7 quality tools

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7 QC TOOLS

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Quality

A subjective term for which each person has his or her own definition. In technical usage, quality can have two meanings:

1. The characteristics of a product or service that bear on its ability to satisfy stated or implied needs.

2. A product or service free from deficiencies.

Note: ISO 9000 : 2000 version defines Quality as “Degree to which a set of inherent characteristics fulfils

requirements.

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Can also be termed as ‘A measure of excellence’

Quality

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Quality - an essential and distinguishing attribute of something.

Attribute - an abstraction belonging to or characteristic of an entity

Appearance, visual aspect - outward or visible aspect of a thing

Attractiveness, attraction - the quality of arousing interest; being attractive or something that attracts;

Uncloudedness, clarity, clearness - the quality of clear water;

Ease, easiness, simplicity - freedom from difficulty or hardship or effort.

Suitability, suitableness - the quality of having the properties that are right for a specific purpose.

Excellence - the quality of excelling.

Characteristic - a distinguishing quality

Simpleness, simplicity - the quality of being simple or uncompounded

Meaning of “Quality”

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Meaning of “Quality”

Q = PE

P = Performance or resultE = Expectations

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Many people think that quality costs money and adversely effects profits. But these costs are the costs of doing it wrong first time .

Quality in the long run results in increased profitability.

Quality, Cost & Profit relationship

Cost

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Cost

Quality and Profit : Traditional thinking

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Quality and Profit : Paradigm shift

Cost

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1.Higher production due to improved cycle time and reduced errors and defects

2.Increased use of machine and resources.

3.Improved material use from reduced scrap and rejects

4.Increased use of personnel resources

5.Lower level of asset investments required to support operations.

6.Lower service and support costs for eliminated waste, rework and non value added activities.

QU

AL

ITY

Higher productivity Increased profitability

due to :

•Larger sales

•Lower production costs

•Faster turnover

Quality and Profit

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Quality and Profit

If the organization does not offer high quality product or service , it will soon go out of business . But just having high quality will not be enough , because your competitors will also have the high quality. To win , companies will need to offer high quality for a lower price than their competitors.This requires organizations to identify and reduce their quality costs

HighQuality

Lowerprice

C2A2C

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Offer high quality for a lower price than their competitors. Reduce quality costs Stop producing defective thru’

Process up-gradation Improving quality of analysis to identify and eliminate root causes Taking necessary countermeasure as when required Usage of right analytical tools Designing robust problem solving process

CHELLANGES

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PROBLEM SOLVING PROCESS

Evaluating solution(6)

Implementing solution

(5)

Selecting & planning solution

(4)

Generating potential solutions

(3)

Analysing problem causes

(2)

Identifying & selecting problem

(1)

PROBLEM SOLVING PROCESS

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IDENTIFYING AND SELCTING PROBLEM

Write Statement of the problem(s) Define Gap Between Actual & target Prioritize

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ANALYSIS PROBLEM AND CAUSES

Collect Data Sort symptoms & Causes (effects) Brain Storm Fishbone - cause & effect analysis Prioritize

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GENERATING POTENTIAL SOLUTIONS

Brainstorm Build on each other’s ideas Analysis potential helps & hinders

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SELECTING AND PLANNING SOLUTION

Prioritize solutions Clarify tasks / Action plan Resource / Costs Present proposals

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IMPLEMENTING SOLUTION

Establish controls Maintain Commitments Plan Contingencies

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EVALUATING SOLUTION

Monitor results Restart Process if necessary

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7 QC TOOLS

Used to identify,analyze and resolve problemsSimple but very powerful tools to solve day to

day work related problemsFind solutions in a systematic mannerWidely used by Quality Circle members world

over

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Check sheets

Histograms

Pareto charts

Cause & effect diagram (Ishikawa diagram)

Scatter plot

Defect concentration diagram

Control charts

7 QC TOOLS

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12

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43

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9

0

50

1160-170 170-180 180-190 190-200 200-210

Histogram for distribution of Center Distance (mm)

HISTOGRAM

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HISTOGRAM A HISTORY OF PROCESS OUT PUT

024

810121416

6Fre

qu

ency

47 48 49 50 51 52 53 54kg

Distribution

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Based on “80/20” rule (or ABC analysis)

Pareto(V.Pareto,an Italian economist) discovered this universal law-80% of anything is attributed to 20% of its causes 80% of the wealth is held by 20% of the population.

• 80% of our income goes into 20% of our needs.• 80% of road accidents occur on 20% of the road.• 80% of the absenteeism in a company is due to 20% of workmen

“Significant few & in-significant many”

PARETO CHART

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PARETO CHART

Pareto analysis begins by ranking problems from highest to lowest in order to fix priority

The cumulative number of problems is plotted on the vertical axis of the graph against the cause/phenomenon

Pareto by Causes e.g. Man,Machine,Method etc

Pareto by Phenomenon e.g.Quality,Cost,Delivery

Tells about the relative sizes of problems indicates an important message about biggest few problems, if corrected, a large % of total problems will be solved

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63.8

81.4

96.2 100.0

0

500

1000

1500

2000

2500

3000N

o o

f p

eic

es

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Cu

m.

Perc

en

tag

e

DEFECT QTY 2064.0 567.0 480.0 122.0

CUM % 63.8 81.4 96.2 100.0

SHORT SHOT SILVER SINK MARK FLASH

PARETO ANALYSIS

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CAUSE n EFFECT (FISH BONE) DIAGRAM

This diagram (resembles skeleton of a fish) helps to separate out causes from effects and to see problem in its totality

It’s a systematic arrangement of all possible causes,generated thru’ brain storming

This can be used to :

Assist individual / group to see full picture.

Serve as a recording device for ideas generated.

Reveal undetected relationships between causes.

Discover the origin/root cause of a problem

Create a document or a map of a problem which can be posted in the work area.

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The problem categories considered are :Man, Machine, Method, Materials, Equipments & Environmental.

EFFECT

MACHINE METHOD ENVIRONMENT

MAN MATERIAL EQUIPMENT

CAUSE n EFFECT (FISH BONE) DIAGRAM

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SCATTER DIAGRAM

The scatter diagram is used for identifying the relationships and performing preliminary analysis of relationship between any two quality characteristics. Clustering of points indicate that the two characteristics may be related e.g.

Increasing in component weight with increase in hold time during plastic injection molding ( + ve co-relation)Increase in toughness components with decreasing injection pressure (-ve co-relation) during molding

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SCATTER DIAGRAM (POSITIVE CORRELATION)

0102030405060708090

100

0 5 10

XY (Scatter) 1

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SCATTER DIAGRAM (NEGATIVE CORERLATION)

0

10

20

30

40

50

60

70

80

0 5 10

XY (Scatter) 1

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SCATTER DIAGRAM (NO CORERLATION)

0

10

20

30

40

50

60

70

80

0 5 10

XY (Scatter) 1

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DEFECT CONCENTRATION DIAGRAM

This is used to understand the potential defect prone area of the parts produced

The “Concentration Diagram” check sheet carries the diagram of the problematic part,defects whenever observed to be updated in the same using tally marks

Based on the distribution of defects countermeasures are taken at process/system level

This tool is very useful to solve problems like Scratch, Dent,Breakage thru’ handling improvement

For plastic molded parts this tool is used to identify stress points,weak joints,effect of gate shape/position on the quality of parts etc.

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DEFECT CONCENTRATION DIAGRAM

Component name : XYZConcentration diagram for Scratches produced ion 21-Aug-03Total no of defective produced is 11 Nos

Area of concern

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Control Chart

Quality control charts, are graphs on which the quality of the product is plotted as manufacturing or servicing is actually proceeding.

It graphically, represents the output of the process and uses statistical limits and patterns of plot, for decision making

Enables corrective actions to be taken at the earliest possible moment and avoiding unnecessary corrections.

The charts help to ensure the manufacture of uniform product or providing consistent services which complies with the specification.

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Elements of Typical Control Chart

1. Horizontal axis for sample number

2. Vertical axis for sample statistics e.g.

mean, range, standard deviation of sample.

3. Target Line

4. Upper control line

5. Upper warning line

6. Lower control line

7. Lower warning line

8. Plotting of sample statistics

9. Line connecting the plotted statistics

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Interpreting Control Chart

The control chart gets divided in three zones.

Zone - 1 If the plotted point falls in this zone, do not make any adjustment, continue with the process.

Zone - 2 If the plotted point falls in this zone then special cause may be present. Be careful watch for plotting of another sample(s).

Zone - 3 If the plotted point falls in this zone then special cause has crept into the system, and corrective action is required.

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Zones for Mean Control Chart

11 22 33 44 55 66 77Sample NumberSample Number

UCLUCL

TargetTarget

LCLLCL

UWLUWL

LWLLWL

Zone - 3Zone - 3

Sam

ple

Me a

nS

amp

le M

e an

Zone - 2Zone - 2

Zone - 3Zone - 3

Zone - 2Zone - 2

Zone - 1Zone - 1

ActionAction

ActionAction

WarningWarning

WarningWarning

ContinueContinue

ContinueContinueZone - 1Zone - 1

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UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tistic

s

UWL

LCL

Target

LWL


Point outside the Control limit

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Control Chart Views Process in Real Time

Time Intervals

Ran

geM

ean

LCLx

Output of the process in real time

Target

Target

UCLx

UCLr

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Change in Location of Process Mean

43 48 49 50 51 52 5344 45 46 47

Process with mean at Target

Process with mean at more

than target

Process with mean at less

than target

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Case When Process Mean is at Target

43 48 49 50 51 52 5344 45 46 47

Target ProcessMean

Chances of getting a reading beyond U & L is almost nil

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UL

- 3 s +3 sU - L = 6 s

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Case - Small Shift of the Process Mean

43 48 49 50 51 52 5344 45 46 47

Target

ProcessMean

Chances of getting a reading outside U is small

Small shift in process

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Shaded area shows the

probability of getting

a reading beyond U

UL

U-L = 6 s

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ProcessMean

Case - Large Shift of the Process Mean

43 48 49 50 51 52 5344 45 46 47

Target

Chances of getting a reading outside U is large

Large shift in process

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Shaded area shows the

probability of getting

a reading beyond U

UL

U-L = 6 s

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Change in Spread of Process

43 48 49 50 51 52 5344 45 46 47

Larger spread dueto special causes

Spread dueto common causes

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Special cause & Common cause

Special Special / / Assignable cause : Causes due to negligence in following work instructions, problem in machines etc.This types of causes are avoidable and cannot be neglected.

Common cause : Causes which are unavoidable and in-evitable in a process.It is not practical to eliminate the Chance cause technically and economically.

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Most Commonly Used Variable Control Charts

To track the accuracy of the process

- Mean control chart or x-bar chart

To track the precision of the process

- Range control chart

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Control ChartPART NAME :GLASS RUN PART NO : MODEL : Page

THICKNESS SPECS : MIN 1.10 TO 1.50 MAX REASON : PROCESS CAPABILITY STUDYAUDIT DATE 25/9/01

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 n d2 A2 D41 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.60 1.50 1.60 1.50 1.60 1.55 1.60 1.55 1.50 1.50 1 1.123 2.66 3.27

2 1.50 1.50 1.50 1.53 1.50 1.50 1.50 1.50 1.50 1.55 1.60 1.55 1.55 1.60 1.55 1.45 1.60 1.50 1.50 1.48 2 1.128 1.88 3.27

3 1.60 1.48 1.50 1.50 1.48 1.50 1.50 1.50 1.50 1.55 1.50 1.55 1.50 1.55 1.50 1.50 1.50 1.55 1.60 1.55 3 1.693 1.02 2.57

4 1.50 1.48 1.52 1.50 1.53 1.50 1.50 1.50 1.45 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.60 1.60 1.50 4 2.059 0.73 2.29

5 1.50 1.50 1.60 1.50 1.50 1.50 1.55 1.55 1.45 1.55 1.55 1.50 1.50 1.50 1.50 1.50 1.45 1.50 1.55 1.55 5 2.326 0.58 2.11SUM X SUM X1+..+Xn 30.37

X 1.52 1.49 1.52 1.51 1.50 1.50 1.51 1.51 1.48 1.53 1.55 1.52 1.53 1.53 1.53 1.50 1.53 1.54 1.55 1.52 X SUM X1+..+Xn/n1.519R 0.10 0.02 0.10 0.03 0.05 0.00 0.05 0.05 0.05 0.05 0.10 0.05 0.10 0.10 0.10 0.10 0.15 0.10 0.10 0.07 R SUM R1+..+Rn/n0.074

SIGMA R/d2 0.0323 SIGMA 3 * R/d2 0.0956 SIGMA 6 * R/d2 0.190

Cp = 2.11 Cpk=

MIN OF -0.20Cpu OR Cpl 4.41

Cpk =USL 1.500LSL 1.100

FOR XUCL = X + A2.R 1.561LCL = X - A2.R 1.476

FOR R (D3 = 0)UCL = D4.R 0.155LCL = D3.R 0.000

PROCESS STATAUSCONTROLLEDNOT CONTROLLED

XYZ Ltd

O

-0.050.000.050.100.150.200.25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

R -

CH

AR

T

R UCL LCL CL

1.4001.4201.4401.4601.4801.5001.5201.5401.5601.5801.600

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

X -

CH

AR

T

X UCL LCL CL

How to draw?

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Establishing Control Chart

Step No.1

Select quality characteristics which needs to be controlled

- Weight- Length- Viscosity- Tensile Strength- Capacitance

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Step No.2

Decide the number of units, n to be taken in a sample.

The minimum sample size should be 2. As the sample size increases then the sensitivity i.e. the quickness with which the chart gives an indication of shift of the process increases. However, with the increase of the sample size cost of inspection also increases.

Generally, n can be 4 or 5.

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Step No. 3

Decide the frequency of picking up of sample

If the shift in the process average causes more loss, then take smaller samples more frequently.

If the cost of inspection is high then take smaller samples at large interval.

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As and general guidance, for deciding the frequency of taking a sample, we can use the table given in the next slide.

If our lot size in a shift is say 3000, then in a shift we require 50 units. If the sample size n, is say 4 then

Number of visits to the process is = 50÷4 = 12

The time of an 8-hour shift, be divided in 12 equal parts. Samples should be taken round about every 45 minutes.

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Lot Size Total Number of items

66 - 100 10

101 - 180 15

181 - 300 25

301 - 500 30

501 - 800 35

801 - 1300 40

1301 - 3200 50

3201 - 8000 60

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Step No. 4

Collect data on a special control chart datacollection sheet. ( Minimum 100 observations)

The data collection sheet has following main portions:1. General details for part, department etc.2. Columns for date and time sample taken3. Columns for measurements of sample4. Column for mean of sample5. Column for range of sample

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Typical Data Collection Sheet

Part Operation Other Details

Measurement SN

Date

Time

X1 X2 X3 X4 Mean Range

1

2

3

…..

25

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Step No. 5

Fill up the control chart data sheet

1) As per the plan, visit the process and

collect a sample of required number of units.

2) Measure the units and record.

3) Take requisite number of samples ( 20-25).

4) Calculate the mean of each of the sample.

5) Calculate the range of each of the sample.

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Example - Establishing Trial Control Limits

A supervisor decided to put his process under statistical control. For the purpose of establishing control chart he collected 10 samples (Normally it should be 20 samples) containing 5 units. The samples were measured and the same is shown in the next slide. The desired target of the process, T is 50. Establish control chart for monitoring the process.

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Example - Data Collection

Subgroup Reading Subgroup No. X1 X2 X3 X4 X5

Mean of subgroup

Range of subgroup

1 47 45 48 52 51

2 48 52 47 50 50

3 49 48 52 50 49

4 49 50 52 50 49

5 51 50 53 50 48

6 50 50 49 51 47

7 51 48 50 50 54

8 50 48 50 50 52

9 48 48 49 50 51

10 49 50 50 52 51

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Example - Calculation of Subgroup No.1

Measurements are 47, 45, 48, 52 & 51

Mean of measurements of subgroup No. 1

= (47 + 45 + 48 + 52 + 51)/5 = 48.6

Range of measurements of subgroup No. 1

= ( largest reading - smallest reading )= ( 52 - 45 )= 7

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Example - Calculation of subgroup Mean & Range

Subgroup Reading Subgroup No. X1 X2 X3 X4 X5

Mean of subgroup

Range of subgroup

1 47 45 48 52 51 48.6 7

2 48 52 47 50 50 49.4 5

3 49 48 52 50 49 49.6 4

4 49 50 52 50 49 50.0 3

5 51 50 53 50 48 50.4 5

6 50 50 49 51 47 49.4 4

7 51 48 50 50 54 50.6 6

8 50 48 50 50 52 50.0 4

9 48 48 49 50 51 49.2 3

10 49 50 50 52 51 50.2 3

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Calculate Mean Range, R

R = Sum of ranges of subgroups

Total number of subgroups

In our case

R = (7 + 5 +4 3 + 5 + 4 + 6 + 4 + 3 + 3 )

Total number of subgroups

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Step No. 7Using following table of constants find trial control limit for mean and range control chart’

Sub GroupSize

A2 D4 D3

2 1.880 3.267 0

3 1.023 2.527 0

4 0.729 2.282 0

5 0.577 2.115 0

6 0.483 2.004 0

7 0.419 1.924 0.076

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Step No. 8

Calculate Trial control Limits with target value, T

Trial control limits for mean control chartUpper Control Limit, UCLx = T + A2 x R

Lower Control Limit, LCLx = T - A2 x R

Trial control limits for range control chartUpper Control Limit, UCLr = D4 x R

Lower Control Limit, LCLr = D3 x R

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Calculation of Trial Control Limits

Size of Subgroup, n = 5

Factor A2, when n is 5 = 0.577

Factor D4, when n is 5 = 2.115

Factor D3, when n is 5 = 0

Target value, T = 50

Mean Range, R = 4.4

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Step No. 8

Trial control Limits in our case

For mean control chartUpper Control Limit, UCLx = 50 + 0.577 x 4.4=52.5

Lower Control Limit, LCLx = 50 - 0.577 x 4.4=47.5

For range control chartUpper Control Limit, UCLr = 2.115 x 4.4 = 9.3Lower Control Limit, LCLr = 0 x 4.4 = 0

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Step No. 9

Discard the outliers

Outliers are those observations which do not belong to

normal population. If Outliers are included in the

calculation, then the information is distorted.

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Checking for Outliers

Checking for mean outliers

Scan column of sample means. If any mean of sample is more than UCLx or less than LCLx then drop that sample.

Checking for range outliers

Scan column of sample range. If any range is more than UCLr then drop that sample.

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If any sample(s) is dropped then recalculate the trial control limits using remaining sample(s).

Continue this exercise till there is no further droppings. When there is no further dropping trial control limits becomes control limits for control chart.

In all we can drop up to 25% of the samples


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In our case

- None of the subgroup mean is more than 52.5

- None of the subgroup mean is less than 47.5

- None of the range is more than 9.3

- None of the range is less than 0

Hence there is no revision of trial control limits is required. These limits can be used for maintaining the control charts.

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Calculation of Control Limits for Mean Control Chart

Step No. 10

Compute warning limits for mean control chart

Upper warning limit, UWLx = T +2 x A2 x R

3

Lower warning limit, LWLx = T -2 x A2 x R

3

70

Calculation of Control Limits for Mean Control Chart

Warning limits for mean control chart in our example

Uwlx = 50 +2 x 0.577 x 4.4

3= 51.7

Lwlx = 50 -2 x 0.577 x 4.4

3= 48.3

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1 2 3 4 5 6 7

Sample Number

Mea

n

UCLx UCLx

LCLxLCLx

UWLx UWLx

LWLx LWLx

TargetTarget

Action and Warning Limits for Mean Control chart

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Action and Warning Limits for Mean Control Chart for Example

1 2 3 4 5 6 7

Sample Number

Me

an

UCLx=52.5 UCLx=52.5

LCLx= 47.5LCLx= 47.5

UWLx=51.7 UWLx=51.7

LWLx=48.3 LWLx=48.3

Target=50Target=50

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Sample size, n

D4 D3 DWLR DWUR

2 3.27 0 0.04 2.81

3 2.57 0 0.18 2.17

4 2.28 0 0.29 1.93

5 2.11 0 0.37 1.81

6 2.00 0 0.42 1.72

7 1.92 0.08 0.46 1.66

Constants for Range Control chart

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Calculation of Control Limits for Range Control Chart

Step No. 11

Compute warning limits for range control chart

Upper Warning Limit, UWLr = DWUR x R

Lower Warning Limit, LWLr = DWLR x R

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Calculation of Warning Limits for Range Control Chart

In our case

Size of sub group, n = 5

Mean range R = 4.4

DWUR when n is 5 = 1.81

DWLR when n is 5 = 0.37

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Calculation of Warning Limits for Range Control Chart

In our case warning limits for range control chart

Upper Warning Limit, UWLr = DWUR x R

= 1.81 x 4.4

= 8

Lower Warning Limit, LWLr = DWLR x R

= 0.37 x 4.4

= 1.6

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Action and Warning Limits for Control Chart

1 2 3 4 5 6 7

Mea

nUCLx = 52.5 UCLx = 52.5

LCLx = 47.5LCLx = 47.5

UCLr = 9.3UCLr = 9.3

Ra

nge

UWLr = 8UWLr = 8

LWLr = 1.6LWLr = 1.6

Target = 50Target = 50

R = 4.4R = 4.4

Sample Number

LWLx = 48.3 LWLx = 48.3

UWLx = 51.7 UWLx = 51.7

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Flow Chart for Establishing Control Chart

Decide subgroup size

Record observations

Find mean and range of each subgroup

Calculate mean range, R

Start

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Is any sub-group mean or range

out side the controllimit ?

Drop thatGroup

UCLx = T + A2 x RLCLx = T - A2 x R

UCLr = D4 x RLCLr = D3 x R

Yes

No


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Select suitable scale formean control chart and

range control chart

Draw Lines forTarget, UCL, UWL, LCL & LWL for mean

Mean range, UCL , UWL, LCL & LWL for range

Stop


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Summary of Effect of Process Shift

When there is no shift in the process nearly all the

observations fall within -3 s and + 3 s.

When there is small shift in the mean of process some

observations fall outside original -3 s and +3 s zone.

Chances of an observation falling outside original -3

s and + 3 s zone increases with the increase in the shift

of process mean.

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Our Conclusion from Normal Distribution

When an observation falls within original +3 s and -3 s zone of mean of a process, we conclude that there is no shift in the mean of process. This is so because falling of an observation between these limits is a chance.

When an observation falls beyond original +3 s and -3 s zone of process mean, we conclude that there is shift in location of the process

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Because the basis for control chart theory follows the normal distribution, the same rules that governs the normal distribution are used to interpret the control charts.

These rules include:

- Randomness.- Symmetry about the centre of the distribution.

- 99.73% of the population lies between - 3 s of and + 3 s the centre line.

- 95.4% population lies between -2 s and + 2 s of the centre line.

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If the process output follows these rules, the process is

said to be stable or in control with only common causes

of variation present.

If it fails to follow these rules, it may be out of control

with special causes of variation present.

These special causes must be found and corrected.

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UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tistic

s

UWL

LCL

LWL

One point outsidecontrol limit

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UCLUCL

1 2 3 4 5 6 7 8Sample Number

Sta

tistic

s

UWLUWL

LCLLCL

LWLLWL

Two points out of three consecutive points between warning limit and corresponding control limit

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UCL

1 2 3 4 5 6 7 8Sample Number

Sta

tistic

s

UWL

LCL

LWL

Two consecutive points between warning limit and corresponding control limit

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UCLUCL

1 2 3 4 5 6 7 8

UWLUWL

LCLLCL

LWLLWL

Seven consecutive points on one side of the centre line

Sample Number

Sta

tistic

s

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UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tistic

s

UWL

LCL

LWL

Seven consecutive points having upward trend

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UCLUCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tistic

s

UWL

LCLLCL

LWL

Seven consecutive points having downward trend

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Learning

Concept and definition of “Quality” Importance of improving Quality as a tool for cost

reduction Importance of proper analysis of Quality problems Usage of 7 QC tools to ensure “Defect free production”

92

Thank You

7 quality tools

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