TOPIC 9 & 10TOOLS TO IMPROVE QUALITY AND QUALITY DIAGNOSIS PROCEDURE :

STATISTICAL QUALITY CONTROL

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Topic 9.0 : Statistical Process Control For Variables Data

1. Statistical Fundamentals

2. Process Control Charts / SPC

3. Some Control Chart Concepts for

Variables

4. Process Capability for Variables

5. Other Statistical Techniques in Quality

ManagementBJMQ3013-Quality Management: Dr Che Azlan Taib

Topic 10.0 : Statistical Process Control For Attributes Data

1. What is an Attribute

2. Generic Process for developing structure

Charts

3. Understanding Attributes Control Charts

4. Choosing the Right Attributes Chart

BJMQ3013-Quality Management: Dr Che Azlan Taib

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‘Data are required to obtain the average dimensions and the degree of dispersion (in process) so that we can determine ….. Whether the production

process used for manufacturing the lot was suitable, of if some action

must be taken. In other words, action can be taken on a process on the basis

of data gained from the samples’.

KAORU ISHIKAWA

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STATISTICAL FUNDAMENTALS

Is a decision-making skill demonstrated by the ability to draw conclusions based on data.Statistical thinking is based on three concepts:

1. What Is Statistical Thinking

All work occurs in a system of interconnected processes.

All processes have variation (the amount of variation tends to be underestimated).

Understanding variation and reducing variation are important keys to success.

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Lack of knowledge about the tools.General disdain for all things mathematical creates a natural barrier to the use of statistics.

2. Why Do Statistics Sometimes Fall in the Workplace?

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3. What Do We Mean by the Term Statistical Quality Control?

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4. Understanding Process Variation Processes involve variation. Some variation can be

managed and some cannot. If too much variation, the process not fit

correctly., product not function properly and firms will, get bad reputation/image.

TWO types of variation commonly occur:

1. Random variation2. Non-random variation

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Random Variation

Is uncontrollable In centered around a mean and occurs with a

somewhat consistent amount of dispersion. The amount of random variation in a process

may be either large or small

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Non-Random Variation

The event may be shift in a process mean or some unexpected occurrence.

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Process Stability

Means that the variation we observe in the process is random variation (common csuse) and not nonrandom variation.

To determine process stability, we use process chart.

Process charts are graphs designed to signal process workers when nonrandom variation is occurring in a process.

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PROCESS CONTROL CHARTS / STATISTICAL PROCESS CONTROL (SPC)

A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate

SPC relies on control charts

HISTOGRAMS VS. CONTROL CHARTS Histograms do not take into account changes over time.

Control charts can tell us when a process changes

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CONTROL CHART APPLICATIONS

Establish state of statistical control

Monitor a process and signal when it goes out of control

Determine process capability

Process capability calculations make little sense if the process is not in statistical control because the data are confounded by special causes that do not represent the inherent capability of the process.

QUALITY CONTROL APPROACHES

Statistical process control (SPC)• Monitors the production process to prevent • poor quality

Acceptance sampling• Inspects a random sample of the product • to determine if a lot is acceptable

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STATISTICAL PROCESS CONTROL

Take periodic samples from a process

Plot the sample points on a control chart

Determine if the process is within limits

Correct the process before defects occur

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SPC APPLIED TO SERVICES

Nature of defect is different in services

Service defect is a failure to meet customer requirements

Monitor times, customer satisfaction

Service Quality Examples

• Hospitals

– timeliness, responsiveness, accuracy

• Grocery Stores

– Check-out time, stocking, cleanliness

• Airlines

– luggage handling, waiting times, courtesy

• Fast food restaurants

– waiting times, food quality, cleanliness

PROCESS CONTROL CHART

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1 2 3 4 5 6 7 8 9 10

Sample number

Uppercontrollimit

Processaverage

Lowercontrollimit

CONSTRUCTING A CONTROL CHART

Decide what to measure or count

Collect the sample data

Plot the samples on a control chart

Calculate and plot the control limits on the control chart

Determine if the data is in-control

If non-random variation is present, discard the data (fix the problem) and recalculate the control limits

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A Process Is In Control If

• No sample points are outside control limits

• Most points are near the process average

• About an equal # points are above & below the centerline

• Points appear randomly distributed

99.74 %

Ch 4 - 14© 1998 by Prentice-Hall IncRussell/Taylor Oper Mgt 2/e

THE NORMAL DISTRIBUTION

95 %

= 0 1 2 3-1-2-3

Area under the curve = 1.0

CONTROL CHART Z VALUES

Smaller Z values make more sensitive charts

Z = 3.00 is standard

Compromise between sensitivity and errors

CONTROL CHARTS AND THE NORMAL DISTRIBUTION

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Mean

UCL

LCL

+ 3

- 3

TYPES OF DATA

Attribute data (p-charts, c-charts)Product characteristics evaluated with a

discrete choice (Good/bad, yes/no, count)

Variable data (X-bar and R charts)Product characteristics that can be

measured (Length, size, weight, height, time, velocity)

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CONTROL CHARTS FOR ATTRIBUTES

p Charts

• Calculate percent defectives in a sample;• an item is either good or bad

c Charts

• Count number of defects in an item

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P - CHARTS

Based on the binomial distribution

• p = number defective / sample size, n

• p = total no. of defectives

total no. of sample observations

UCLp =

LCLp =

P-CHART CALCULATIONS

Proportion

Sample Defect Defective

1 6 .06

2 0 .00 3 4 .04

. . .

. 20 18 .18 200 1.00

= 0.10

=

total defectives total sample observations 200 20 (100)

p =

100 jeans in each sample

LCL = p - 3 p(1-p) /n

= 0.10 + 3 0.10 (1-0.10) /100

= 0.010

UCL = p + 3 p(1-p) /n

= 0.10 + 3 0.10 (1-0.10) /100

= 0.190

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. .

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 2 4 6 8

10 12 14 16 18 20

Prop

ortio

n de

fect

ive

Sample number

C - CHART CALCULATIONS

Count # of defects per roll in 15 rolls of denim fabric

Sample Defects

1 12

2 8

3 16

. .

. .

15 15

190

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c = 190/15 = 12.67

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

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

EXAMPLE C - CHART

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.

0

3

6

9

12

15

18

21

24

0 2 4 6 8

10

12

14

Sample number

Nu

mb

er

of

de

fect

s

CONTROL CHARTS FOR VARIABLES

Mean chart (X-Bar Chart)

• Measures central tendency of a sample

Range chart (R-Chart)

• Measures amount of dispersion in a sample

Each chart measures the process differently. Both the process average and process variability must be in control for the process to be in control.

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EXAMPLE: CONTROL CHARTS FOR VARIABLE DATA

Slip Ring Diameter (cm)

Sample 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 0.08

4 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

CONSTRUCTING A MEAN CHART

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4.92

4.94

4.96

4.98

5.00

5.02

5.04

5.06

5.08

5.10

1 2 3 4 5 6 7 8 9 10

Sample average

Sample number

EXAMPLE X-BAR CHART

UCL

X

LCL

CONSTRUCTING AN RANGE CHART

UCLR = D4 R = (2.11) (.115) = 2.43

LCLR = D3 R = (0) (.115) = 0

where R = R / k = 1.15 / 10 = .115

k = number of samples = 10

R = range = (largest - smallest)

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3 CONTROL CHART FACTORSSample size X-chart R-chart

n A2 D3

D4

2 1.88 03.27

3 1.02 02.57

4 0.73 02.28

5 0.58 02.11

6 0.48 02.00

7 0.42 0.081.92

8 0.37 0.141.86

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0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 4 5 6 7 8 9 10

Range

Sample number

EXAMPLE R-CHART

UCL

R

LCL

Ch 4 - 34© 1998 by Prentice-Hall IncRussell/Taylor Oper Mgt 2/e

UCL

LCL LCL

UCL

Sample observationsconsistently below thecenter line

Sample observationsconsistently above thecenter line

CONTROL CHART PATTERNS

Ch 4 - 35© 1998 by Prentice-Hall IncRussell/Taylor Oper Mgt 2/e

CONTROL CHART PATTERNS

LCL LCL

UCL UCL

Sample observationsconsistently increasing

Sample observationsconsistently decreasing

Ch 4 - 36© 1998 by Prentice-Hall IncRussell/Taylor Oper Mgt 2/e

CONTROL CHART PATTERNS

UCL

LCL LCL

UCL

Sample observationsconsistently below thecenter line

Sample observationsconsistently above thecenter line

CONTROL CHART PATTERNS

1. 8 consecutive points on one side of the center line

2. 8 consecutive points up or down across zones

3. 14 points alternating up or down

4. 2 out of 3 consecutive points in Zone A

but still inside the control limits

5. 4 out of 5 consecutive points in Zone A or B

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ZONES FOR PATTERN TESTS

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UCL

LCL

Zone A

Zone B

Zone C

Zone C

Zone B

Zone A

x + 2 sigma

x + 1 sigma

x + 3 sigma

x - 1 sigma

x - 2 sigma

x - 3 sigma

X

5.08

5.05

5.03

5.01

4.98

4.965

4.94

Values for example 4.4

Ch 4 - 41© 1998 by Prentice-Hall IncRussell/Taylor Oper Mgt 2/e

SAMPLE SIZE DETERMINATION

Attribute control charts

• 50 to 100 parts in a sample

Variable control charts

• 2 to 10 parts in a sample