# quality and statistical quality control

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8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL

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` Conformance to specifications

` Fulfilling customer needs

` Fitness for use

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` According to Feigenbaumthe underlying principle

of total quality is that ,to provide genuine

effectiveness, control must start with the design of

the product and end only when the product hasbeen in the hands of a customer who remains

satisfied.

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` Performance

` Features

` Reliability

` Conformance` Durability

` Serviceability

` Aesthetics

` Safety` Other perceptions

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` system for verifying and maintaining a desired

level of quality in a product or process by careful

planning, use of proper equipment, continued

inspection, and corrective action as required

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` The production processes are not perfect!

` Which means that the output of these processes will not be

perfect correct and deterministic.

` Successive runs of the same production process will produce

non-identical parts.

` Alternately, seemingly similar runs of the production process

will vary, by some degree, and impart the variation into the

some product characteristics.

` Because of these variations in the products, we needprobabilistic models and robust statistical techniques to

analyze quality of such products.

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` No matter how carefully a production process is controlled,these quality measurements will vary from item to item, andthere will be a probability distribution associated with the

population of such measurements.

` If all important sources of variations are under control in aproduction process, then the slight variations among thequality measurements usually cause no serious problems.

` Such a process should produce the same distribution of qualitymeasurements no matter when it is sampled, thus this is a

stable system.

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` Objective ofquality control is to develop a scheme forsampling a process, making a quality measurement of intereston sample items, and then making a decision as to whether ornot the process is in the stable state, or in control.

` If the sample data suggests that the process is out of control,a cause is for the abnormality is sought.

` A common method for making these decisions involves theuse ofcontrol charts.

` These are very important and widely used techniques in

industry, and everyone in the industry, even if not directlyrelated to quality control, should be aware of these.

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Statistical process control

` Methodology formonitoring a process to identify special

causes of variation and signaling the need to take corrective

action.

` Whenspecial causes are present, the system said to be

statistically out of control.

` If the variations are due to common causes alone, the process

is said to be in statistical control.

` SPC relies heavily on control charts.

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Control Chart Selection: Attribute DataControl Chart Selection: Attribute Data

X, R chart

Process ControlProduct Control

Variables Attributes Variables Attributes

Acceptance Sampling (Single/Double

Sampling Plan)c, p, np chart

In Process control Techniques

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Control Charts: Recognizing Sources ofControl Charts: Recognizing Sources of

VariationVariation

Why Use a Control Chart? To monitor, control, and improveprocess performance over time by

studying variation and its source.

What Does a Control Chart Do? Focuses attention on detecting and monitoring process variation over

time;

Distinguishesspecialfrom common causes of variation, as a guide tolocal or management action;

Serves as a tool for ongoing control of a process;

Helps improve a process to perform consistently and predictably forhigher quality, lower cost, and higher effective capacity;

Provides a common language for discussing process performance.

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Control Charts:Control Charts:

Recognizing Sources of VariationRecognizing Sources of Variation

How Do I Use Control Charts?

There are many types of control charts. The control

charts that you or your team decides to use should be

determined by the type of data that you have.

Use the following tree diagram to determine whichchart will best fit your situation. Only the most

common types of charts are addressed.

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` Attributes A performance characteristics that is either

present or absentin the product or service under

consideration.

` Examples: Order is either complete or incomplete; an invoice

can have one, two, or more errors.

` Attributes data are discrete and tell whether the characteristics

conforms to specifications.

` Attributes measurements typically represented as proportions

or rates. e.g. rate of errors per opportunity.` Typically measured by Go-No Go gauges.

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` Variable Continuous data that is concerned with degree ofconformance to specifications.

` Generally expressed with statistical measures such as averagesand standard deviations.

` Sophisticated instruments (caliper) used.

` In statistical sense, attributes inspection less efficient thanvariable inspection.

` Attribute data requires larger sample than variable inspectionto obtain same amount of statistical information.

` Most quality characteristics in service industry are attributes.

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Statistical Process ControlStatistical Process Control

Statistical Process Control (SPC) can be

thought of as the application of statistical

methods for the purposes of quality controland improvement.

Quality Improvement is perhaps foremost

among all areas in business for applicationof statistical methods.

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Control Chart ConstructionControl Chart Construction

Initiate data collection:

Run the process untouched, and gather sampled data. Record data on an appropriate Control Chart sheet or

other graph paper. Include any unusual events that occur.

Calculate the appropriate statistics and control limits:

Use the appropriate formulas.

Construct the control chart(s) and plot the data.

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CL

U1SL

U2SWL

UCL

L1SL

L2SWL

LCL

A

B

C

C

B

A

Control Charts: Colors UsedControl Charts: Colors Used

*

** *

*

* *

**

**

*

*

*

*

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Control Chart InterpretationControl Chart Interpretation

Center line (CL) positioned at the estimated mean

Upper and lower one standard deviation lines (U1SL and

L1SL) positioned one standard deviation above andbelow the mean.

Upper and lower two standard deviation warning lines(U2SWL and L2SWL) positioned at two standard

deviations above and below the mean.

Upper and lower control lines (UCL and LCL) positionedat three standard deviations above and below the mean.

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Control Charts for theControl Charts for the

Process Mean and DispersionProcess Mean and Dispersion

X bar ChartTypically used to monitor process centrality (or location)

Limits depend on the measure is used to monitor process dispersion(R or S may be used).

S orStandard Deviation Chart:Used to monitor process dispersion

R orRange Chart:

Also used to monitor process dispersion

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m = 20 to 40 initial samples of n observations each.

Xi = mean of ith sample

Si = standard deviation of ith sample

Ri = range of ith sample

Sample Summary InformationSample Summary Information

X = (X1 + X2 +... + Xm) / mR = (R1 + R2 + ... +Rm)/m

S = (S1 + S2 + ... + Sm)/m

W = R/d2 where d2 depends only on n

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Coordinates for the XCoordinates for the X--bar Control Chart: Rbar Control Chart: R

CL= X,

UCL= X+ A2R,

UCL= X- A2R

U2SWL= X+ 2A2R/3

L2SWL= X- 2A2R/3

U1SL= X+ A2

R/3

L1SL= X- A2R/3

A2 is a constant that depends only on n.

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Coordinates for an R Control ChartCoordinates for an R Control Chart

CL= R

UCL= D4R

LCL= D3R U2SWL= R+ 2(D4-1)R/3

L2SWL= R- 2(D4-1)R/3

U1SL= R+ (D4

-1)R/3

L1SL= R- (D4-1)R/3

where D3 and D4 depend only on n

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Championship

Championship Card CompanyChampionship Card Company

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Championship Card CompanyChampionship Card Company

Championship Card Company (CCC) produces collectiblesports cards of college and professional athletes.

CCCs card-front design uses a picture of the athlete, bordered

all-the-way-around with one-eighth inch gold foil. However,

the process used to center an athletes picture does not functionperfectly.

Five cards are randomly selected from each 1000 cards produced

and measured to determine the degree of off-centeredness of each

cards picture. The measurement taken represents percentageof total margin (.25) that is on the left edge of a card. Data

from 30 consecutive samples is included with your materials,

and summarized on the following slides.

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Championship Card CompanyChampionship Card Company

Sample X-bar R Sample X-bar R Sample X-bar R

1 55.6 22 11 51.2 15 21 50.0 11

2 61.0 23 12 49.4 14 22 47.0 14

3 45.2 20 13 44.0 32 23 50.6 15

4 46.2 11 14 51.6 14 24 48.8 165 46.8 18 15 53.2 12 25 44.6 22

6 49.8 23 16 52.4 23 26 46.8 16

7 46.8 18 17 50.6 8 27 49.2 88 44.2 20 18 56.0 18 28 45.6 19

9 50.8 32 19 50.2 19 29 57.6 40

10 48.4 16 20 44.0 23 30 51.4 17

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Championship Card CompanyChampionship Card Company

Summary InformationSummary Information

n = 5

X = 49.63S = 7.42

R = 18.63

d2 = 2.326

A2 = 0.577

A3 = 1.427

B3 = NAB4 = 2.089

D3 = NA

D4 = 2.115

W = R/d2 = 8.01

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3020100

60

50

40

Sample Number

SampleMean

X Bar Chart for Sports Cards Centering Values

Samples of 5 from each 1000 Cards Printed

1

=49.63

1.0S L=53 .22

2.0S L=56 .80

3.0S L=60 .38

-1.0SL=46.05

- 2.0S L=42.47

- 3.0S L=38.89

Championship Card CompanyChampionship Card Company

Limits Based on R

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3020100

40

30

20

10

0

Sample Number

SampleRang

e

R Chart for Sports Card Centering

Samples of 5 Cards from each 1000 Produced

R=18.63

1.0SL=25.55

2.0S L=32.48

3.0S L=39.40

- 1.0S L=11.71

- 2.0SL =4.791

- 3.0SL =0.000

Championship Card CompanyChampionship Card Company

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Championship Card Company XChampionship Card Company X--bar & Rbar & R

Chart InterpretationChart Interpretation

Application of all eight PATs to the X-bar chart indicated aviolation of PAT 1 (one point plotting above the UCL) at sample2. Apparently, a successful process adjustment was made, as

suggested by examination of the remainder of the chart.

Application of PATs one through four to the R chart indicated aviolation of PAT 1 at sample 29. Measures would be investigatedto reduce process variation at that point. The violation was a

close call and was out of character with the remainder of thedata.

We are close to being able to apply PDCA to the process for thepurpose of achieving lasting process improvements.

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Coordinates for the X bar Control Chart: SCoordinates for the X bar Control Chart: S

CL= X

UCL=X=A3S

LCL=X- A3S

U2SWL= X+ 2A3S/3

L2SWL= X- 2A3S/3

U1SL= X+ A3S/3

L1SL= X- A3S/3

where A3 depends only on n

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Coordinates on an S Control ChartCoordinates on an S Control Chart

CL= S

UCL= B4S

LCL= B3S

U2SWL= S+ 2(B4-1)S/3

L2SWL= S- 2(B4-1)S/3

U1SL= S+ (B4-1)S/3 L1SL= S- (B4-1)S/3

where B3 and B4 depend only on n

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Championship Card CompanyChampionship Card CompanyChampionship Card CompanyChampionship Card Company

Sample X-bar S Sample X-bar S Sample X-bar S

1 55.6 9.63 11 51.2 6.83 21 50.0 5.15

2 61.0 8.63 12 49.4 5.46 22 47.0 5.15

3 45.2 7.40 13 44.0 14.35 23 50.6 5.55

4 46.2 4.09 14 51.6 5.18 24 48.8 6.505 46.8 7.22 15 53.2 5.36 25 44.6 8.96

6 49.8 8.76 16 52.4 9.48 26 46.8 6.50

7 46.8 6.72 17 50.6 3.44 27 49.2 3.19

8 44.2 8.53 18 56.0 7.00 28 45.6 7.96

9 50.8 11.95 19 50.2 7.60 29 57.6 14.38

10 48.4 6.19 20 44.0 8.46 30 51.4 6.80

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UCL

U2SWLU1SL

CL

L1SLL2SWL

LCL

X based on S S

60.22

56.6953.16

49.63

46.1142.58

39.05

15.49

12.8010.11

7.42

4.722.03

------

Championship Card CompanyChampionship Card Company

XX--bar and S Chart imitsbar and S Chart imits

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3020100

60

50

40

Samp l mber

SampleMean

X Bar Chart for Sports Cards Centering Values

Samples of 5 from each 1000 Cards Printed

1

X=49.63

1.0S L=53 .16

2.0S L=56.69

3.0S L=60.22

- 1.0S L=46 .11

- 2.0S L=42.58

- 3.0S L=39.05

Championship Card CompanyChampionship Card Company

Limits Based on S

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3020100

15

10

5

0

Sample Number

SampleStdev

S Chart for Sports Card Centering Values

5 Cards Sampled from each 1000 Cards Produced

S =7.416

1.0S L=10.11

2.0S L=12.80

3.0S L=15.49

- 1.0S L=4.724

- 2.0SL =2.032

- 3.0SL =0.000

Championship Card CompanyChampionship Card Company