statistical quality control (sqc) final

7/31/2019 Statistical Quality Control (SQC) Final

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Statistical Process Control


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Content

Basics of Statistical Process Control

Control Charts

Control Charts for Attributes

Control Charts for Variables

Control Chart Patterns

SPC with Excel

Process Capability

Six Sigma

Design of Six Sigma System


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Basics of Statistical Process

Control Statistical Process Control (SPC)

monitoring production process to detect and prevent poorquality

Sample

subset of items produced to use for inspection Control Charts

process is within statistical control limits


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Variability

Random

common causes

inherent in a process

can be eliminated only

through improvements

in the system

Non-Random

special causes

due to identifiable

factors

can be modified

through operator or

management action


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SPC in TQM

SPC

tool for identifying problems andmake improvements

contributes to the TQM goal of

continuous improvements


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Quality Measures

Attribute

a product characteristic that can be evaluatedwith a discrete response

good bad; yes - no Variable

a product characteristic that is continuous and canbe measured

weight - length


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Where to Use Control Charts

Process has a tendency to go out of control

Process is particularly harmful and costly if it goes

out of control Examples at the beginning of a process because it is a waste of time

and money to begin production process with bad supplies

before a costly or irreversible point, after which product isdifficult to rework or correct

before and after assembly or painting operations thatmight cover defects

before the outgoing final product or service is delivered


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Control Charts

A graph that establishescontrol limits of a process

Control limits upper and lower bands of a

control chart

Types of charts

Attributes

p-chart

c-chart

Variables

range (R-chart) mean (x bar chart)


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Normal Distribution

=0 1 2 3-1-2-3

95%

99.74%


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Control Charts for

Attributes p-charts

uses portion defective in a sample

c-charts uses number of defects in an item

The primary difference between using a p-chart and a c-chart

is as follows.

A p-chart is used when both the total sample size andthe number of defects can be computed.

A c-chart is used when we can compute only the

number of defects but cannot compute the proportion that

is defective.


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p-Chart

UCL = p+ z p

LCL = p- z p

z= number of standard deviations fromprocess average

p= sample proportion defective; an estimateof process average

p = standard deviation of sample proportion

p=p(1 - p)

n


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p-Chart Example

20 samples of 100 pairs of jeans

NUMBER OF PROPORTIONSAMPLE DEFECTIVES DEFECTIVE

1 6 .062 0 .00

3 4 .04

: : :

: : :

20 18 .18

200


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p-Chart Example (cont.)

UCL = p+ z = 0.10 + 3p(1 - p)

n

0.10(1 - 0.10)

100

UCL = 0.190

LCL = 0.010

LCL = p- z = 0.10 - 3p(1 - p)

n0.10(1 - 0.10)

100

= 200 / 20(100) = 0.10total defectives

total sample observationsp =


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p-Chart

Example(cont.)

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Proportiond

efective

Sample number

2 4 6 8 10 12 14 16 18 20

UCL = 0.190

LCL = 0.010

p= 0.10


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c-Chart

UCL = c+ z cLCL = c- z c

where

c= number of defects per sample

c= c


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c-Chart (cont.)Number of defects in 15 sample rooms

1 122 8

3 16

: :

: :15 15

190

SAMPLE

c= = 12.67

190

15

UCL = c+ z c= 12.67 + 3 12.67= 23.35

LCL = c+ z c= 12.67 - 3 12.67= 1.99

NUMBEROF

DEFECTS


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c-Chart

(cont.)

3

6

9

12

15

18

21

24

Numb

erofdefects

Sample number

2 4 6 8 10 12 14 16

UCL = 23.35

LCL = 1.99

c= 12.67


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Control Charts for

Variables

Mean chart ( x -Chart )

uses average of a sample

Range chart ( R-Chart )

uses amount of dispersion in a

sample


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x-bar Chart

deviationstandard

XLCL

XUCL

z

z

z = standard normal variable (2 for 95.44%

confidence, 3 for 99.74% confidence)


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x-bar Chart Example

OBSERVATIONS (SLIP- RING DIAMETER, CM)

SAMPLE k 1 2 3 4 5 x R

1 5.02 5.01 4.94 4.99 4.96 4.98 0.08

2 5.01 5.03 5.07 4.95 4.96 5.00 0.12

3 4.99 5.00 4.93 4.92 4.99 4.97 0.084 5.03 4.91 5.01 4.98 4.89 4.96 0.14

5 4.95 4.92 5.03 5.05 5.01 4.99 0.13

6 4.97 5.06 5.06 4.96 5.03 5.01 0.10

7 5.05 5.01 5.10 4.96 4.99 5.02 0.14

8 5.09 5.10 5.00 4.99 5.08 5.05 0.119 5.14 5.10 4.99 5.08 5.09 5.08 0.15

10 5.01 4.98 5.08 5.07 4.99 5.03 0.10

50.09 1.15


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x- bar Chart Example

(cont.)

UCL = x+ A2R= 5.01 + (0.58)(0.115) = 5.08

LCL = x- A2R= 5.01 - (0.58)(0.115) = 4.94

=

=

x= = = 5.01 cm= x

k

50.09

10

Retrieve Factor Value A2


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x- bar

Chart

Example

(cont.)

UCL = 5.08

LCL = 4.94

Mean

Sample number

|1

|2

|3

|4

|5

|6

|7

|8

|9

|10

5.10

5.08

5.06

5.04

5.02

5.00

4.98

4.96

4.94

4.92

x= 5.01=


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R- Chart

UCL = D4R LCL = D3R

R=Rk

where

R= range of each samplek= number of samples


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R-Chart Example

OBSERVATIONS (SLIP-RING DIAMETER, CM)

SAMPLE k 1 2 3 4 5 x R

1 5.02 5.01 4.94 4.99 4.96 4.98 0.08

2 5.01 5.03 5.07 4.95 4.96 5.00 0.12

3 4.99 5.00 4.93 4.92 4.99 4.97 0.084 5.03 4.91 5.01 4.98 4.89 4.96 0.14

5 4.95 4.92 5.03 5.05 5.01 4.99 0.13

6 4.97 5.06 5.06 4.96 5.03 5.01 0.10

7 5.05 5.01 5.10 4.96 4.99 5.02 0.14

8 5.09 5.10 5.00 4.99 5.08 5.05 0.11

9 5.14 5.10 4.99 5.08 5.09 5.08 0.15

10 5.01 4.98 5.08 5.07 4.99 5.03 0.10

50.09 1.15


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R-Chart Example (cont.)

RkR= = = 0.1151.1510 UCL = D

4R= 2.11(0.115) = 0.243LCL = D3R= 0(0.115) = 0

Retrieve Factor Values D3 and D4


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R-Chart Example (cont.)

UCL = 0.243

LCL = 0

Range

Sample number

R= 0.115

|1

|2

|3

|4

|5

|6

|7

|8

|9

|10

0.28

0.24

0.20

0.16

0.12

0.08

0.04

0


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Using x- bar and R-Charts Together

Process average and

process variability must

be in control. It is possible for samples

to have very narrow

ranges, but their

averages is beyond

control limits. It is possible for sample

averages to be in control,

but ranges might be very

large.


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A Process Is in

Control If

1. no sample points outside limits

2. most points near process average

3. about equal number of points above

and below centerline

4. points appear randomly distributed


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Control Chart Patterns

UCL

LCL

Sample observationsconsistently above thecenter line

LCL

UCL

Sample observations

consistently below thecenter line


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Control Chart Patterns (cont.)

LCL

UCL

Sample observations

consistently increasing

UCL

LCL

Sample observationsconsistently decreasing


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Revise the charts

Interpret the original charts Isolate the causes

Take corrective action

Revise the chart

Only remove points for which you can determine an assignablecause

DOE (d i f i t ) A l th


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DOE - (design of experiments) Analyse the

Process

The Process

X1 X2 X3

Controllable Inputs

N1 N2 N3

Inputs:

Raw

Materials,

components

, etc.

Uncontrollable Inputs

Y1, Y2, etc.

Quality

Characteristics:

OutputsLSL USL

Key Outputs: Variable How Measured When Measured

1

2

3

Noise Variables: Variable How Measured When Measured

1

2

3

4

5

Con trol la ble I np ut s V ar ia ble How M ea su re d Wh en M ea su re d

1

2

3

4

5

Overall Sampling Plan:

Run Temperature Pressure

1 Hi Hi2 Hi Hi

3 Lo Hi

4 Lo Hi

5 Hi Lo

6 Hi Lo

7 Lo Lo

8 Lo Lo

3.52.51.5

Capability Histogram

4321

3.0

2.5

2.0

1.5

Xbar and R Chart

S u b g r

Means

M U=2 . 3 7 6UCL =2 . 5 6 8

L CL =2 . 1 8 3

0.9

0.6

0.3

0.0

Ranges

R=0 . 5 1 6 2

UCL =0 . 9 6 2 1

L CL =0 . 0 7 0 2 7

4321

Last 4 Subgroups

3.0

2.5

2.0

1.5

Su b g ro u p Nu mb e r

Values

41

2 . 9 1 9 5 81.83175

Cp :2 .7 6CPU:2 .9 9

CPL :2 .5 3Cp k :2 .5 3

Capability PlotPro c e s s To le ra n c e

Sp e c i f i c a t i o n s

StDev :0.181306

III

III

3.52.51.5

Normal Prob Plot

Capab i l i t y us ing Poo led S tandard Dev ia t ion

DOE (d i f i t ) I th


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DOE - (design of experiments) Improve the

Process

Uncontrollable Inputs

The Process

X1 X2 X3Controllable Inputs

N1 N2 N3

Inputs:

Raw

Materials,

components

, etc.

Y1, Y2, etc.

Quality

Characteristics:

OutputsX

X

XLSL USL

LSL USL

ScrewRPM

PrimWdth

Nip FPM

Three Factor Design


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Examine the process

A process is considered to be stable and in

a state of control, or under control, when

the performance of the process fallswithin the statistically calculated control

limits and exhibits only chance, or

common causes.


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Process Capability

Tolerances

design specifications reflecting product

requirements

Process capability

range of natural variability in a process what we

measure with control charts


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Process Capability

(b) Design specificationsand natural variation thesame; process is capableof meeting specificationsmost of the time.

DesignSpecifications

Process

(a) Natural variationexceeds designspecifications; processis not capable of

meeting specificationsall the time.


Process


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Process Capability (cont.)

(c) Design specificationsgreater than naturalvariation; process iscapable of always

conforming tospecifications.


Process

(d) Specifications greaterthan natural variation,but process off center;capable but some outputwill not meet upperspecification.


Process


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Process Capability Measures

Process Capability Ratio

Cp =

=

tolerance range

process range

upper specification limit -lower specification limit

6


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Computing Cp

Net weight specification = 9.0 oz 0.5 oz

Process mean = 8.80 oz

Process standard deviation = 0.12 oz

Cp =

= = 1.39

upper specification limit -lower specification limit

6

9.5 - 8.5

6(0.12)


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What is a Sigma process


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Precision

Lesser the standard deviation of the process, more precise or

consistent is the process


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Meaning of a Sigma process

From a sigma process we come to know that at what

distance, in terms of the standard deviation, the

specification limits are placed from the target value.


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3 Sigma Vs 6 Sigma

The goal of Six Sigma program is to reduce the variation in every

process to such an extent that the spread of 12 sigmas i.e. 6Sigmas on either side of the mean fits within the process

specifications. The figure on next slide shows what this looks

like.

3 Si V 6 Si


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2 3 4 5 6 7 8 9 1210 16151413111

LSL USL

6 Sigma curve

3 Sigma curve

3 Sigma Vs 6 Sigma

In a 3 sigma process the values are widely spread along the center line,

showing the higher variation of the process. Whereas in a 6 Sigma

process, the values are closer to the center line showing

less variation in the process.


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Why 6 sigma?

LSL USL1.5SD

By shifting 3 sigma

process 1.5 SD, we

create 66,807 defects

per billion

opportunities

By shifting 6 sigma

process 1.5 SD, we

create 3.4defects per

billion opportunities

1.5SD


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Sigma Level

Sigma level DPMO PercentdefectivePercentage

yield Cp

1 691,462 69% 31% 0.33

2 308,538 31% 69% 0.67

3 66,807 6.7% 93.3% 1.00

4 6,210 0.62% 99.38% 1.33

5 233 0.023% 99.977% 1.67

6 3.4 0.00034% 99.99966% 2.00

7 0.019 0.0000019% 99.9999981% 2.33
http://en.wikipedia.org/wiki/Defects_per_million_opportunitieshttp://en.wikipedia.org/wiki/Defects_per_million_opportunities


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statistical quality control (sqc) final

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