Quality Control[1]

7/29/2019 Quality Control[1]

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1

Statistics -Quality Control

Alan D. Smith


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2

UpComing Events

Complete CD-ROM certifications

Review

Final Examination


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3

Statistical Quali ty

Control

CD-ROM

SSIGNMENT


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4TO DISCUSS THE ROLE OF STATISTICAL

QUALITY CONTROL

TO DEFINE THE TERMS CHANCE CAUSES,

ASSIGNABLE CAUSES, I N CONTROL , & OUT

OF CONTROL .

TO CONSTRUCT AND DISCUSS

VARIABLES CHARTS: MEAN& RANGE.

GOALS


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5GOALS (next class)

TO CONSTRUCT AND DISCUSS

ATTRIBUTES CHARTS: PERCENTAGE

DEFECTIVE& NUMBER OF DEFECTS.

TO DISCUSS ACCEPTANCE SAMPLING.

TO CONSTRUCT OPERATING

CHARACTERISTIC CURVESFOR VARIOUS

SAMPLING PLANS.


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6

Statistical Quali ty Controlemphasizes in-process

control with the objective of controlling the

quality of a manufacturing process or service

operation using sampling techniques.

Statistical sampling techniquesare 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 Chartsare useful for monitoring a

process.

CONTROL CHARTS


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7 There is variationin all parts produced by a

manufacturing process. There are two sourcesof variation:

Chance Var iation -random in nature. Cannot be

entirely eliminated.

Assignable Var iation -nonrandom in nature.

Can be reduced or eliminated.

CAUSES OF VARIATION


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8

The purposeof quality-control charts is to

determine 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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9

The meanor the x-barchart is designed to

control 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 foraverages 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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11

The rangechart is designed to show whether the

overall 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 BR is the mean of the sample ranges

4 3

3 4


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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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13EXAMPLEA manufacturer 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 the

bearings 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 average

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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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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n A2 d2 D3 D4

2 1.880 1.128 0 3.2673 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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20

Control Charts

W. Edwards Deming

Short Video Clip



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21

The percent defectivechart is also called a

p-chart or the p-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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22

The equation below gives the UCL and LCL for

the p-chart.


CHARTS - ATTRIBUTES

The UCL and LCL are computed

as the mean percent defectiveplus or times the

standard error of the percents

UCL and LCL p p pn

minus 3

3 1

:

( ).


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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

0 08 30 08 1 0 08

4000 08 0 041

.. ( . )

. .



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24

The c-chart of the c-barchart is designed to

control the number of defects per unit. The

UCL and LCL are found by:

UCL and LCL c c 3


CHARTS - ATTRIBUTES


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25A manufacturer of computer circuit boards

tested 10 after they were manufactured. Thenumber 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

2610

26

26 3 2626 484

. .

. .. . .

CC C S G


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26 Acceptance samplingis a method of determining

whether an incoming lot of a product meetsspecified standards.

It is based on random sampling techniques.

A random sample ofnunits is obtained from theentire lot.

cis 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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27

An OCcurve, or operating character isticcurve, is

developed using the binomial probability

distribution, in order to determine the

probabilities of accepting lots of various quality

levels.

OPERATING CHARACTERISTIC CURVE

EXAMPLE


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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(rn= 10, p= 0.05) = 0.599 + 0.315 = 0.914. P(rn= 10, p= 0.1) = 0.349 + 0.387 = 0.736 etc.

P rn

r n rprq n r( )

!!( )!

St ti ti l Q lit C t l H k


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29Statistical Quality Control HomeworkComplete CD-ROM exercises

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Quality Control[1]