Chapter 18 Student Lecture Notes 18-1 · PDF fileChapter 18 Student Lecture Notes 18-1 ... Statistical Applications in Quality and Productivity ... It is sometimes said to be in a

Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.

Chapter 18 Student Lecture Notes 18-1

© 2004 Prentice-Hall, Inc.

Basic Business Statistics(9th Edition)

Chapter 18Statistical Applications in Quality and Productivity Management

Chap 18-1

© 2004 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 ChartsCommon-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 PhilosophyBetter to be proactive and change before

crisis occurs.Point 3. Cease Dependence on Mass

Inspection to Achieve QualityAny 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 theShewhart-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.


8. Drive Out Fear9. Break Down Barriers between Staff Areas10. Eliminate Slogans11. Eliminate Numerical Quotas for Workforce and Numerical Goals for Management12. 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 TransformationContinually 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 MillionA Method for Breaking Processes into a Series of Steps in Order to Eliminate Defects and Produce Near Perfect Results

(1) Define: Define the problem along with costs, benefits and the impact on customers(2) Measure: Develop operational definitions for each Critical-to-Quality characteristic and verify measurement procedure to achieve consistency over repeated measurements


Six Sigma® Management

(3) Analyze: Use control charts to monitor defects and determine the root causes of defects(4) Improve: 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) Control: 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 DataExhibit trend - make correction before process is out of control

A Process - A Repeatable Series of Steps Leading to a Specific Goal


Control Charts

Show When Changes in Data are Due to:Special or assignable causes

Fluctuations not inherent to a processRepresent problems to be correctedData outside control limits or trend

Chance or common causesInherent random variationsConsist of numerous small causes of random variability

(continued)


Graph of sample data plotted over time

Process Control Chart

020406080

1 2 3 4 5 6 7 8 9 101112

X

Time

Special Cause Variation

Common Cause Variation

Process Average ±3σ

Mean

UCL

LCL




Control Limits

UCL = Process Average + 3 Standard DeviationsLCL = Process Average - 3 Standard Deviations

Process Average

UCL

LCL

X

+ 3σ

- 3σ

TIME


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


Comparing Control Chart Patterns

X XX

Common Cause Variation: No Points

Outside Control Limits

Special Cause Variation: 2 Points

Outside Control Limits

Downward Pattern: No Points Outside Control Limits but

Trend Exists




When to Take Corrective Action

Corrective Action Should Be Taken When Observing Points Outside the Control Limits or when a Trend Has Been Detected

Eight consecutive points above the center line (or eight below)Eight consecutive points that are increasing (decreasing)


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 variationThe assignable causes of variation must be identified

If detrimental to quality, assignable causes of variation must be removedIf 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 existIt 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 processIf the common-cause variation is too large, the process needs to be altered




p Chart

Control Chart for ProportionsIs an attribute chart

Shows Proportion of Nonconforming ItemsE.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 )3pp pLCL p

n−

= −(1 )3p

p pUCL pn−

= +

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 Proportion1 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 .08641400

k

ii

k

ii

Xp

n

=

=

= = =∑

∑

p Chart Control Limits Solution

16 + 7 +...+ 16

1 1400 2007

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

LCL0.000.050.100.15

1 2 3 4 5 6 7

P

DayIndividual 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


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%

Understanding Process Variability:Example Calculations

113 .188350(12)

p = =(1 ) .1883(1 .1883)3 .1883 3

50 .1883 .1659

p ppn− −

± = ±

= ±

_

.1883 .1659 .0224

.1883 +.1659 .3542LCLUCL

= − == =




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

Understanding Process Variability:Example Control Chart

.30

.20

.10

p

UCL

LCL

_


Morals of the Example

Variation is an inherent part of any process.The system is primarilyresponsible for workerperformance.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 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 Ready1 200 162 200 73 200 214 200 175 200 256 200 197 200 16




c Chart: Control Limits Solution

1 16 7 19 16 17.2867

3 17.286 3 17.285 4.813

3 29.759

k

ii

c

c

cc

kLCL c c

UCL c c

= + + + += = =

= − = − =

= + =

∑ L


c Chart: Control Chart Solution

UCL

LCL0102030

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


Variables Control Charts: R Chart

Monitors Variability in ProcessCharacteristic of interest is measured on numerical scaleIs a variables control chart

Shows Sample Range Over TimeDifference between smallest & largest values in inspection sampleE.g., Amount of time required for luggage to be delivered to hotel room




R Chart Control Limits

Sample Range at Time i or Sample i

# Samples

From Table4RUCL 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 Range1 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 (n = 5)

1 3.85 4.27 4.22 3.8947

k

ii

RR

k= + + +

= = =∑ L

4

3

2.114 3.894 8.232

0 3.894 0R

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 TimeCompute mean of inspection sample over timeE.g., Average luggage delivery time in hotel

Monitors Process AverageMust 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

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





Mean Chart Control Limits Solution

1

1

2

2

5.32 6.59 6.79 5.8137

3.85 4.27 4.22 3.8947

5.813 0.577 3.894 8.060

5.813 0.577 3.894 3.566

k

ii

k

ii

X

X

XX

k

RR

k

UCL X A R

LCL X A R

=

=

+ + += = =

+ + += = =

= + ⋅ = + ⋅ =

= − ⋅ = − ⋅ =

∑

∑

L

L

From Table E.9 (n = 5)


Mean Chart Control Chart Solution

UCL

LCL02468

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




Process CapabilityProcess Capability is the Ability of a Process to Consistently Meet Specified Customer-Driven RequirementsSpecification Limits are Set by Management in Response to Customer’s ExpectationsThe Upper Specification Limit (USL) is the Largest Value that Can Be Obtained and Still Conform to Customer’s ExpectationThe Lower Specification Limit (LSL) is the Smallest Value that is Still Conforming


Estimating Process Capability

Must Have an In-Control Process First

Estimate the Percentage of Product or Service Within Specification

Assume the Population of X Values is Approximately Normally Distributed with Mean Estimated by and Standard Deviation Estimated by

X2/R d



For a Characteristic with an LSL and a USL

where Z is a standardized normal random variable

(continued)

2 2

P(an outcome will be within specification) P( )

= P/ /

LSL X USL

LSL X USL XZR d R d

= < <

⎛ ⎞− −⎜ ⎟< <⎜ ⎟⎝ ⎠





For a Characteristic with Only a LSL


(continued)

2


= P/

LSL X

LSL X ZR d

= <

⎛ ⎞−⎜ ⎟<⎜ ⎟⎝ ⎠



For a Characteristic with Only a USL


(continued)

2


= P/

X USL

USL XZR d

= <

⎛ ⎞−⎜ ⎟<⎜ ⎟⎝ ⎠


You’re manager of a 500-room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect dataon 5 deliveries per day. Is the process capable?

Process Capability Example




Process Capability:Hotel Data



Process Capability:Hotel Example Solution

5.813X = 3.894R = 2and 2.326d =

P(A delivery is made within specification)= P( 10)

10 5.813= P3.894 / 2.326

= P( 2.50) .9938

X

Z

Z

<

−⎛ ⎞<⎜ ⎟⎝ ⎠

< =

5n =

Therefore, we estimate that 99.38% of the luggage deliveries will be made within the 10 minutes or less specification. The process is capable of meeting the 99% goal.


Capability Indices

Aggregate Measures of a Process’ Ability to Meet Specification Limits

The larger (>1) the values, the more capable a process is of meeting requirements

Measure of Process Potential Performance

Cp>1 implies that a process has the potential of having more than 99.73% of outcomes within specifications

( )2

specification spreadprocess spread6 /p

USL LSLCR d−

= =




Capability Indices

Measures of Actual Process PerformanceFor one-sided specification limits

CPL (CPU) >1 implies that the process mean is more than 3 standard deviations away from the lower (upper) specification limit

(continued)

( )23 /X LSLCPL

R d−

=

( )23 /USL XCPU

R d−

=


Capability Indices

For two-sided specification limits

Cpk = 1 indicates that the process average is 3 standard deviations away from the closest specification limitLarger Cpk indicates larger capability of meeting the requirements

(continued)

( )min ,pkC CPL CPU=


You’re manager of a 500-room hotel. You have instituted a policy that all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day. Compute an appropriate capability index for the delivery process.

Process Capability Example




Process Capability:Hotel Data



Process Capability:Hotel Example Solution

5.813X = 3.894R = 2and 2.326d =5n =

Since there is only the upper specification limit, we need to only compute CPU. The capability index for the luggage delivery process is .8337, which is less than 1. The upper specification limit is less than 3 standard deviations above the mean.

( ) ( )2

10 5.813 0.8336723 3.894 / 2.3263 /

USL XCPUR d− −

= = =


Chapter Summary

Described Total Quality Management (TQM)Addressed the Theory of Management

Deming’s 14 Points

Described the Six Sigma® Management ApproachDiscussed the Theory of Control Charts

Common-cause variation versus special-cause variation




Chapter Summary

Computed Control Charts for the Proportion of Nonconforming ItemsDescribed Process VariabilityDescribed c ChartComputed Control Charts for the Mean and the RangeDiscussed Process Capability

(continued)

Documents

Chapter 18 Student Lecture Notes 18-1 · PDF fileChapter 18 Student Lecture Notes 18-1 ... Statistical Applications in Quality and Productivity ... It is sometimes said to be in a