ies 331 quality control chapter 6 control charts for attributes week 7-8 july 19-28, 2005

IES 331 Quality Control Chapter 6 Control Charts for Attributes

Week 7-8 July 19-28, 2005

2

Dr. Karndee Prichanont IES331 1/2005

Attribute Data If item does not conform to standard on

one or more of these characteristics, it is classified as nonconforming Conforming / Nonconforming units

Non-defective / Defecting units

Good / Bad

Pass / Fail

Nonconforming unit will contain at least on nonconformity

Nonconformities / Defects Each specific point at which a specification

is not satisfied

ex: scratch, chip, dirty spots, accident

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6-2 Control Chart for Fraction Nonconforming Fraction of Nonconforming: Ratio of the

number of nonconforming items in a population to the total number of items in that population

Fraction of nonconforming ~ Binomial Distribution

p Probability that any unit will not conform to specificationsn Random sample of n unit. Sample sizeD The number of units of products that are nonconforming

4


The Control Chart for Fraction Nonconforming

Sample fraction nonconforming: ratio of the number of nonconforming units in the sample, D, to the sample size n

Mean and Variances

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With specified standard value

6


When p is not known, it must be estimated from collected data

Average of these individual sample fractions nonconforming

Fraction Nonconforming control chart: No Standard Given

“Trial Control Limit”


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Ex 1 (Exercise 6-1)

Also see Example 6-1

The data that follow give the number of nonconforming bearing and seal assemblies in sample size of 100

Construct a fraction nonconforming control chart for these data.

If any points plot out of control, assume that assignable causes can be found and determine the revised control limits

Sample #Number of

Noncomforming Assemblies

1 7

2 4

3 1

4 3

5 6

6 8

7 10

8 5

9 2

10 7

11 6

12 15

13 0

14 9

15 5

16 1

17 4

18 5

19 7

20 12

8


The np Control Chart Alternative to p Control Chart

Based on the number nonconforming rather than the fraction nonconforming

If standard value p is not known, use the estimator

Revisit Ex 1

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Variable Sample Size3 approaches to deal with variable sample size

1. Variable-width control limits: to determine control limits for each individual sample that are based on specific sample size

2. Control limits based on average sample size: to obtain an approximate set of control limits (constant control limits)

3. The standardized control chart:

The points are plotted in standard deviation units

Center line at zero

Upper and lower control limits +3 and - 3

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Ex 2 (Exercise 6-3)


Day

Units Inspecte

d

Nonconforming units

Fraction Nonconforming

1 80 4 0.050

2 110 7 0.064

3 90 5 0.056

4 75 8 0.107

5 130 6 0.046

6 120 6 0.050

7 70 4 0.057

8 125 5 0.040

9 105 8 0.076

10 95 7 0.074

The following data represent the results of inspecting all units of a personal computer produced for the last 10 days.

Does the process appear to be in control?

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The Operating-Characteristic Function OC curve provides a measure

of the sensitivity of the control chart

Ability to detect the shift in the process fraction nonconforming from the nominal value to some other value

Probability of incorrectly accepting the hypothesis of statistical control (i.e., type II or β-error)

}|{}|{

}|ˆ{}|ˆ{

pnLCLDPpnUCLDP

pLCLpPpUCLpP

}|{}|{

}|ˆ{}|ˆ{

pnLCLDPpnUCLDP

pLCLpPpUCLpP

12


13


Average Run Length (ARL) ARL for any Shewhart

control chart

If the process in control, ARL0

If the process is out of control, ARL1

control) ofout plotspoint sample(

1ARL

P

control) ofout plotspoint sample(

1ARL

P

1

ARL0 1

ARL0

1

1ARL1

1

1ARL1

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6-3 Control Charts for Nonconformities (Defects) We can develop control

charts for Total number of

nonconformities in a unit, or

Average number of nonconformities per unit

Defects or nonconformities ~ Poisson Distribution

Where x is the number of nonconformities and C > 0

c chart: same sample size

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Ex 3 (Exercise 6-41)


The data represent the number of nonconformities per 1000 meters in telephone cable.

From analysis of these data, would you conclude that the process is in control?

Sample Number

Number of Nonconformities

1 1

2 1

3 3

4 7

5 8

6 10

7 5

8 13

9 0

10 19

11 24

12 6

13 9

14 11

15 15

16 8

17 3

18 6

19 7

20 4

21 9

22 20

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Choice of Sample Size:u chart

It may requires several inspection units in the sample

u chart: setting up the control chart based on the average number of nonconformities per inspection unit

Average number of nonconformities per inspection unit

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Ex 4 (Exercise 6-44)


An automobile manufacturer wishes to control the number of nonconformities in a subassembly area producing manual transmissions.

The inspection unit is defined as four transmissions, and data from 16 samples (each of size 4) are shown here.

Set up a control chart for nonconformities per unit

Sample Number

Number of Nonconformities

1 1

2 3

3 2

4 1

5 0

6 2

7 1

8 5

9 2

10 1

11 0

12 2

13 1

14 1

15 2

16 3

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Control charts for nonconformities with variable sample size c chart will be difficult to interpret –

varying center line and control limits

Alternative approaches are:

1. u chart (nonconformities per unit)

Constant center line

Control limit will vary inversely with the n1/2

2. Use control limits based on an average sample size

3. Use a standardized control chart (preferred)

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Demerit Systems for Defects

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The Operating Characteristic Function OC curves for c and u charts

can be obtained from the Poisson distribution

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Action taken to improve a process

ies 331 quality control chapter 6 control charts for attributes week 7-8 july 19-28, 2005

Documents

control charts

control chartability

karndee prichanont ies331

standardized control

lower control limits

number nonconforming

np control chartalternative

quality control chapter