Quality tools

Quality Tools
1email: deeneshgoundory@yahoo.com

Deenesh Goundory
deeneshgoundory@yahoo.com
Mauritius
19.10.2015

Defining Quality Tools
Continuous quality improvement process assumes and
requires that a team of experts together with the
company leadership actively use quality tools in their
improvement activities and decision making process.
WHAT ARE QUALITY TOOLS ?
Devices used in understanding and
improving production processes.
Any type of device or tool that is used to support the
quality of all products. It can take the shape of a chart,
technique or strategy that can be used to ensure quality
is maintained during production techniques.

Tools & Techniques for Process
Improvement
Understanding processes so that they can be
improved by means of a systematic approach requires
the knowledge of a simple kit of tools or techniques.
The effective use of these tools and techniques
requires their application by the people who actually
work on the processes and their commitment to this
will only be possible if they are assured that
management cares about improving quality.
Managers must show they are committed by providing
the training and implementation support necessary.
Defining a Process (S-I-P-O-C)
Supplier – Inputs – Process – Outputs - Customers

What Are Quality Tools?
Quality tools are any chart, device, software, strategy
or technique that supports quality management
efforts.
Currently there is a significant number of quality
assurance and quality management tools available, so
the selection of the most appropriate is not always an
easy task.
Tools are essential ingredients of a process and basic
instruments for the success of a quality program.
Quality Tools cannot remedy every quality problem
but they certainly are a means for solving problems.

Nature of Quality Tools
Today there are more than a hundred different tools
available. Many scientists have tried to define them and
differentiate among them on various bases. Tools are
generally a means of accomplishing change.
They are easy to learn and handle and are used to analyse
solutions to existing problems. The tools and techniques
most commonly used in process improvement are:
Problem solving methodology (DRIVE)
Process mapping
Process flowcharting
Force field analysis
Cause & effect diagrams
Brainstorming
Pareto analysis
Statistical process control (SPC)
Control charts
Check sheets
Bar charts
Scatter diagrams
Dot plot or tally

Application of Quality Tools
These simple but effective "tools of improvement"
are widely used as "graphical problem-solving
methods" and as general management tools in
every process between design and delivery. The
challenge for the manufacturing and production
industry is for: "Everyone to understand and use the
improvements tools in their work".
Some of the seven tools can be used in process
identification and/or process analysis.

Process Identification and Analysis

1. Process Mapping
 Process mapping is a method to graphically
describe the steps that make up a process.
 It consists of a set of tools that enable us to
systematically document, analyse, improve and
redesign a process.
 It is the first step of process management.

Understanding Process Mapping
One of the initial steps to understand or improve a
process is Process Mapping. By gathering information we
can construct a “dynamic” model - a picture of the
activities that take place in a process. Process maps are
useful communication tools that help improvement
teams understand the process and identify opportunities
for improvement.
ICOR (inputs, outputs, controls and resources) is an
internationally accepted process analysis methodology
for process mapping. It allows processes to be broken
down into simple, manageable and more easily
understandable units. The maps define the inputs,
outputs, controls and resources for both the high level
process and the sub-processes.

Construct a Process Map
• Brainstorm all activities that routinely occur
within the scope of the process
• Group the activities into 4-6 key sub-
processes
• Identify the sequence of events and links
between the sub-processes
• Define as a high level process map and sub-
process maps using ICOR

Benefits of Process Mapping
 Ability to visually understand and document
a process
 Ability to take a holistic view of process
objectives
 Develop true “buy-in” from employees
 Develop a sense of pride among employees
 Create customer-focused processes

Map Analysis – Elimination of Waste
Delays, Duplication, Approvals, Hand-offs, Errors,
Uncertainties …
Potential Pitfalls of Process Mapping
• Mapping without a clear purpose
• Lost in the details
• Failure to finalize mapping
• Not verifying the facts
• Hidden bias or agenda
• Not focusing on customers’ needs

2. Flowchart
A flowchart is a type of diagram that represents an
algorithm, workflow or process, showing the steps as
boxes of various kinds, and their order by connecting
them with arrows. This diagrammatic representation
illustrates a solution model to a given problem.
Flowcharts are used in analysing, designing,
documenting or managing a process or program in
various fields.

Benefits of
Flowcharts
Gives everyone a clear
understanding of the process.
Helps to identify non-value-
added operations.
Facilitates teamwork and
communication.
Keeps everyone on the same
page.
Use of Flowchart
To develop understanding
of how a process is done.
To study a process for
improvement.
To communicate to others
how a process is done.
When better
communication is needed
between people involved
with the same process.
To document a process.
When planning a project.

Flowchart Basic Procedure
Define the process to be diagrammed. Write its title at the top
of the work surface.
Discuss and decide on the boundaries of your process: Where
or when does the process start? Where or when does it end?
Discuss and decide on the level of detail to be included in the
diagram.
Brainstorm the activities that take place. Write each on a card
or sticky note. Sequence is not important at this point, although
thinking in sequence may help people remember all the steps.
Arrange the activities in proper sequence.
When all activities are included and everyone agrees that the
sequence is correct, draw arrows to show the flow of the process.
Review the flowchart with others involved in the process
(workers, supervisors, suppliers, customers) to see if they agree
that the process is drawn accurately. 18email: deeneshgoundory@yahoo.com

3. Force Field Analysis
Force Field Analysis is a technique for identifying
forces which may help or hinder achieving a change
or improvement. By assessing the forces that
prevent making the change, plans can be developed
to overcome them. It is also important to identify
those forces that will help with the change. Once
these forces have been identified and analysed, it is
possible to determine if a proposed change is viable.

Nature of Force Field Analysis
Force Field Analysis is widely used to inform decision
making, particularly in planning and implementing
change management programmes in organisations. It
is a powerful method of gaining a comprehensive
overview of the different forces acting on a potential
organisational change issue, and for assessing their
source and strength. A Force Field analysis is a simple
visual representation of the factors that encourage
change, and those which inhibit change. The analysis
provides a framework for identifying and thinking
about the impact of these factors. If the restraining
forces are stronger than the driving forces the change
will not happen.

Steps
 Describe the current and the future situation. Use
Adjectives / phrases to describe the situation as it is
now and the vision for the future
 Identify the driving forces and the restraining forces
 Examine the key restraining factors and determine
their relative severity and explore the best ways to
address them (the size of the arrow can be used to
depict relative strength)
 Examine the key driving forces that need to be
encouraged, determine their relative strength and
explore ways of advancing them
 Identify priorities and produce an action plan –
including communications required to key groups
identified

Procedure for F F A
List all forces for change in one column, and all
forces against change in another column.
Assign a score to each force, from 1 (weak) to 5
(strong).
Draw a diagram showing the forces for and against,
and the size of the forces.

Brings into the open factors which will
work for and against the closing of a gap
Identified by a needs analysis.
Helps to recognize circumstances which
can and cannot be changed.
Provides a means to analyse ways to
minimize or eliminate barriers to goal
attainment.
Advantages of F F A

Limitations of F F A
• Process is subjective and requires
collaborative thinking and agreement
• Concerning forces for and against the
solution to a particular problem.
• May oversimplify the relationships
between factors that impact a problem.
• All aspects of a problem may not be
identified.

4. Cause & Effect Diagrams
Cause and Effect Diagrams also known as Fishbone
Diagrams, Ishikawa Diagrams, Herringbone
Diagrams, and Fishikawa Diagrams.
Cause-and-effect diagrams are causal diagrams
that show the causes of a specific event. Common
uses of the Ishikawa diagram are product design
and quality defect prevention to identify potential
factors causing an overall effect. Each cause or
reason for imperfection is a source of variation.
Causes are usually grouped into major categories
to identify these sources of variation.

Philosophy of C & E D
When you have a serious problem, it's important to
explore all of the things that could cause it, before
you start to think about a solution.
That way you can solve the problem completely,
first time round, rather than just addressing part of
it and having the problem run on and on.
Cause and Effect Analysis gives you a useful way of
doing this. This diagram-based technique, which
combines Brainstorming with a type of Mind Map ,
pushes you to consider all possible causes of a
problem, rather than just the ones that are most
obvious.

Purpose of the C & E D
The CE Diagram is basically used to investigate a
problem, exploring, identifying, and displaying the
possible causes.
Discover the root cause of a problem.
Uncover bottlenecks in your processes.
Identify where and why a process isn't working.

Steps to Solve a Problem With C & E D
1. Agree on a problem statement (effect). Write it at the center right
of the flipchart or whiteboard. Draw a box around it and draw a
horizontal arrow running to it.
2. Brainstorm the major categories of causes of the problem. If this
is difficult use generic headings: Methods, Machines (equipment),
People, (manpower), Materials, Measurement and Environment
3. Write the categories of causes as branches from the main arrow.
4. Brainstorm all the possible causes of the problem. Ask: “Why
does this happen?” As each idea is given, the facilitator writes it as
a branch from the appropriate category. Causes can be written in
several places if they relate to several categories.
5. Again ask “why does this happen?” about each cause. Write sub–
causes branching off the causes. Continue to ask “Why?” and
generate deeper levels of causes. Layers of branches indicate
causal relationships.
6. When the group runs out of ideas, focus attention to places on
the chart where ideas are few.

5. Check Sheet
The check sheet is a form (document) used to collect data in
real time at the location where the data is generated. The data
it captures can be quantitative or qualitative. When the
information is quantitative, the check sheet is sometimes
called a tally sheet.
When to Use a Check Sheet?
When data can be observed and collected repeatedly by the
same person or at the same location.
When collecting data on the frequency or patterns of events,
problems, defects, defect location, defect causes, etc...
When collecting data from a production process.

Check Sheet Procedure
Decide what event or problem will be observed;
develop operational definitions.
Decide when data will be collected and for how long.
Design the form. Set it up so that data can be recorded
simply by making check marks or Xs or similar symbols
and so that data do not have to be recopied for analysis.
Label all spaces on the form.
Test the check sheet for a short trial period to be sure it
collects the appropriate data and is easy to use.
Each time the targeted event or problem occurs, record
data on the check sheet.

Criteria for Check Sheets
 Who filled out the check sheet?
 What was collected (what each check
represents, an identifying batch or lot number)?
 Where the collection took place (facility,
room, apparatus)?
 When the collection took place (hour, shift,
day of the week)?
 Why the data were collected?

Creating Check Sheets
Step One
Identify the question
Develop and understand the question(s) that
need to be answered before the data collection
process
Step Two
Identify potential problem areas
Outline the production process
Figure out the potential processes that could
be causing defects
Get employees involved who know the
processes well

Creating Check Sheets (contd.)
Step Three
Tracking problems/defects
Construct a tabular or schematic diagram in
order to track problems in production processes
Step Four
Recording problems/defects
Physically record every instance that a
problem/defect is encountered

Benefits of Check Sheets
 Efficiency/ Speed
 Systematic and Organised
 Ease of use/ Simplicity
 Can be used in conjunction with other
charts and diagrams for a more in depth
analysis

6. Histogram
A histogram is a graphical tool used to visualise data. It
is a bar chart, where the height of each bar represents
the number of observations falling within a range of
rank-ordered data values.
The Histogram is a frequency distribution that shows
how often each different value in a set of data occurs.
A histogram is the most commonly used graph to
show frequency distributions. It looks very much like a
bar chart, but there are important differences
between them.

Application of Histogram
 When the data are numerical.
 When you want to see the shape of the data’s
distribution, especially when determining whether the
output of a process is distributed approximately normally.
 When analysing whether a process can meet the
customer’s requirements.
 When analysing what the output from a supplier’s
process looks like.
 When seeing whether a process change has occurred
from one time period to another.
 When determining whether the outputs of two or more
processes are different.
 When you wish to communicate the distribution of data
quickly and easily to others.
email: deeneshgoundory@yahoo.com 40

Methodology
 Rank order the data from the smallest value to the largest
value.
 Calculate the number of bars (or cells) as approximately
equal to the square root of the number of data values. The
number of cells (or bars) will influence the shape of the
perceived distribution, so never base it on convenience, the
data resolution, or anything other than the number of data
observations.
 The width of each bar is calculated by dividing the range of
the data (the maximum value minus the minimum value) by
the number of bars.
 Count the number of data observations in each bar.
 The vertical axis plots the count of observations in each bar.
The horizontal axis displays the data values for each bar
(usually either the starting point, ending point, or midpoint).

Symmetric, Unimodal Skewed right
Skewed left Biomodal

Interpreting the Histogram
If your data is from a symmetrical distribution, such as the Normal
Distribution, the data will be evenly distributed about the center
of the data. If the data is not roughly evenly distributed about the
center of the Histogram, it is commonly called "skewed". If it
appears skewed, you should understand the cause of the
"skewness". Some processes will naturally have a skewed
distribution, and may also be bounded. If the variable is waiting
time, the lower bound may be physically limited to zero.
If double or multiple peaks occur, look for the possibility that the
data is coming from two different sources, such as two separate
personnel groups, or two differently adjusted machines.
Remember that if the process is out of control, then by definition
a single distribution cannot be fit to the data. Therefore, always
use a control chart to determine statistical control before
attempting to fit a distribution (or interpet the histogram).

Advantage
Visually strong.
Can compare to
normal curve.
Usually vertical axis
is a frequency count
of items falling into
each category.
Disadvantage
Cannot read exact
values because data is
grouped into
categories.
More difficult to
compare two data
sets.
Use only with
continuous data.

7. Pareto Analysis
For those in charge, there are usually lots of
decisions to be made. The question is, which
should be tackled first?
To help answer that question, many business
leaders conduct a Pareto analysis.
A Pareto analysis helps prioritise decisions so
leaders know which ones will have the greatest
influence on their overall goals and which ones
will have the least amount of impact.

Understanding the P A
The Pareto analysis is also known as the 80/20 rule
because it is based on the idea that 80 percent of a
project's benefit can come from doing 20 percent of
the work. Conversely, 80 percent of a situation's
problems can be traced to 20 percent of the causes.
Hence, the Pareto analysis is named after Italian
economist Vilfredo Pareto, who observed that 80
percent of Italy's wealth belonged to only 20 percent
of the population.

Concept of P A
"The Pareto Principle is the observation (not law) that
most things in life are not distributed evenly,"
Among the examples they give include:
20 % of the input creates 80 % of the result
20 % of the workers produce 80 % of the result
20 % of the customers create 80 % of the revenue
20% of your products and services account for 80% of
your profit.
20% of your sales-force produces 80% of your company
revenues.
20% of a systems defects cause 80% of its problems.

When to Use a Pareto Chart?
 When analysing data about the frequency of
problems or causes in a process.
 When there are many problems or causes
and you want to focus on the most significant.
 When analysing broad causes by looking at
their specific components.
 When communicating with others about your
data.

How to Use the Tool?
Step 1: Identify and List Problems
Firstly, write a list of all of the problems that you need to resolve.
Step 2: Identify the Root Cause of Each Problem
For each problem, identify its fundamental cause. (Techniques such as
Brainstorming , the 5 Whys , Cause and Effect Analysis , and Root Cause
Analysis will help with this.)
Step 3: Score Problems
Now you need to score each problem (as per occurrence).
Step 4: Group Problems Together By Root Cause
Next, group problems together by cause. For example, if three of your
problems are caused by lack of staff, put these in the same group.
Step 5: Add up the Scores for Each Group
You can now add up the scores for each cause group. The group with the
top score is your highest priority, and the group with the lowest score is
your lowest priority.
Step 6: Take Action
Now you need to deal with the causes of your problems, dealing with
your top-priority problem, or group of problems, first.

Pareto Analysis
Eight steps to identifying the principal causes you should focus on,
using Pareto Analysis:
1. Create a vertical bar chart with causes on the x-axis and count
(number of occurrences) on the y-axis.
2. Arrange the bar chart in descending order of cause importance, that
is, the cause with the highest count first.
3. Calculate the cumulative count for each cause in descending order.
4. Calculate the cumulative count % for each cause in descending order.
(% calculation: {Individual Cause Count} / {Total Causes Count} x 100)
5. Create a second y-axis with percentages descending in increments of
10 from 100% to 0%.
6. Plot the cumulative count percentage of each cause on the x-axis.
7. Join the points to form a curve.
8. Draw a line at 80% on the y-axis running parallel to the x-axis. Then
drop the line at the point of intersection with the curve on the x-axis.
This point on the x-axis separates the important causes on the left (vital
few) from the less important causes on the right (trivial many).

(490/1000) x 100 = 49%
(690/1000) x 100 = 69%
(770/1000) x 100 = 77%
(850/1000) x 100 = 85%
(900/1000) x 100 = 90%
(940/1000) x 100 = 94%
(980/1000) x 100 = 98%
(988/1000) x 100 = 98.8%
(996/1000 ) x 100 = 99.6%
(1000/1000) x100 = 100%

Focused of P A
The above is a simple example of a Pareto diagram,
using sample data showing the relative frequency of
causes for errors on websites. It enables you to see what
20% of cases are causing 80% of the problems and
where efforts should be focused to achieve the greatest
improvement. In this case, we can see that broken links,
spelling errors and missing title tags should be the focus.
The value of the Pareto Principle for a project manager
is that it reminds you to focus on the 20% of things that
matter. Of the things you do during your project, only
20% are crucial. Those 20% produce 80% of your results.
Identify and focus on those things first, but don't
entirely ignore the remaining 80% of causes.

Benefits of P A
1. Enhanced problem-solving skills
You can improve your problem-solving skills when you conduct a
Pareto analysis, because it enables you to organize work-related
problems into cohesive facts. Once you’ve clearly outlined these
facts, you can begin the planning necessary to solve the problems.
Members of a group can conduct a Pareto analysis together.
Arriving at a group consensus about the issues that require change
fosters organisational learning and increases group cohesiveness.
2. Improved decision making
Individuals who conduct a Pareto analysis can measure and
compare the impact of changes that take place in an organisation.
With a focus on resolving problems, the procedures and processes
required to make the changes should be documented during a
Pareto analysis. This documentation will enable better preparation
and improvements in decision making for future changes.

Benefits of P A (contd.)
3. Organisational efficiency
A Pareto analysis requires that individuals list changes
that are needed or organisational problems. Once the
changes or problems are listed, they are ranked in
order from the biggest to the least severe. The
problems ranked highest in severity should become the
main focus for problem resolution or improvement.
Focusing on problems, causes and problem resolution
contributes to organisational efficiency. Companies
operate efficiently when employees identify the root
causes of problems and spend time resolving the
biggest problems to yield the greatest organisational
benefit. email: deeneshgoundory@yahoo.com 54

Disadvantages of P A
1. Inaccurate Problem Scoring
A major step in a Pareto analysis starts with scoring the severity of the problems
facing the small businesses. For instance, if the small-business owner applies a
Pareto analysis to finding cost centers, he may choose to assign values to
problems based on how much they are costing the company. The cost centers
with the highest scores should receive the highest priority. However, if those
cost centers are vital to how the business operates, any attempts at cutting
costs could do more harm than good. Small-business owners should examine
the quality and relationships within each problem, rather than using a Pareto
analysis for a strictly quantitative conclusion.
2. Mistaken Applications
Although Pareto analysis can be useful in many situations, some small-business
owners may extend its usefulness beyond its intended applications. For
instance, a small-business owner may wish to apply Pareto analysis to his clients
to determine which ones bring in the most revenue. The results should show
that the clients who bring in the highest revenue deserve the most time, while
those lower on the revenue scale should receive less attention. However, the
owner should also evaluate clients on a qualitative basis, as well as evaluating
their quantitative returns. A business owner who disregards customers who
don't deliver massive revenue dollars stands to lose those clients.

Disadvantages of P A (contd.)
3. Cost implication
While this approach is great for identifying the most important
root cause to deal with, it doesn't take into account the cost of
doing so. Where costs are significant, you'll need to use techniques
such as Cost/Benefit Analysis to determine which changes you
should implement.
4. Focus On The Past
Although Pareto analysis provides a useful interpretation of how
some factors have contributed to past problems, the sole reliance
on past information can be deceptive. Small-businesses owners
may find that the past data used in a Pareto analysis does not
accurately represent the company's current situation. For instance,
the data may include past changes in the price of raw materials
but may not accurately reflect how frequently and in which
direction those changes are likely to occur in the future. The
Pareto analysis may also fail to take into account recent policy
changes, economic conditions or government regulations, which
can lead to faulty decisions and inefficient allocation of resources.

Disadvantages of P A (contd.)
5. Output Time Factors
Pareto analysis may show the fraction of revenues or costs the small business
incurs from various factors, but it disregards the time that goes into producing
each of those factors. These factors can include the time taken to recruit a
client, the time needed to gather raw materials or the hours used in producing
software programs. Pareto analysis also does not account for factors outside the
scope of production, such as customer service, advertising efforts and market
considerations. Small businesses must also consider these factors when
examining where their resources should be allocated, rather than relying strictly
on a Pareto chart.
6. Inaccurate Scoring
The core facet of a successful Pareto analysis lies in the accuracy of the scoring
of each issue. Small-business owners who fail to assign the proper scoring to
each factor on the Pareto chart will receive inaccurate results. For example, say
the company's shipping manager conducts a Pareto analysis on problems within
his department. He wants to see where the most problems occur within the
shipping process. If the scores reflect that the problem lies in the transportation
section, when the real problems stem from packaging and preparing items for
shipping, the manager will focus on the wrong problem while the real issue
persists.

8. Statistical Process Control
Statistical Process Control (SPC) is a scientific, data-driven
methodology for quality analysis and improvement. SPC is
defined as "the application of statistical techniques to
control a process. SPC is a method for monitoring,
controlling and ideally improving a process through
statistical analysis. The philosophy states that all processes
exhibit intrinsic variation. However, sometimes processes
exhibit excessive variation that produces undesirable or
unpredictable results. SPC, in a manufacturing process
optimisation context, is used to reduce variation to achieve
the best target value. SPC is used in monitoring production
process to detect and prevent poor quality. It is a tool for
identifying problems and make improvements. It
contributes to the TQM goal of continuous improvements.
SPC is concerned with quality of conformance.

Nature of SPC
SPC is applied in order to monitor and control a
process or the behaviour of the 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.

SPC and Control Chart
In the early 1920s, Dr. Walter A. Shewhart
developed the fundamentals of SPC and the
associated tool of the Control Chart. Arguably the
most successful SPC tool is the control chart. A
control chart helps in recording data and highlights
unusual event, e.g., a very high or low observation
compared with “typical” process performance.
Control charts attempt to distinguish between two
types of process variation:
Common cause variation, which is intrinsic to the
process and will always be present.
Special cause variation, which stems from external
sources and indicates that the process is out of
statistical control.

Common and Special Causes
During his statistical research/ observation, Shewart
discovered that data from measurements of
variation in manufacturing did not always behave
the way as data from measurements of natural
phenomena.
He concluded that while every process displays
variation, some processes display variation that is
natural to the process ("common" sources of
variation)- these processes were described as in
(statistical) control.
Other processes additionally display variation that is
not present in the causal system of the process at all
times ("special" sources of variation), and these
were described as 'not in control'.

Control Chart
A control chart is one of many process improvement
techniques. It is not the answer to all your problems
nor should a control chart be used alone. There are
always other process improvement tools that should
be used along with control charts.
A control chart is used to monitor a process variable
over time. That variable can be in any type of company
or organisation - service, manufacturing, non-profit
etc. It provides a picture of the process variable over
time and tells you the type of variation you are dealing
with as you move forward with continuous
improvement.
This understanding of variation is the key to using
control charts effectively.

Understanding Control Chart
The control chart is a graph used to study how a
process changes over time. Data are plotted in
time order. A control chart always has a central
line for the average, an upper line for the upper
control limit and a lower line for the lower
control limit. These lines are determined from
historical data. By comparing current data to
these lines, you can draw conclusions about
whether the process variation is consistent (in
control) or is unpredictable (out of control,
affected by special causes of variation)

Special
Cause
Common
Causes

Specifications of the Control Chart
The general approach to on-line quality control is
straightforward: We simply extract samples of a
certain size from the ongoing production process.
We then produce line charts of the variability in
those samples and consider their closeness to target
specifications. If a trend emerges in those lines, or if
samples fall outside pre-specified limits, we declare
the process to be out of control and take action to
find the cause of the problem.

Purpose of a Control Chart
When controlling ongoing processes by finding and
correcting problems as they occur.
When predicting the expected range of outcomes from a
process.
When determining whether a process is stable (in
statistical control).
When analysing patterns of process variation from special
causes (non-routine events) or common causes (built into
the process).
When determining whether your quality improvement
project should aim to prevent specific problems or to
make fundamental changes to the process.

Mean (X-bar) Chart and Range (R) Chart
The following collection of data represents
samples of the amount of force applied in a
gluing process:
Determine if the process is IN CONTROL by
calculating the appropriate upper and lower
control limits of the X-bar and R charts.

Example
Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 5
1 10.68 10.689 10.776 10.798 10.714
2 10.79 10.86 10.601 10.746 10.779
3 10.78 10.667 10.838 10.785 10.723
4 10.59 10.727 10.812 10.775 10.73
5 10.69 10.708 10.79 10.758 10.671
6 10.75 10.714 10.738 10.719 10.606
7 10.79 10.713 10.689 10.877 10.603
8 10.74 10.779 10.11 10.737 10.75
9 10.77 10.773 10.641 10.644 10.725
10 10.72 10.671 10.708 10.85 10.712
11 10.79 10.821 10.764 10.658 10.708
12 10.62 10.802 10.818 10.872 10.727
13 10.66 10.822 10.893 10.544 10.75
14 10.81 10.749 10.859 10.801 10.701
15 10.66 10.681 10.644 10.747 10.728

Calculate sample means, sample ranges,
mean of means, and mean of ranges.
Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Avg Range
1 10.68 10.689 10.776 10.798 10.714 10.732 0.116
2 10.79 10.86 10.601 10.746 10.779 10.755 0.259
3 10.78 10.667 10.838 10.785 10.723 10.759 0.171
4 10.59 10.727 10.812 10.775 10.73 10.727 0.221
5 10.69 10.708 10.79 10.758 10.671 10.724 0.119
6 10.75 10.714 10.738 10.719 10.606 10.705 0.143
7 10.79 10.713 10.689 10.877 10.603 10.735 0.274
8 10.74 10.779 10.11 10.737 10.75 10.624 0.669
9 10.77 10.773 10.641 10.644 10.725 10.710 0.132
10 10.72 10.671 10.708 10.85 10.712 10.732 0.179
11 10.79 10.821 10.764 10.658 10.708 10.748 0.163
12 10.62 10.802 10.818 10.872 10.727 10.768 0.250
13 10.66 10.822 10.893 10.544 10.75 10.733 0.349
14 10.81 10.749 10.859 10.801 10.701 10.783 0.158
15 10.66 10.681 10.644 10.747 10.728 10.692 0.103
Averages 10.728 0.220400

Steps
MEAN (x-bar) CHART
1. Calculate x-bar (average)
2. Calculate and draw the x-bar bar (average of all means)
3. Calculate R-bar
4. Check sample size (n) and its value in chart (see below)
5.
6.
x Chart Control Limits
UCL = x + A R
LCL = x - A R
2
2
R Chart Control Limits
UCL = D R
LCL = D R
4
3
n A2 D3 D4
2 1.88 0 3.27
3 1.02 0 2.57
4 0.73 0 2.28
5 0.58 0 2.11
6 0.48 0 2.00
7 0.42 0.08 1.92
8 0.37 0.14 1.86
9 0.34 0.18 1.82
10 0.31 0.22 1.78
11 0.29 0.26 1.74
Formulae Sheet

Calculate x-bar Chart and Plot Values
60110220405872810
85610220405872810
2
2
.)=.(-..R- AxLCL =
.)=.(..R+ AxUCL =


10.550
10.600
10.650
10.700
10.750
10.800
10.850
10.900
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Means
Sample
Sample
mean
UCL
LCL
grand mean
of x

Calculate R-chart and Plot Values
0
0.46504


)2204.0)(0(RD=LCL
)2204.0)(11.2(RD=UCL
3
4
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample
R
Range
UCL
LCL
R-bar

Thank You
Any Question?

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