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Prepared by
M.Ganesh Murugan 9715447621

The QC circle was formally organized in Japan in 1962 by Japanese Union of Scientists and Engineers (JUSE) and the man who initiated the idea is Dr.Kaoru Ishikawa

The organization gets the total man Humanize the work i.e. Quality of work life is stressed and improved Brings out extra-ordinary qualities from ordinary people To display the human capabilities fully and eventually draw out infinite possibilities Prepares the employer and employees to meet the challenges of the changing time and conditions

         

Ensure harmony Effective team work Job satisfaction Problem solving capacity Communication Self development Leadership development Safety awareness and housekeeping Productivity Team building Participation Self-discipline

    

 

Not just for only quality problems Not a forum for grievances Not a spring-board for demands Not a tool for management to unload problems Not problem-focussed, but performance-oriented Not for changing the existing organisational structure or chain of command Not a “cure all” or “sure cure” technique Not a panacea for all ills

One of the prime objectives of QC is to improve the quality of work life and environment The survival and prosperity of any enterprise depends on the bottom line of the balance sheet i.E.
Net profit/economic viability and stability. A higher level of quality will result in satisfied customer, repeat business, which in turn will improve the profitability, job security and overall harmony of enterprise.  Hence, the emphasis on “quality”

 

  

 

Everybody participates and contributes in the process of decision-making Problems are chosen, not given Decision by consensus, not by majority Performance-oriented, not problem-oriented Bottom-up approach Management-blessed, not management-directed Members are responsible from the identification of a problem to implementation of the solution i.E. For total performance Aims at the quality of work life Does not replace or substitute any of the systems or structure

Problem identification emanates from
The members of the circle  Management  Staff or technical experts

Several problems are identified and the selection of the problem is the prerogative of the circle Problem analysis and discuss alternatives

Data from specialist, if necessary Circle members discuss various alternatives also before reaching the best solution

Arrive at best solution

Management presentation

The circle makes its recommendations directly to its incharge using a powerful communication

Review of recommendations and approval by management

Thoroughly in consultation and coordination with peripheral departments and approves or disapproves

Approved recommendations are implemented. Recommendations that are not approved are  Communicated to the circle members. It is imperative to explain the reasons to the members of the circle for not approving their recommendations. Communication should be effective in either case

 

From the familiarity of the members as well as leaders with the operation in which they are involved In day-to-day work From the proposals or suggestions by clients From the suggestions by the HOD‟s From the suggestions or proposals by any employee in the organisation From the objectives set out in the company‟s annual plan/target
However, it is the prerogative of the circle to select the problem although the suggestions can emanate from various sources

Positive attitude Frank discussions and brainstorming with everyone participating in a cooperative manner

QC should exercise a systematic approach
  

   

Confirms the existence of the problem Understands the nature of the problem Identifies the symptoms Finds out the causes Prepares a systematic programs for study Checks those programs with the other members Delegates assignment to members Seeks advice and assistance if required from outside agencies

    

Finds out the various possibilities Uses the relevant techniques that are learnt for problemsolving Prepares a report of its proposal once it arrives at a solution Evaluates the relevance and practicability of the solution Recommends the solution Implements the solution

A QC meeting must be the focal point of all activities  The meeting time should be such that it is convenient and acceptable for all members

2.Subject (themes)
     

The subject chosen should be in consonance with the policies of management A subject which is familiar and of common concern to all the members of the circle should be handled first Only work related problem should be chosen A problem whose solution is within the capability of the members of QC should be selected The subject should be so chosen for the impact of its solution As a rule, a problem should be selected which can be solved within reasonable period of time

3.Managing the activities
     

 

Give opportunities for simple and brief presentation for those members who are not used to speaking Before others Familiarize all the members with the environment gradually Utilize every opportunity of praise Suggest better ways of doing things after appreciating their efforts What is salt to food is humor to effective discussion without tension. A sense of humor is a necessary ingredient but strict discipline should prevail Circle members should display their respective role by earmarking their responsibility Use simple techniques effectively and thoroughly

A problem must be selected and solved only if the members can assure themselves that it will not reoccur  People must be sufficiently motivated even to the point of becoming greedy in getting the most out of activities

4.Education of QC members
  

QC members must make it a habit to study Read text books as many times as possible and make the best use of them Develop the habit of getting as much data as possible from as many sources as possible and utilize them to the maximum extent Knowledge is not sufficient, but the application of knowledge is more important What is digestion to food is contemplation to knowledge. Hence applying the knowledge that is acquired in solving the problem is key to the success of circle Apply the techniques in such a simple manner that everyone can understand

5.Key factors for the success of QC activities
Make a master plan and divide into elements  Study, discuss and solve the problem with the co-operation of all the members so that their commitment is assured for the implementation  Constantly review the progress and the status of the solution

6.How is a QC program organized?
    

A qc program is an integrated system made up of several components – The members The leader The facilitator The executive committee

The facilitator takes direction from the executive committee and co-ordinates the activities of the circle meeting and the leader conducts the meeting in such a way that the members of the circle participate

7.How to ensure longevity of QC activities? The following essential ingredients are imperative  7.1.To be problem conscious

The leader, who is normally the group head/shift head should understand the role and function of  Leading the sub-ordinates. They should continuously and constantly learn about the technique.  Support from top and middle management is essential to make qc self-motivating  Peripheral departments also must give their blessings for the continued effort of QC activities. Participation by everyone should not only be encouraged but ensured

7.2.To enhance people‟s awareness in 3 areas
Quality (quality of entire working life)  Problem  Improvement

People must be quality conscious in order to promote QC activities. Once people become problem conscious, improvement is bound to follow

7.3.Ensuring voluntary participation
People get real satisfaction when they are totally committed to think and act on their own  For the overall prosperity. If one understands why the activities should be carried out voluntarily, the commitment is bound to follow

7.4.To find pleasure and sense of satisfaction in the QC activities There are ten kinds of happiness in QC activities

     

Happiness of developing self-confidence Happiness of being recognized for one‟s activities Happiness of displaying one‟s ability and capability Happiness of acquiring the ability to identify one‟s capability Happiness to develop and enrich one‟s potential ability Happiness to be able to recognize one‟s potential ability Happiness to understand and co-operate with the members of the circle Happiness to have friends and affectionate sub-ordinates

Happiness to belong to a company where the QC activities are encouraged and promoted  Happiness of gaining indirect material reward through the prosperity and growth of the company


Training and re-training from the top management to the circle member is an indispensable and inevitable part of ensuring longevity of circles

The members must also be taught value engineering, job
instruction, job method, job relations, creativity development and leadership qualities

7.6.How often the circle meetings are held?

As a rule of the thumb, circle meetings are held once in a week However, some companies have introduced variations

It is desirable to reduce the duration and increase the frequency of the meeting.

Format enclosed

Format enclosed

The QC circle is program is an integrated system consisting of the following
 

Steering committee Divisional review committee

 

Coordinators and facilitators
Circle leader Circle members

Steering committee

This committee comprises of the executive director, general managers and a member secretary (nominated by management). This committee sets goals and objectives for the QCC activities and establishes operational guidelines It meets as often as necessary but at least once a quarter to review the progress. The secretary is responsible for the overall coordination of QC circle activity in the company

Divisional review committee

This committee comprises of the divisional head, departmental heads, coordinators and facilitators(member secretary). It provides active support to the circles The committee meets as often as necessary but at least once a month to review the progress


Organizes training programs for members as and when new circles are formed Convenes the steering committee meeting regularly once in two to three months and maintains the minutes thereof. Organizes top management presentations regularly once in two to three months

Centrally registers circles as and when formed and also
maintains records of number of members, frequency of management representations, etc.

Co-ordinates and evolves a consensus for norms to asses the
performance of different quality circles and of different divisions Co-ordinates and ensures availability of common facilities to all quality circles Prepares a budget for the functioning of quality circles and submits the same to the steering committee for adoption


Is responsible for the successful operation of the quality circles in his area. He has to be a guide, counselor, teacher and a catalyst Ensures necessary facilities for quality circles to operate effectively lends assistance and support to the leader whenever required and also helps in the training of members Is invited to the meetings of the departmental or steering committees wherein he gives a resume of the activities of quality circles in his jurisdiction

Circle leader/deputy leader

Makes the necessary facilities available, with the help of facilitators and others, for enabling quality circles to perform without constraints Assigns tasks to different member from time to time to maintain a high degree of individual involvement and participation Trains the members in various problem-solving techniques and other facets of quality circle operations, and gives them necessary guidance whenever required, with the help of the facilitator and others, if necessary

Maintains a high degree of cohesiveness of his team. He
does not act as a boss in quality circle activities but as a friend and partner so that conflicts are avoided and group cohesiveness is maintained all the time

Ensures that every circle member is involved in circle
activity and a high level of enthusiasm and involvement is maintained Plans the agenda of meetings carefully and conduct meetings regularly and effectively Ensures discipline and decorum during the meetings

Chalks out action plans for a progressive solution of
problems through data collection, interaction and sets time bound programs for implementation of the circle‟s recommendations

Encourages and evolves consensus decision-making
processes so that win-lose situations are obviated Ensures that record-notes of meetings and progress of problems are maintained in two separate registers regularly and effectively Interfaces with other levels of management, the facilitator and different functional agencies to ensure the effective

working of his quality circle

Takes necessary steps continuously in conjunction with
other members, facilitators, executives and the department head to ensure that his quality circle maintains a high degree of morale and enthusiasm continuously and

thereby catalyses the quality circle movement in the
organization to grow steadily and healthily

Organizes presentations to departmental head and top management at least once in two to three months Feeds the information relating to the highlights of his circle activities to the agency concerned for publication in appropriate newsletters and journals

Circle members

Participate actively in the discussions during the meeting and all other activities of the circle. They willingly execute specific assignments that may be given to them as decided in the circle meetings. Thus they actively assist leader/deputy leader in effectively and efficiently conducting the circle activities Contribute towards building of a cohesive group through which they try to achieve the highest standards of performance

Take part in management presentation
Through their personal conduct and enthusiasm, help in propagating the quality circles concept in other areas where circles are yet to be launched Assimilate the inputs given to them during training and develop in themselves the capability for systematically identifying analyzing and resolving problems and also attain leadership qualities

 

Check sheet
Stratification Pareto chart

 

Cause and effect diagram
Histogram Scatter diagram

Graph and control chart

A scientific approach of solving problems and making
workplace improvements Helps individuals/teams of diagnose, solve and

prevent problems
 

Can be used to solve 90% of workplace problems Simple yet powerful histogram

Check sheet is a systematic method of collecting,
recording and presenting the relevant data in a simple manner Helps individuals/teams of diagnose,

solve and prevent problems

Rationale and Benefits

To make data gathering simple, systematic, easy and effective To arrange and present data in such a way that it can be understood and used easily Enables “management by facts” as opposed to

“management by opinion”

 

Process performance check sheet
Defect item check sheet Defect location check sheet

Defect cause check sheet
Task conformation check sheet

Establish what information is needed
Establish “operational definition” for the data to be collected

  

Determine 5W and 2H of check sheet
Construct the check sheet Test the check sheet

Use the check sheet
Use the information (remember three rules of QC)

  

Why is the data needed?

What type of check sheet should be used?
Where should the data should be collected from? (Plant/machine/place)

Who has to collect the data?
(Operator/ supervisor/manager) When will the data be collected?

(Every hour/ at the time of receipt)

How should the data should be measured? (Instrument/clock)

How much data is essential?

Check sheet should broadly have three types of information

Title of the check sheet
Source information

Name of the project/ problem theme

 

Location of data collection
Date and/or time Name of the person recording data

Content information
  

Column with defect/event name Column to record frequency Column to record total

Test the check sheet with at least three different


Check if the operational definition is really “operational” Reconfirm that the columns are relevant and required Check if the check sheet is easy to record and use Make changes based on the feedback

  

 

Explain the check sheet to the data collector

Ensure that the data collector understands the reason
for which the data is being collected Collect data

  

Standardize its use to assure consistency
Tally mark =5

Pay particular attention to irregular data and

irregular conditions

Use data from the check sheet for further analysis - Pareto chart, histogram, scatter diagram

Ensure that all the data that is recorded is put to use
OR is likely to be put in future Regularly audit the use and the usefulness of check


 

Goals are too vague
No agreed operational definition Data is not collected on time

Too much time and effort being spent on recording in
the check sheet Check sheet is too complex

Different people are using different check sheet for
the same issue

Project Name: Name of Data Recorder: Location:

Data Collection Dates:

Dates Defect Types/ Event Occurrence Defect 1 Defect 2 Defect 3 Defect 4 Defect 5 Defect 6 Defect 7 Defect 8 Defect 9 Defect 10 TOTAL Sunday Monday Tuesday Wednesday Thursday Friday Saturday TOTAL

 check-sheet-histogram.xls

A technique used to divide the data into subcategories or classification to provide useful insight into the problem
Root word is “strata” which means
  

Group Division Sub-class


Stratification is an act of dividing the data based on groups, division, sub-class, causes etc.

Data comes from different sources. e.g: different
machines, instruments, cities, operators etc. Data sometimes masks real information.

 

Stratification helps in getting meaningful information
from data. Divide the data and conquer the information

 

List all conditions
Collect and stratify data Interpret the data

List all conditions that may seem to be cause of the problem

     

Shift Location Operator Product Machine Inspection equipment

Raw material source

   

Day of week
Time of the day Material batch Inspector Production batch

Collect additional data based on classification, if

Stratify data based on the classification

Calculate average of each classification or plot
appropriate graph

Look for significant differences or abnormalities in data

Generate a list of possible causes

Un – stratified data

Date Rejection

23/2 24/2 25/2 33 30 32

Stratified data
Time 9:00-10:00 10:00-11:00 11:00-12:00 12:00-1:00 1:00-1:30 1:30-2:30 2:30-3:30 3:30-4:30 10 3 0 23/2 15 1 2 1 24/2 14 2 0 0 lunch 11 1 2 12 0 1 25/2 16 0 1 1





Pareto chart is a diagram that shows the order of the
largest number of occurrences by item or by classes, and the cumulative sum total

Vilfredo Pareto (1848-1923), an
Italian economist discovered in 1897 that 80% of a nation‟s wealth was owned by 20% of the population

Dr. Joseph.M.Juran applied this
principle to quality management and called it the pareto principle

Pareto principle: 80% of the problems come from 20%
of the causes

  

Distinguishes between vital few and trivial many Displays relative importance of causes of problem Helps the team to focus on those causes that will have the greatest impact when solved

Inputs Causes Effort

20% 80%
Outputs Effects Results

      

Select the problem Collect data Sort data & calculate cumulative frequency Draw the axes Construct the bars Draw the cumulative percentage line Title and label the chart Identify vital few from the trivial many and plan further action

Select the problem for investigation
Decide what data will be necessary and how to classify them

Determine the method of collecting data and period of
data collection Design a separate check sheet if necessary

E.g: causes for service complaints of computer system

Causes Print problems Rodent problems Server crash Boot problems

Frequency 11 3 23 8

Bad configuration Virus attack
System re-configuration Operating system corrupted Email not functioning properly Loose connection Others

6 52
3 9 4 5 12

Code A B C D E F G H I J K

Causes Virus attack Server crash Print problems Operating system corrupted Boot problems Bad configuration Loose connection Email not functioning properly System re-configuration Rodent problems Others

Frequency 52 23 11 9 8 6 5 4 3 3 12

Cumulative frequency 52 75 86 95 103 109 114 118 121 124 136

Cumulative percentage 38.24 55.15 63.24 69.85 75.74 80.15 83.82 86.76 88.97 91.18 100.00


It is undesirable that “others” represent high
percentage (should be < 10%) If the cause of a problem can be solved easily,

implement it even if it belongs to trivial many

Wherever possible, compare monetary data with frequency data

Draw the Pareto chart before and after improvement

A diagram which represents meaningful relationship
between an effect and its causes

A diagram which shows the relation between a quality characteristic and the cause factor

Enables a team to identify, explore and graphically
display all the possible causes related to a problem

A cause and effect diagram is good for seeing the whole “causal” relationship

Enables identification of root causes and not


Dr. Kaoru Ishikawa developed the
first cause and effect diagram in 1943 while consulting for Kawasaki steel works

Dr.Joseph.M.Juran named it as Ishikawa diagram

Big Bone
Medium Sized Bone

Effect (characteristic)

Small Bone

 

Dispersion Analysis Type.
Process Flow Classification Type. Cause – Enumeration Type.

Note Dispersion analysis type and Cause – Enumeration type

differ only in the method of construction

  

State the undesirable effect
Identify the main cause groups Identify causes and sub-causes Identify potential root causes

Draw the back Bone and draw a line

Such as man, machine, method, material, measurement, tool Measurement Machine Man




Brainstorm: Ask “why” questions
Measurement Machine Man

Poor handling Rod bent



No Inspection

High Hardness

Runs out of ideas, focus attention to place
Measurement Machine Man

Poor handling Rod bent



No Inspection

High Hardness

that some ideas appear in two different places. “Calibration” shows up under “methods” as a factor in the analytical procedure, and also under “measurement” as a cause of lab error. “Iron tools” can be considered a “methods” problem when taking samples or a “manpower” problem with maintenance personnel.

 

State the undesirable effect
Identify the main process flow diagram Identify the causes and sub – causes at each stage of the process

Identify the potential root cause(s)

Draw a vertical line state the undesirable effect

Draw a vertical line state the undesirable effect

 

State the undesirable effect
List all possible causes using brainstorming Arrange causes and sub – causes showing the relationship between cause and effect

Identify potential root cause(s)

Identify all the relevant causes (factors) & the causes most strongly influencing the effect (characteristic)

Express the effect (characteristic) “negatively”
The linking question between effect and its cause is “why?”

Make the same number of causes and effect diagrams as that of effects

It is a type of run chart used for studying the process
performance over time in order to understand and reduce variation

Dr.Walter.A.Shewart invented the
control chart

He was working in bell labs on a project to make all telephones alike

Published the book called “Economic control of quality of manufactured product” in 1931

Every process is subject to variation

More the variation in the process, more the loss to the

Two types of causes affect variation

Common cause (also known as chronic cause, chance cause)

The cumulative effect of many small and “individually uncontrollable” causes of variation in a process. Express the effect (characteristic) “negatively”

Special cause (also known as sporadic or assignable cause)

One of a few causes of variation that result in a large variation in

the process

Action on variation entirely depends on type of cause identified
Common cause Consists of many individual causes Results in relatively smaller variation Process need not be tampered with Process is considered stable Special cause Consists of one or few causes

Results in large variation
Process need to be investigated and corrected Process is unstable

Control chart is used for differentiating between

common causes and special causes of variation

Control charts also helps in determining whether the
 

Process is stable Process is capable

It helps in predicting process performance

Variable data

Data that can be measured
E.g. Weight, height, length, hardness, diameter, angle

Attribute data
 

Data that can be counted E.g. Defects, scratches, dent, spatters, blow, holes, cracks

Control chart Variable data -R chart Attribute data p chart c chart np chart u chart

X – mR chart
mX – mR chart

40 30 20 10 0 -10 -20 -30 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121

40 35

25 20 15 10 5 0 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121

Y - Axes Variable Data

Central line

Control limits

Data Points


Sub groups

Smaller groups of sample data collected over time

Central line

The average of all the sub group averages

Control limits

The outer limits of “Process Variation”

Control limit
 

Specification limit

Variation in the process “Noise of the process”

Requirement of the customer

Limits changes with
setting, correction, process

“voice of the customer”
Limits changes only

change, etc.

when customer wishes to

Indicates capability

Indicates requirement

       

Collect the data Calculate sub – group average Calculate overall average Calculate the range Compute average of range Calculate control limit for X and R Plot the chart Interpret the chart

Collect and stratify data into sub groups







1 2
3 4

47 19
29 28

32 37
11 29

44 31
16 42

35 25
11 59

20 34
44 38


= X1+X2+X3+X4+X5 n = 47+32+44+35+20 5 = 35.6


Where n is the size of the groups



2+ 3+


= 35.6+29.2+22.2+39.2
4 = 35.6 Where K is the size of the sub group

= Maximum value – Minimum value
= 47 – 20 = 27






= 27 + 18 + 33 + 31 4

Where K is the size of the sub group

Central line =
Upper control limit : UCL = + A2

Lower control limit : LCL


- A2

A2 is the coefficient whose value depends on the

subgroup size

Central line =
Upper control limit : UCL = D4

Lower control limit : LCL

= D3

D3 and D4 are the coefficient whose value depends on

the subgroup size

Subgroup size

Chart A2 D3

R chart D4 d2

3 4 5

1.023 0.729 0.577

0 0 0

2.574 2.282 2.114

1.693 2.059 2.326






     

Vertical axis :

and R values

Horizontal axis : sub – group number Draw the central line : Draw the control limits Plot the and R values and join the points and R

Write necessary items like name of the process, product, size of the subgroup, work conditions, shift, etc.

Process stability

Process capability
 

Look at the pattern of variation

Establish process variation Compare with specification and establish process

Should be random and not

a systematic pattern


Look for presence of special causes

5 rules of special cause identification

 

Random variation and no systematic pattern No action required (if Cpk > 1.67)

 

Presence of special cause Identify root cause and take action

 

Presence of special cause Process has shifted

 

Presence of special cause Process is deteriorating

 

Presence of special cause Periodic Interference in the process

 

Presence of special cause Identify root cause and take action

Process capability is a measure of inherent variability of the process when compared with the customer requirements

Assess capability of a process to meet customer‟s requirement

  

Assist in selecting or modifying a process Assist in selection of machine To build quality into the product and process rather than achieving quality by inspection

Establish process variation = = d2 6σ .

process variation σ

d2 is a constant based on sub – group size

Refer slide number 124


= Customer Requirement Process variation = USL –LSL 6σ


Cp > 1.33; Process is more capable than customer requirement Cp = 1.0; Process is just capable of meeting customer‟s requirement Cp < 1.0; Process is not capable of meeting customer‟s requirement

Cpk = Minimum (USL 3σ


- LSL) 3σ

Cpk = Cp; process is centered with respect to customer‟s requirement

Cpk љ Cp; Process is not centered with respect to customer‟s requirement

Histogram is a type of bar chart representing the
frequency distribution of the data from a process

Displays large amount of data, that are difficult to
interpret in tabular & graphical form

Shows the relative frequency of occurrence of the various data values

Provides useful information for understanding the present performance and predict future performance of the process

Reveals the centering, variation & shape of the data
Helps evaluate process capability & the question “is the process capable of meeting customers requirements?”

Enables corrective action to keep the process within specification limits

Excellent planning and forecasting tool

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 analyzing whether a process can meet the customer‟s requirements

When analyzing 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

 

Decide on the process measure
Gather data Prepare of frequency table

Calculate range, class intervals, class width and boundaries

  

Draw the axes Draw the bars Interpret the histogram

Only one parameter can be used for constructing the

The data should be variable data, i.e., Measured on a continuous scale (weight, time, temperature, dimensions, speed, etc.)

Example : weight of a rice bag

For accurate analysis of mean, dispersion and
patterns, collect at least 50 to 100 data points
98.7 100.0 100.4 99.6 101.5 100.5 99.2 100.6 100.3 99.7 100.3 99.3 101.1 100.0 100.2 99.9 100.2 99.4 101.3 100.0 99.6 100.6 99.9 99.8 100.4 99.2 101.2 100.0 100.3 99.9 100.1 99.0 100.9 100.1 100.2 100.3 100.8 99.7 99.9 100.1 99.4 101.4 98.6 100.5 100.4 99.5 101.6 99.1 101.0 99.6 99.5 99.8 99.2 100.2 100.1 100.2









     

Calculate the number of data points, n
Determine the range, R Determine the number of class intervals, k Determine the class width, H Establish the class boundaries

Establish class intervals
Construct the frequency table

Calculate the number of data points, n

Count the number of data points “n” in the sample

n = 64 data points

Calculate the number of data points, n
Determine the range, R

Determine the range “R” in the sample. Range is the smallest value in the set of data subtracted from the largest value

R = Xmax – Xmin R = 101.6 – 98.6 = 3.0

 

Calculate the number of data points, n
Determine the range, R Determine the number of class intervals, k

Determine the number of class intervals, “k” needed. The following table can be used as a thumb rule

No. of data points No. of classes “k”

< 50
50 – 100 100 – 250

6 – 10 7 – 12

> 250

10 - 20

  

Calculate the number of data points, n
Determine the range, R Determine the number of class intervals, k Determine the class width, H

Determine the class width “H”. The formula for this is

H = R/k

This should be rounded off to a suitable value depending upon the data collected

H = 3.0 / 7 H = 0.428 ~ 0.5

    

Calculate the number of data points, n Determine the range, R Determine the number of class intervals, k Determine the class width, H Establish the class boundaries

Use the smallest individual measurement in the sample or round off to the next appropriate lowest round number.

This will be the lower end point for the first class interval

Do the same for the highest number. This will be the higher end point for the last class interval

Class Boundaries – 98.5 & 102.0

Establish class intervals

Add the class width “H” to the lower end point. This will be the lower end point for the next class interval

 

Each class interval must be mutually exclusive Add the class width to the lower class boundary until the “K” class intervals and/or the range of all the numbers are obtained

98.50 – 98.99 99.00 – 99.49 99.50 – 99.99

100.00 – 100.49 100.50 – 100.99 101.00 – 101.49

101.50 – 101.99

Construct the frequency table
Class # 1 2 Class Boundaries 98.50 – 98.99 99.00 – 99.49 Frequency Total 3 8

4 5 6

99.50 – 99.99
100.00 – 100.49 100.50 – 100.99 101.00 – 101.49

23 9 6


101.50 – 101.99


  

Process Centering
Process Variation (Dispersion) Histogram Shape

Process Comparison with specification(Process

Process Centering

Process Centering

Process Centering

Process Variation (Dispersion)

What is the


variation or
spread of the data? Is


it too



Histogram Shape

Normal distribution

Bi-modal distribution

Skewed distribution

Distribution with isolated island

Process Comparison with specification(Process Capability)

Process capable and centered

Process capable but not centered Re-set to centre the Process

Maintain Process

Process Comparison with specification(Process Capability)

Process just capable and centered Reduce variation to avoid defects

Process just capable but not centered Centre process and reduce variations

Process Comparison with specification(Process Capability)

Process not capable but centered Reduce process variation to avoid defects

  

Choose critical process parameters
Gather as much as data as possible Choose appropriate class intervals, width, boundaries

and scale
 

Specify targets and specification limits Take corrective action and verify

Before drawing any conclusions from your histogram,

satisfy yourself that the process was operating
normally during the time period being studied. If any unusual events affected the process during the time

period of the histogram, your analysis of the
histogram shape probably cannot be generalized to all time periods

Analyze the meaning of your histogram‟s shape

A chart used to study and identify the possible

relationship between two variables

To identify the possible relationship between the changes observed in two variables

To establish the
  

Existence of correlation Type of correlation Strength of the relation

To confirm a hypothesis (assumption) that two

variables are related

Provide both visual and statistical means to test the strength of a potential relationship

Provide a good follow up to a cause and effect
diagram to find out if there is more than just a consensus connection between causes and effects

    

Cake height and Oven temperature Weight and Height of a man Population & Literacy levels in a state Weight error and Earthing voltage Nonconformance & Operator experience. Hardness and carbon content Inspection mistakes and Illumination levels

   

Elongation of threads and moisture content
Child‟s height and Father‟s height Quality characteristic and the factor affecting it

Weight and Height of a Person

 

Collect paired data
Choose independent and dependent variable Draw the axes

 

Plot the points
Label and title the charts Interpret the chart

Collect 50 – 100 paired data (X,Y) between which you
want to study the relation, and construct a data chart

1 2 3 . . 60

Oven temperature
60o 49o 57o . . 68o

Cake height
3.2cm 2.8cm 3.0cm . . 3.3cm

Always choose „X‟ axis for the cause and „Y‟ axis for
the effect, when the two variables consists of a factor and quality characteristics

Oven temperature = independent
Cake height = dependent

Find the respective maximum and minimum values of the variables

M.Ganesh Murugan 9715447621

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