cause-and-effect diagrams to brainstorm the causes
of a problem from a multidimensional perspective.
3. Analyze the Data
 Run charts show the variability in data over time and the potential
relationships between multiple variables.
 Control charts identify process variation using a set of statistical
tools, enabling the identification of out-of-control variation.
 Process capability analysis is used to show the amount of variation
in an in-control process, and can be useful in improving a process.
 The Taguchi loss function assigns an economic value to variation,
helping to make trade-off decisions in process and product design.

Source: NSS Quality Data Tools

9. Software for SPC
Mostly widely software used for Statistical Process Control by
organizations is Ms Excel. Tools for SPC are not included in the original
version of the software but it is available as an Add-In. This Add-In
could be purchased from different vendors for e.g. - SPC for Excel.
Here are some Screen Shots of the add in –

Summary:
Statistical Process Control (SPC) is a way of using statistical methods
and visual display of data to allow us to understand the variation in a
process. By understanding the types of variation in the process we can
make improvements to the process that we predict will lead to better
outcomes. SPC can also then be used to see whether our predictions
were correct. Statistical process control is the application of statistical
method to the measurement and analysis of any process. Decreased
process variability has important advantages. A statistical control chart
is a graphic comparison of process performance data to computed
statistical control limits drawn as limit lines on the chart. A control chart
distinguishes between common causes and special causes of variation.
Control charts come in many types for both variable or continuous data
and attribute or categorical data. Process capability is the measured,
inherent reproducibility of a product turned out by a process. Capability
ratios help to quantify process capability. With today's growing
emphasis on quality improvement, training individuals in fundamental
quality control skills is a major challenge. Professionals in
manufacturing industries need to bring processes into statistical control
and maintain them.

Bibliography:
 Amsden, r. b. (1986). simplified:practical steps to quality,. new york: white
plains.
 Bothe, D. (1997). Measuring process capability. new york: McGraw-Hill.
 Craig Gygi, B. W. (2012). Six Sigma For Dummies, 2nd Edition (Vols.
ISBN: 978-1-118-12035-4). seattle: paperback.
 McFadden, F. (1993). Six sigma quality programs. new york: paperback.

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