© 2003 Prentice-Hall, Inc. Quantitative Analysis Chapter 17 Statistical Quality Control Chap 17-1.

© 2003 Prentice-Hall, Inc.

Quantitative Analysis

Chapter 17Statistical Quality Control

Chap 17-1

© 2003 Prentice-Hall, Inc. Chap 18-2

Chapter Topics

Total Quality Management (TQM) Theory of Management (Deming’s

Fourteen Points) Six Sigma® Management Approach The Theory of Control Charts

Common-cause variation versus special-cause variation

Control Charts for the Proportion of Nonconforming Items


Chapter Topics

Process Variability The c Chart Control Charts for the Mean and the

Range Process Capability

(continued)


Themes of Quality Management

1. Primary Focus on Process Improvement2. Most Variation in Process Due to System3. Teamwork is Integral to Quality

Management4. Customer Satisfaction is a Primary Goal5. Organizational Transformation Necessary6. Remove Fear7. Higher Quality Costs Less


Deming’s 14 Points: Point 1:

Plan

DoStudy

Act

Point 1. Create Constancy of Purpose

The Shewhart-Deming CycleFocuses on Constant Improvement


Point 2. Adopt New Philosophy

Better to be proactive and change before crisis occurs.

Point 3. Cease Dependence on Mass Inspection to Achieve Quality

Any inspection whose purpose is to improve quality is too late.

Deming’s 14 Points: Points 2 and 3


Point 4. End the Practice of Awarding Business on the Basis of Price Tag Alone

Develop long term relationship between purchaser and supplier.

Point 5. Improve Constantly and Forever

Reinforce the importance of the Shewhart-Deming cycle.




Point 6. Institute Training

Especially important for managers to understand the difference between special causes and common causes.

Point 7. Adopt and Institute Leadership

Differentiate between leadership and supervision. Leadership is to improve the system and achieve greater consistency of performance.


Points 8-12.

Drive Out Fear

Break Down Barriers between Staff Areas

Eliminate Slogans

Eliminate Numerical Quotas for Workforce and Numerical Goals for Management

Remove Barriers to Pride of Workmanship

Deming’s 14 Points: Points 8 to 12

300


Point 13. Encourage Education and Self-Improvement for Everyone

Improved knowledge of people will improve the assets of

the organization.

Point 14. Take Action to Accomplish Transformation

Continually strive toward improvement.


Quality is important


Six Sigma® Management A Managerial Approach Designed to

Create Processes that Result in No More Than 3.4 Defects Per Million

A Method for Breaking Processes into a Series of Steps in Order to Eliminate Defects and Produce Near Perfect Results (1) Define:Define: Define the problem along with

costs, benefits and the impact on customers (2) MeasureMeasure: Develop operational definitions

for each Critical-to-Quality characteristic and verify measurement procedure to achieve consistency over repeated measurements


Six Sigma® Management

(3) AnalyzeAnalyze: Use control charts to monitor defects and determine the root causes of defects

(4) ImproveImprove: Study the importance of each process variable on the Critical-to-Quality characteristic to determine and maintain the best level for each variable in the long term

(5) ControlControl: Avoid potential problems that occur when a process is changed and maintain the gains that have been made in the long term

(continued)


Control Charts

Monitor Variation in Data Exhibit trend - make correction before

process is out of control A Process - A Repeatable Series of Steps

Leading to a Specific Goal


Characteristics for which you focus on defects

Classify products as either ‘good’ or ‘bad’, or count # defects e.g., radio works or

not

Categorical or discrete random variables

AttributesVariables

Quality Characteristics

Characteristics that you measure, e.g., weight, length

May be in whole or in fractional numbers

Continuous random variables


Statistical technique used to ensure process is making product to standard

All process are subject to variability Common (or Natural) causes: Random

variations Special (or Assignable) causes: Correctable

problems

Machine wear, unskilled workers, poor material

Objective: Identify assignable causes Uses process control charts

Statistical Process Control (SPC)


Graph of sample data plotted over time

Process Control Chart

020406080

1 3 5 7 9 11

X

Time

Special Cause Variation

Common Cause Variation

Process Average

Mean

UCL

LCL


Control Charts

Show When Changes in Data are Due to: Special (or Assignable) causes

Fluctuations not inherent to a process Represent problems to be corrected Data outside control limits or trend

Common causes (or Natural Causes) Inherent random variations Consist of numerous small causes of random

variability

(continued)


Control Limits

UCL = Process Average + 3 Standard Deviations

LCL = Process Average - 3 Standard Deviations

Process Average

UCL

LCL

X

+ 3

- 3

TIME


Out-of-Control Processes

If the Control Chart Indicates an Out-of-Control Condition (a Point Outside the Control Limits or Exhibiting Trend) Contains both common causes of variation

and assignable causes of variation The assignable causes of variation must be

identified If detrimental to quality, assignable causes of

variation must be removed If increases quality, assignable causes must

be incorporated into the process design


In-Control Process

If the Control Chart is Not Indicating Any Out-of-Control Condition, then Only common causes of variation exist It is sometimes said to be in a state of

statistical control If the common-cause variation is small, then

control chart can be used to monitor the process

If the common-cause variation is too large, the process needs to be altered


Types of Error

First Type: Belief that observed value represents special

cause when, in fact, it is due to common cause

Second Type: Treating special cause variation as if it is

common cause variation


Control Chart Patterns: How to tell the Process is Out of ControlUpper controlchart limit

Target

Lower controlchart limit

Normal behavior. One point out above.Investigate for cause.

One point out below.Investigate for cause.


Control Chart Patterns: How to tell the Process is Out of Control (Cont.)

Upper control limit

Target

Lower control limit

Run of 5 points belowcentral line. Investigate for cause.

Trends in eitherDirection.Investigate for cause of progressive change.

Erratic behavior. Investigate.


Control Chart Patterns: How to tell the Process is Out of Control cont.

Upper control chart limit

Target

Lower control chart limit

Two points near upper control. Investigatefor cause.

Two points near lowercontrol. Investigatefor cause.

Run of 5 points above central line. Investigate for cause.


Produce GoodProvide Service

Stop Process

Yes

No

Assign.Causes?Take Sample

Inspect Sample

Find Out WhyCreate

Control Chart

Start

Statistical Process Control Steps


4 Basic Types of Control Charts

Control Charts

For Variables For Attributes

Chart for meansof sample n

R Chart RangeOf sample n

p - Chart

Sample Size, n known

c - Chart

Sample Size, n unknown

X

What is the difference between Variables and Attributes?


Variables Control Charts: R Chart

Monitors Variability in Process Characteristic of interest is measured on

numerical scale Is a variables control chartvariables control chart

Shows Sample Range Over Time Difference between smallest & largest

values in inspection sample E.g., Amount of time required for luggage to

be delivered to hotel room


R Chart Control Limits

Sample Range at Time i or Subgroup i

# Samples

From Table 17.2 Page 683

4RUCL D R

3RLCL D R

1

k

ii

RR

k


R Chart Example

You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?


R Chart and Mean Chart Hotel Data

Sample SampleDay Average Range

1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22


R Chart Control Limits Solution

From Table 17.2 page 683 (n = 5)

1 3.85 4.27 4.223.894

7

k

ii

RR

k

4

3

2.114 3.894 8.232

0 3.894 0

R

R

UCL D R

LCL D R


R Chart Control Chart Solution

UCL

02468

1 2 3 4 5 6 7

Minutes

Day

LCL

R_


Variables Control Charts: Mean Chart (The Chart)

Shows Sample Means Over Time Compute mean of inspection sample over

time E.g., Average luggage delivery time in hotel

Monitors Process Average Must be preceded by examination of the R

chart to make sure that the process is in control

X


Mean Chart

Sample Range at Time i

# Samples

Sample Mean at Time i

Computed From Table 17.2 Page 683

2XUCL X A R

2XLCL X A R

1 1 and

k k

i ii i

X RX R

k k


Mean Chart Example

You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?


R Chart and Mean Chart Hotel Data

Sample SampleDay Average Range

1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22


Mean Chart Control Limits Solution

1

1

2

2

5.32 6.59 6.795.813

7

3.85 4.27 4.223.894

7

5.813 0.577 3.894 8.060

5.813 0.577 3.894 3.566

k

i

i

k

ii

X

X

XX

k

RR

k

UCL X A R

LCL X A R

From Table 17.2 Page 683(n = 5)


Mean Chart Control Chart Solution

UCL

LCL

02468

1 2 3 4 5 6 7

Minutes

Day

X__


R Chart and Mean Chartin PHStat

PHStat | Control Charts | R & Xbar Charts …

Excel Spreadsheet for the Hotel Room Example

Microsoft Excel Worksheet


Examples

17.8 Monitor the performance of Refrigerators. Calculate Upper and Lower Control Limits for Average and Range.

Overall average Temperature =46 o Fahrenheit Average Range is 2 o Fahrenheit Samples of 6 have been taken to get this data. (Samples

Size, n= 6)

17.10 Monitor the Weight of Cereal in Boxes. Calculate Upper and Lower Control Limits for Average and Range.

Overall average Weight = 17 grams Average Range is 0.5 grams Samples of 8 Boxes have been taken to get this data.

(Samples Size, n= 8)


Do Example 17.5

Time Sample Taken Box1 Box2 Box3 Box49 9.89 10.4 9.9 10.3

10 10.1 10.2 9.9 9.811 9.9 10.5 10.3 10.112 9.7 9.8 10.3 10.21 9.7 10.1 9.9 9.9

Total

Raw Data

Find UCL and LCL for Mean Chart and Range Chart.

You need to Know: -

1. the Mean of the Sample Averages (Symbol__)

2. the Mean of the Range (Symbol ___)

3. the Sample Size (Symbol n)


Other Examples

Do 17-12 for Homework


p Chart Control Chart for Proportions

Is an attribute chartattribute chart Shows Proportion of Nonconforming

(Success Success ) Items E.g., Count # of nonconforming chairs &

divide by total chairs inspected

Chair is either conforming or nonconforming Used with Equal or Unequal Sample Sizes

Over Time Unequal sizes should not differ by more than

±25% from average sample size


p Chart Control Limits

(1 )max 0, 3p

p pLCL p

n

(1 )3p

p pUCL p

n

1

k

ii

nn

k

Average Group Size

1

1

k

ii

k

ii

Xp

n

Average Proportion of Nonconforming Items

# Defective Items in Sample i

Size of Sample i

# of Samples


p Chart Example

You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?


p Chart Hotel Data

# NotDay # Rooms Ready Proportion

1 200 16 0.0802 200 7 0.0353 200 21 0.1054 200 17 0.0855 200 25 0.1256 200 19 0.0957 200 16 0.080


1

1

121.0864

1400

k

ii

k

ii

Xp

n

p Chart Control Limits Solution

16 + 7 +...+ 16

1 1400200

7

k

ii

nn

k

1 .0864 1 .08643 .0864 3

200

.0864 .0596 or .0268,.1460

p pp

n


Mean

p Chart Control Chart Solution

UCL

LCL

0.00

0.05

0.10

0.15

1 2 3 4 5 6 7

P

Day

Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.

p

p


p Chart in PHStat

PHStat | Control Charts | p Chart …

Excel Spreadsheet for the Hotel Room Example

Microsoft Excel Worksheet


Example

Day Number of Packages Late Packages1 136 42 153 63 127 24 157 75 144 56 122 57 154 68 132 39 160 8

10 142 711 157 612 150 913 142 814 137 1015 147 816 132 717 136 618 137 719 153 1120 141 7

The Delivery company wants to monitor its delivery service.

Draw a p-chart.

Does the process give an out of Control Signal? Control Chart Patterns:

How to tell if

the Process is

Out of Control


Worker Day 1 Day 2 Day 3 All Days

A 9 (18%) 11 (12%) 6 (12%) 26 (17.33%)

B 12 (24%) 12 (24%) 8 (16%) 32 (21.33%)

C 13 (26%) 6 (12%) 12 (24%) 31(20.67%)

D 7 (14%) 9 (18%) 8 (16%) 24 (16.0%)

Totals 41 38 34 113

Understanding Process Variability:

Red Bead Example

Four workers (A, B, C, D) spend 3 days to collect beads, at 50 beads per day. The expected number of red beads to be collected per day per worker is 10 or 20%.


Average Day 1 Day 2 Day 3 All Days

X 10.25 9.5 8.5 9.42

p 20.5% 19% 17% 18.83%


Example Calculations

113.1883

50(12)p

(1 ) .1883(1 .1883)3 .1883 3

50 .1883 .1659

p pp

n

_

.1883 .1659 .0224

.1883 +.1659 .3542

LCL

UCL


0 A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3


Example Control Chart

.30

.20

.10

p

UCL

LCL

_


Morals of the Example

Variation is an inherent part of any process. The system is primarily responsible for worker performance. Only management can change the system. Some workers will always be above average, and some will be below.


The c Chart

Control Chart for Number of Nonconformities (Occurrences) in a Unit (an Area of Opportunity) Is an attribute chartattribute chart

Shows Total Number of Nonconforming Items in a Unit E.g., Count # of defective chairs

manufactured per day Assume that the Size of Each Subgroup

Unit Remains Constant


c Chart Control Limits

3cLCL c c 3cUCL c c

1

k

ii

cc

k

Average Number of Occurrences

# of Samples

# of Occurrences in Sample i


c Chart: Example

You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?


c Chart: Hotel Data

# NotDay # Rooms Ready

1 200 162 200 73 200 214 200 175 200 256 200 197 200 16


c Chart: Control Limits Solution

1 16 7 19 1617.286

7

3 17.286 3 17.285 4.813

3 29.759

k

ii

c

c

cc

k

LCL c c

UCL c c


c Chart: Control Chart Solution

UCL

LCL0

10

20

30

1 2 3 4 5 6 7

c

Day

c

Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.

c


Example 17.8

Number of small paint errors on each Ornaments.

1. Draw a c-chart.2. Does the process give an out of Control

Signal?

Ornament Number 1 2 3 4 5 6 7 8 9 10Number of Defects 0 2 1 0 0 3 2 0 4 1Ornament Number 11 12 13 14 15 16 17 18 19 20Number of Defects 2 0 0 1 2 1 0 0 0 1


Example 17.8 (cont)

The same exercise is repeated one week later. Number of small paint errors on each Ornaments are recorded as follows.

1. Draw a c-chart.2. Does the process give an out of Control

Signal? Control Chart Patterns:

How to tell if

the Process is

Out of Control

Ornament Number 1 2 3 4 5 6 7 8 9 10Number of Defects 0 2 1 0 1 2 3 4 0 3Ornament Number 11 12 13 14 15 16 17 18 19 20Number of Defects 2 0 0 1 2 1 0 0 0 1


Chapter Summary

Described Total Quality Management (TQM)

Addressed the Theory of Management Deming’s 14 Points

Described the Six Sigma® Management Approach

Discussed the Theory of Control Charts Common-cause variation versus special-

cause variation


Chapter Summary

Computed Control Charts for the Mean and the Range

Computed Control Charts for the Proportion of Nonconforming Items

Described Process Variability Described c Chart

(continued)

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© 2003 Prentice-Hall, Inc. Quantitative Analysis Chapter 17 Statistical Quality Control Chap 17-1.

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