7 tools for statistical

8/13/2019 7 Tools for Statistical

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Inputs Transformation Process Throughput

Managing Operations AFocus on ExcellenceCox, Blackstone, and

Schleier, 2003

Chapter 14

The Tools of Quality:

Exceeding Customers Expectations

CBS Chapter 14 14-2

The Seven Tools of Quality

1. Control chart

2. Run chart

3. Pareto chart

4. Flow chart

5. Cause and effect diagram

6. Histogram

7. Scatter diagram

CBS Chapter 14 14-3

Statistical Process Control

A method of inspection by which it canbe determined whether a process is in

control

Differs from Acceptance Sampling in

that SPC does not make judgements

about the quality of the item processed.

Key tool is the Control Chart of which

several types exist.


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CBS Chapter 14 14-4

SPC Defined

All processes are affected by multiple factorsand, therefore, SPC can be applied to anyprocess.

There is inherent variation in any process whichcan be measured and controlled.

SPC does not eliminate variation, but it doesallow the user to track special cause variation.

SPC is a statistical method of separatingvariation resulting from special causes fromnatural variation and to establish and maintainconsistency in the process, enabling processimprovement. (Goetsch & Davis, 2003. p. 631)

CBS Chapter 14 14-5

Variation in Processes

Common Cause variation - the variation

which in inherent in the process itself; when

sampled, a normal distribution is found; a

process is said to be in statistical control

when only common cause variation exists. Special (or Assignable) Cause variation - the

variation in process output that might be

traced to a specific cause; the process is said

to be out of control when a special causevariation exists.

CBS Chapter 14 14-6

Rationale for SPC

Control of Variation

Continuous Improvement

Predictability of Processes

Elimination of Waste

Product Inspection


3/15

CBS Chapter 14 14-7

Creating Control Charts

All control charts rely on the periodic

sampling and measurement of items.

The data collected will allow thecalculation of a centerline, and upper

and lower control limits.

The centerline is the mean of all

samples, whereas the control limits are,

conceptually, the mean +/- three

standard deviations.

CBS Chapter 14 14-8

Interpreting Control Charts

4 (95.5%)

6 (99.7%)

2(68%)

SPC is based upon the

Central Limit Theorem

which tells us, in effect,

that the samples will

follow a normal

distribution regardless

of the shape of the

parent distribution.

Interpreting control charts is, then, all about probabilities if

the observations arent probable, then there must be a

special cause variation.

CBS Chapter 14 14-9

Interpreting Control ChartsSpecial Cause Variation is assumed

to exist if:1. Any point falls outside the

control limits.

2. Nine consecutive observationsfall on one side of the mean.

3. Six consecutive observationsare increasing (or decreasing.)

4. 14 observations alternateabove and below the mean.

5. Two of three consecutivepoints fall in zone C in one-halfof the chart.

6. Four of five consecutive pointsfall in zone B in one-half of thechart.

7. 15 consecutive observationsin the A zones.

8. Eight consecutive pointsoutside of the A zones.

LCL

UCL

-3x

+3x

+2

+2

+1+1

A = 34%

A = 34%

B = 13.75%

B = 13.75%

C = 2.1%

C = 2.1%


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CBS Chapter 14 14-10

Risks of SPC

SPC has the same Type I and Type II

risks as acceptance sampling

If the process if in fact in control but we

conclude that it is out of control, we

have committed a Type I error.

If the process if in fact out of control but

we conclude that it is in control, we

have committed a Type II error.


Common control charts for

variables & attributes

Number of defects per

unit (area, time, length,

etc.)

U-chart

Number of defectsC-chart

Number of defectivesNp-chart

Percent defectiveP-chartAttributes data

Individual valuesX-Rs

Median & RangeX-tilde & R

Mean & RangeX-bar & RVariables data

Statistical QtyChart TypeData Category


What SPC does not do

SPC only determines whether a process isin statistical control NOT whether theprocess is producing within specifications

nor whether the process is even capable

of producing within specifications.

We must rely on another measure AFTER

we have assured that the process is in

control using SPC.


5/15


Process Capability

Process capability is the ability of the

process, as it currently exists, to

product within specifications.

One measure known as Cp comparesthe natural variation of the process to

the specification width.

Another, more precise, measure known

as Cpk compares the natural variation of

the process to the specification width

and target.


Process Capability

6 (99.7%)

Process Capability (PC) is the range in which "all" output

can be produced the inherent capability of the process.

Definition:PC = 6


Process Capability

and Process Specifications

X

4.90 4.95 5.00 5.05 5.10 5.15cm

Tolerance band

Inherent capability (6 )

LSL USL

OutputOutputout of specout of spec

OutputOutputout of specout of spec

Process outputdistribution

5.010


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Process Capability

and Process Specifications

This process is

NOT CAPABLE.

INSPECT - Sort out

the defectives

This process is

CAPABLE of

producing all good

output.

Control the process.

LowerSpecLimit

UpperSpecLimit


Process Capability Index

3

Upper Spec Limit - X

3

X - Lower Spec LimitORthe smaller of:Cpk =

Index Cpk compares the spread and location

of the process, relative to the specifications.

{


Cpk Values

LSL USL

Cpk = 1.0

LSL USL

Cpk = 1.0

LSL USL

Cpk = 3.0

LSL USL

Cpk = 0.80

LSL USL

Cpk = 0.60

LSL USL

Cpk = 1.33


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Run Charts

Number of

defectives

Time

Figure 14.13. Run chart

x

x

x

x

x

x

x

x


Pareto Chart

Figure 14.14. Pareto Analysis of problems at a pizza parlor

Crusttoohard

Fewtop-pings

Needmorecheese

Toomuchsauce

Servicetooslow

20

40

60

80100

120140

160180200

x

x

xx x

Comments


Flow ChartElement Time distance) Brief Descri ption

5 min. Sale is made. Items sold are entered into POS terminal.D 4 hours Average delay until the end of the day.1 min. Inventory records are updated for sales and receipts by computer.D 14 hours Delay until order review.20 min. Manager builds an order to maximize discount/minimize freight costs by ordering reorder

items and other items required to reach discount. 3 days Mai l o rder to vendor .3 days Vendor processes order. 3 days Vendor ships orde r. 5 min. Inspect shipment for damage. 5 min. Move shipment to stock room.D 2 days Temporarily placed in stock room until time is available to stock shelf. 2 min. Move coffees to proper shelves.30 minutes Coffees/teas placed in correct display containers. 15 days Wait until time to pay invoice.5 min. Pay invoice.Summary of Work ElementsElement Number Time/distance Percentage

6 3 days 61 min. 11D 3 2 days 18 hrs. 11 4 6 days 7 min. 22 1 15 days 56 1 5 min. 0Figure 11.7. Process flow chartcurrent method of inventory replenishment


8/15


Cause and Effect Diagram

Figure 14.15. Ishikawa (cause and effect) diagram for car wont start

Out of Gas

FUEL

BATTERY

Fuel Line Closed

Cable Corroded

Wires CorrodedLoose Wire

Old

Lights Left On

Dead

STARTER

SOLENOID WIRES

CAR WONT

START


Histogram

3

6

8

11

1417

14

11

8

6

3

0

2

4

6

8

10

12

14

16

18

2 3 4 5 6 7 8 9 10 11 12Result

Frequency

Figure 14.16a. Histogram of expected results

2

4

10

11

23

14

15

9

11

4

1

0

5

10

15

20

25

2 3 4 5 6 7 8 9 1 0 11 12

Result

Frequency

Figure 14.16b. Histogram of actual

results


Possible Histogram Shapes

3

6

9

12

4

12

9

6

3

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9Category

Frequency

Figure 14.18. Bimodal histogram

12

9

6

3

2

0

2

4

6

8

10

12

14

1 2 3 4 5C a t e g o r y

Frequency

F igu re 14.19. C liff-l ik e h istogram

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12Category

Frequency

Figure 14.20. Saw-toothedhistogram

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10

Category

Frequency

Figure 14.21. Skewedhistogram


9/15


Scatter Diagram

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350 400 450Yards Gained Rushing

PointsScored

Figure 14.22. Scatter diagram


The Seven New Tools

1. Affinity diagram

2. Relational diagram

3. Tree diagram

4. Matrix diagram

5. Program decision process chart

6. Arrow diagram

7. Matrix data analysis


Affinity Diagram

A method to get your arms around a complex problem.Similar to a brainstorming session wherein each

participant writes his/her idea for a cause on an index

card.

12

10

13

7

4

3 11

5

12

6

8

16

15

9

14


10/15


Affinity DiagramA method to get your arms around a complex problem.

Similar to a brainstorming session wherein each

participant writes his/her idea for a cause on an index

card.

12

10

13

7

4

3

11

5

12

6

8

16

15

9

14

The possible causes are then arranged into groups of

similar causes. The groups might be functional areas.

Group 1 Group 2 Group 3 Group 4


Relational Diagram

Used to logically examine the interrelationships among the

causes within a particular grouping.

The problem is written to the left and the causes are placed

according to their relationship to the problem -- the further away

the weaker the relationship.

1 5

12

16 9 14

Statement of

problem


Relationship Diagram ExampleLosses not

defined

Accepting currentreality

Status quo is

rewarded

Planning work

Too many

projects

Schedule is

overloadedBusy

maximizing

department

profitEmployees lack

understanding

Lack time to

develop

employees

Short-term

profit goals

Lack incentive

for

improvement

Improvement

work competes

with day-to-day

work

Management is

not setting a

good example

Figure 14.23. Relational diagram


11/15


Tree Diagram

Used to identify and sequence the tasks necessary to accomplish

an objective (the opposite of the problem) using the affinity

diagram and the relationship diagram as a reference.

Objective

1

10

5

4

3 13

2

12

14

86

7

11

15

9 16


Tree

Diagram

Example

Improve interaction

among functional

areas represented

in the group, in the

creation and

implementation of

an effective business

plan

Develop

procedures

to assure

team

effectiveness

Interaction

techniques

Make group

meetings

more

Effective

Provide

system to

communicate

progress

Show

functional

interdependencies

in plan

development

Use consensus

building

techniques in plan

development and

implementation

Interaction must

occur with

frequency

Publish and

adhere to agenda,

with team input

Require each

function to

periodically

report status

Distribute

tracking charts

of team

performance

Each function

shows its plan

to fulfill

overall plan

Identify

relationships in

dependencies in

project plan

Participate in

joint trainingof planning

methods

Use facilitator

approach at

meetings

Figure 14.24. Example tree diagram


Matrix Diagram

A5

A4

A3

A2

A1

B5B4B3B2B1A\B

C1

C2

C3

B5B4B3B2B1

C4

C5

A5

A4

A3

A2

A1

D5 D4 D3 D2 D1

C1

C2

C3

B5B4B3B2B1

C4

C5

A5

A4

A3

A2

A1

L-shaped

X-shapedT-shaped


12/15


Matrix Diagram

Example

The matrix L-diagram is

often used to identify and

assign responsibility for

tasks identified in the tree

diagram.

1 = primary

2 = secondary

3 = tertiary

Dept 1 Dept 2 Dept 3

1 1 2

10 3 1 2

5 1

4 1

3 2 3 1

13 1 3 2

2 2 1

12 1 2

14 1

8 2 1

6 1 2

7 3 2 111 3 1 2

15 1 2

9 2 116 1 2

T

A

S

K


Program

Decision

Process

Chart

Case received via mail.

Case scanned by paralegal

No conflict of interest

Attorney and paralegal

meet with client

Attorney and paralegal

"discoverevidence

A settlement offer is made

Plaintiff doesn't settle

File trial motions

Hold hearing on motions

Judge doesn't order mediation

Mediate settlement

Set trial date

Depose witnesses

Go to trial

Figure 14.27. Sample program decision process chart

Conflict of interest

Sent to another attorney

Plaintiff settles

File motion todismiss case

Judge orders mediation

No settlement


Arrow DiagramOperations 1 2 3 4 5 6 7 8 9 10 11 12

Foundation

Framework

Scaffolding

Exterior

Interior walls

Plumbing andelectrical work

Doors andwindows

Interior painting

Interior finished

Final inspectionand delivery

Figure 14.28a. Gantt chart to plan the construction of a house


13/15


Arrow Diagram

32

7

6 10

9

1

4 5

8

Figure 14.28b. Arrow diagram for construction of a house


What is QFD?A specialized method for making customers part of

the product development cycle.

It translates customer wants into what the

organization produces enabling the organization

to:

Prioritize customer needs;

Find innovative responses to those needs; and,

Improve processes to maximize effectiveness.


Structure of QFD

1

1 Customer Input

2

2 Manufacturers Current

Requirements/Specifications

to Suppliers

3

3 Planning Matrix

importance rating

competition rating

target values

scale-up needed

sales points

4

4 Relationships

5

5 Prioritized list of

manufacturers critical

process requirements

6

6 Process requirement

trade-offs


14/15


QFD Example

Good balance

X

X = conflicting requirement

+ = supporting requirement

A = Competitor 1

B = Competitor 2C = Our Boom Box

WORST BEST

PRIORITY

5

4

4

6

1

4

2

Tapes from CD

Large speakers

Light weight

Good sound

Attractive

Inexpensive

A B C

B C C

A C B

B AC

C B A

C AB

BC A

+

+

+

+

XX

Product

characteristics

Plastic

case

Ta

perecorder

6

Speakers

Plasti

chandle

3C

olorchoices

Figure 14.29. House of quality for a boom box


QFD ProcessMatrix 1Technical features

Customer

Requirements

Matrix 2Technical

features

Applied technologies

Applied

technologies Matrix 3

Manufacturing processes

Matrix 4Manufacturing

processes

Quality control processes

Matrix 5Quality control

processes

Statistical process control

Matrix 6Statistical processcontrol

Specifications for the finished product


Taguchi Loss Function

Figure 14.30. The Taguchi loss function

12 OUNCE AMOUNT0

COSTS

$

L = k(T-x)2 where:

L = loss

k = a constant (t ypically a

measure of intolerance ofdeviation)

T = target

x = observed value


15/15


BUSINESS PROCESSES

FIGURE 1.6g. BUSINESS SYSTEM MODEL

INPUT TRANSFORMATION THROUGHPUT

SUPPLIERS

CUSTOMERS

ORGANIZATION

INFORMATION

SYSTEMS

PHYSICALRESOURCES

PEOPLE

MANA

GEME

NTPHILO

SOPH

Y

MANAGEMENT

PLANNING&CONTROL

MANAGEMENTPOLICYGO

ALS&OBJECTIV

ES

STRATEGY

DESIGN

IMPLEMENTATIO

N

PERFO

RMANCE

MEASUREMENTS

THE ENVIRONMENT: GLOBAL COMPETITORS AND

SUPPLIERS, GOVERNMENTS, ECONOMIES,

CONSUMER TASTES, UNIONS, ETC.

Business System Model

7 tools for statistical

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