© 2004 prentice-hall, inc. basic business statistics (9 th edition) chapter 18 statistical...

© 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 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.


8. Drive Out Fear

9. Break Down Barriers between Staff Areas

10. Eliminate Slogans

11. Eliminate Numerical Quotas for Workforce and Numerical Goals for Management

12. 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


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

Chance or common causes Inherent random variations Consist 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

Mean

UCL

LCL


Control Limits

UCL = Process Average + 3 Standard Deviations

LCL = Process Average - 3 Standard Deviations

Process Average

UCL

LCL

X

+ 3

- 3

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 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


p Chart Control Chart for Proportions

Is an attribute chartattribute chart Shows Proportion of Nonconforming 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 )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


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


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 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 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 (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

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


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 E.9 (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


Process Capability Process Capability is the Ability of a Process

to Consistently Meet Specified Customer-Driven Requirements

Specification Limits are Set by Management in Response to Customer’s Expectations

The Upper Specification Limit (USL) is the Largest Value that Can Be Obtained and Still Conform to Customer’s Expectation

The 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

X

2/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 XZ

R d R d



For a Characteristic with Only a LSL


(continued)

2


P( )

= P/

LSL X

LSL XZ

R d



For a Characteristic with Only a USL


(continued)

2


P( )

= P/

X USL

USL XZ

R 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


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


Process Capability:Hotel Example Solution

5.813X 3.894R 2and 2.326d

P(A delivery is made within specification)

= P( 10)

10 5.813= P

3.894 / 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 spread

process spread6 /p

USL LSLC

R d


Capability Indices

Measures of Actual Process Performance For 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 limit

Larger 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


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


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 5.8130.833672

3 3.894 / 2.3263 /

USL XCPU

R d


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 Proportion of Nonconforming Items

Described Process Variability Described c Chart Computed Control Charts for the Mean

and the Range Discussed Process Capability

(continued)

© 2004 prentice-hall, inc. basic business statistics (9 th edition) chapter 18 statistical...

Documents