Statistics -Quality Control

8/3/2019 Statistics -Quality Control

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Statistics -Quality Control

Prof. Rushen Chahal


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UpComing Events Complete CD-ROM certifications

Review

Final Examination


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Statistical Quality

Control

CD-ROM

SSIGNMENT


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TO DISCUSS THE ROLEOF STATISTICALQUALITY CONTROL

TO DEFINETHETERMS CHANCE CAUSES,

ASSIGNABLE CAUSES,IN CONTROL, & OUT

OF CONTROL.

TO CONSTRUCTAND DISCUSS

VARIABLES CHARTS:MEAN&RANGE.

GOALS


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5GOALS (next class)

TO CONSTRUCTAND DISCUSS

ATTRIBUTES CHARTS: PERCENTAGE

DEFECTIVE&NUMBER OF DEFECTS.

TO DISCUSSACCEPTANCE SAMPLING.

TO CONSTRUCTOPERATING

CHARACTERISTIC CURVESFOR VARIOUS

SAMPLING PLANS.


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Statistical Quality Controlemphasizes in-processcontrol with the objective of controlling the

quality of a manufacturing process or service

operation using sampling techniques.

Statistical sampling techniques are used to aid in

the manufacturing of a product to specifications

rather than attempt to inspect quality into the

product after it is manufactured.

Control Charts are useful for monitoring a

process.

CONTROL CHARTS


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There is

variation in all parts produced by amanufacturing process. There are two sources

of variation:

Chance Variation - random in nature. Cannot be

entirely eliminated.

Assignable Variation -- nonrandom in nature.

Can be reduced or eliminated.

CAUSES OF VARIATION


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Thepurpose of quality-control charts is todetermine and portray graphically just when an

assignable cause enters the production system so

that it can be identified and be corrected. This is

accomplished by periodically selecting a small

random sample from the current production.

PURPOSE OF QUALITY CONTROL

CHARTS


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The mean or thex-barchart is designed tocontrol variables such as weight, length, inside

diameter etc. The upper control limit (UCL)

and the lower control limit (LCL) are obtained

from equation:

TYPES OF QUALITY CONTROL

CHARTS - VARIABLES

andUCL X A R LCL X A R

where X is the mean of the sample meansA is a factor from Appendix B

R is the mean of the sample ranges

! ! 2 2

2


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10FACTORS FOR CONTROL CHARTS

Chart for

averages Chart for ranges

Number of Factors for Factors for Factors for items in control limits central line control limitssample,

n A2 d2 D3 D4

2 1.880 1.128 0 3.267

3 1.023 1.693 0 2.575

4 .729 2.059 0 2.282

5 .577 2.326 0 2.115

6 .483 2.534 0 2.004

7 .419 2.704 .076 1.924

8 .373 2.847 .136 1.864

9 .337 2.970 .184 1.816

10 .308 3.078 .223 1.777

11 .285 3.173 .256 1.744

12 .266 3.258 .284 1.716

13 .249 3.336 .308 1.692

14 .235 3.407 .329 1.671

15 .223 3.472 .348 1.652


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The range chart is designed to show whether theoverall range of measurements is in or out of

control. The upper control limit (UCL) and the

lower control limit (LCL) are obtained from

equations:


CHARTS - VARIABLES

UCL D R and LCL D R

where D and D are factors from Appendix B

R is the mean of the sample ranges

! !

4 3

3 4


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Chart for



n A2 d2 D3 D4

2 1.880 1.128 0 3.267

3 1.023 1.693 0 2.575

4 .729 2.059 0 2.282

5 .577 2.326 0 2.115

6 .483 2.534 0 2.004

7 .419 2.704 .076 1.924

8 .373 2.847 .136 1.864

9 .337 2.970 .184 1.816

10 .308 3.078 .223 1.777

11 .285 3.173 .256 1.744

12 .266 3.258 .284 1.716

13 .249 3.336 .308 1.692

14 .235 3.407 .329 1.671

15 .223 3.472 .348 1.652


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13EXAMPLEAmanufacturer of ball bearings wishes to

determine whether the manufacturing process isout of control. Every 15 minutes for a five hour

period a bearing was selected and the diameter

measured. The diameters (in mm.) of thebearings are shown in the table below.


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14Compute the sample means and ranges. The

table below shows the means and ranges.

EXAMPLE (continued)


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15Compute the grand mean (X double bar) and the

average range.

Grand mean = (25.25 + 26.75 + ... + 25.25)/5 =

26.35.

The average range = (5 + 6 + ... + 3)/5 = 5.8.

Determine the UCL and LCL for the averageaverage

diameter.

UCL = 26.35 + 0.729(5.8) = 30.58. LCL = 26.35 - 0.729(5.8) = 22.12.

EXAMPLE (continued)


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Chart for



n A2 d2 D3 D4

2 1.880 1.128 0 3.267

3 1.023 1.693 0 2.575

4 .729 2.059 0 2.282

5 .577 2.326 0 2.115

6 .483 2.534 0 2.004

7 .419 2.704 .076 1.924

8 .373 2.847 .136 1.864

9 .337 2.970 .184 1.816

10 .308 3.078 .223 1.777

11 .285 3.173 .256 1.744

12 .266 3.258 .284 1.716

13 .249 3.336 .308 1.692

14 .235 3.407 .329 1.671

15 .223 3.472 .348 1.652


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17Determine the UCL and LCL for the range

diameter.

UCL = 2.282(5.8) = 30.58.

LCL = 0(5.8) = 0.

Is the process out of control?

Observe from the next slide that the process is in

control. No points are outside the control limits.

EXAMPLE (continued)


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Chart for



n A2 d2 D3 D4

2 1.880 1.128 0 3.267

3 1.023 1.693 0 2.575

4 .729 2.059 0 2.282

5 .577 2.326 0 2.115

6 .483 2.534 0 2.004

7 .419 2.704 .076 1.924

8 .373 2.847 .136 1.864

9 .337 2.970 .184 1.816

10 .308 3.078 .223 1.777

11 .285 3.173 .256 1.744

12 .266 3.258 .284 1.716

13 .249 3.336 .308 1.692

14 .235 3.407 .329 1.671

15 .223 3.472 .348 1.652


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19EXAMPLE (continued)X-bar and R Chart for the Diameters


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Control ChartsW. Edwards Deming

Short Video Clip


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Thepercent defective chart is also called ap-chart or thep-barchart. It graphically shows

the proportion of the production that is not

acceptable.


CHARTS - ATTRIBUTES

The proportion of defectives is found by

pSum of the percent defectives

Number of samples

:

!


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The equation below gives the UCL and LCL forthep-chart.


CHARTS - ATTRIBUTES

The UCL and LCL are computed

as the mean percent defective plus or times thestandard error of the percents

UCL and LCL p p pn

minus 3

3 1

:

( ) .! s


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23A manufacturer of jogging shoes wants to

establish control limits for the percent defective.

Ten samples of 400 shoes revealed the mean

percent defective was 8.0%. Where should the

manufacturer set the control limits?

EXAMPLE

008 3008 1 008

400008 0041

.. ( . )

. .

s

! s


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The cc--chart of the cc--barbarchart is designed tocontrol the number of defects per unit. The

UCL and LCL are found by:

UCL and LCL c c! s 3


CHARTS - ATTRIBUTES


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25A manufacturer of computer circuit boards

tested 10 after they were manufactured. The

number of defects obtained per circuit board

were: 5, 3, 4, 0, 2, 2, 1, 4, 3, and 2. Construct the

appropriate control limits.

EXAMPLE

c Thus

UCL and LCLor

! !

! s

s

26

102 6

2 6 3 2 62 6 484

. .

. .. . .


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26Acceptance samplingis a method of determining

whether an incoming lot of a product meets

specified standards.

It is based on random sampling techniques.

A random sample ofn units is obtained from theentire lot.

c is the maximum number of defective units that

may be found in the sample for the lot to still beconsidered acceptable.

ACCEPTANCE SAMPLING


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An OCcurve,

or operating characteristic curve,

isdeveloped using the binomial probability

distribution, in order to determine the

probabilities of accepting lots of various quality

levels.

OPERATING CHARACTERISTIC

CURVE


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28EXAMPLE

Suppose a manufacturer and a supplier agree on

a sampling plan with n = 10 and acceptancenumber of 1. What is the probability of

accepting a lot with 5% defective? A lot with

10% defective? P(ren = 10,p = 0.05) = 0.599 + 0.315 = 0.914.

P(ren = 10,p = 0.1) = 0.349 + 0.387 = 0.736

etc.

P rn

r n rp

rq

n r( )!

!( )!!


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Statistics -Quality Control