Chapter18 - Statistical Applications in Quality Mgt

Statistics for Managers

Using Microsoft® Excel

5th Edition

Chapter 18

Learning Objectives

In this chapter, you learn:



_{The basic themes of quality management and}

Deming’s 14 points



_{The basic aspects of Six Sigma management}



_{How to construct various control charts}



_{Which control chart to use for a particular}

type of data

Chapter Overview

Quality Management and

Tools for Improvement

Deming’s 14

Points

Six Sigma

®

Management

Process

Capability

Philosophy of

Quality

Tools for Quality

Improvement

Control

Charts

p chart

Total Quality Management



_{Primary focus is on process improvement}



_{Most variation in a process is due to the}

system, not the individual



_{Teamwork is integral to quality management}



_{Customer satisfaction is a primary goal}



_{Organization transformation is necessary}



_{It is important to remove fear}

Deming’s 14 Points

1. Create a constancy of purpose toward improvement



_{become more competitive, stay in business, and provide}

jobs

2. Adopt the new philosophy



_{Better to improve now than to react to problems later}

3. Stop depending on inspection to achieve quality -- build in

quality from the start



_{Inspection to find defects at the end of production is too}

late

4. Stop awarding contracts on the basis of low bids

Deming’s 14 Points

5. Improve the system continuously to improve quality and thus

constantly reduce costs

6. Institute training on the job



_{Workers and managers must know the difference between}

common cause and special cause variation

7. Institute leadership



_{Know the difference between leadership and supervision}

8. Drive out fear so that everyone may work effectively.

Deming’s 14 Points

10. Eliminate slogans and targets for the workforce



_{They can create adversarial relationships}

11. Eliminate quotas and management by numerical goals

12. Remove barriers to pride of workmanship

13. Institute a vigorous program of education and

self-improvement

The Shewhart-Deming Cycle

The

Shewhart-Deming

Cycle

The key is a

continuous cycle

of improvement

Act

Plan

Do

Six Sigma

®

Management

A method for breaking a process into a series of steps:



_{The goal is to reduce defects and produce near}

perfect results



_{The Six Sigma® approach allows for a shift of as}

much as 1.5 standard deviations, so is essentially a

±4.5 standard deviation goal



_{The mean of a normal distribution ±4.5 standard}

The Six Sigma

®

DMAIC Model

DMAIC represents



_{Define -- define the problem to be solved; list costs,}

benefits, and impact to customer



_{Measure – need consistent measurements for each}

Critical-to-Quality characteristic



_{Analyze – find the root causes of defects}



_{Improve – use experiments to determine importance}

of each Critical-to-Quality variable

Theory of Control Charts



_{A process is a repeatable series of steps}

leading to a specific goal



_{Control Charts are used to monitor variation}

in a measured value from a process



_{Inherent variation refers to process variation}

Theory of Control Charts



_{Control charts indicate when changes in data are due}

to:



_{Special or assignable causes}



_{Fluctuations not inherent to a process}



_{Data outside control limits or trend}



_{Represents problems to be corrected or improvements to}

incorporate into the process



_{Chance or common causes}



_{Inherent random variations}

Process Variation

Total Process

Variation

Common Cause

Variation

Special Cause

Variation

=

+



_{Variation is natural; inherent in the world}

around us



_{No two products or service experiences are}

exactly the same



_{With a fine enough gauge, all things can be}

Process Variation

Total Process

Variation

Common Cause

Variation

Special Cause

Variation

=

+



_People



_Machines



_Materials



_Methods



_Measurement



_Environment

Process Variation

Total Process

Variation

Common Cause

Variation

Special Cause

Variation

=

+

Common cause variation



_{naturally occurring and expected}



_{the result of normal variation in materials,}

Process Variation

Total Process

Variation

Common Cause

Variation

Special Cause

Variation

=

+

Special cause variation



_{abnormal or unexpected variation}



_{has an assignable cause}



_{variation beyond what is considered}

Control Limits

Process Average

UCL = Process Mean + 3 Standard Deviations

LCL = Process Mean – 3 Standard Deviations

UCL

LCL

+3σ

-

3σ

time

Control Chart Basics

Process Mean

UCL = Process Mean + 3 Standard Deviations

LCL = Process Mean – 3 Standard Deviations

UCL

LCL

+3σ

-

3σ

Common Cause

Variation: range of

expected

variability

Special Cause Variation:

Range of

unexpected

variability

Process Variability

Process Mean

UCL = Process Mean + 3 Standard Deviations

LCL = Process Mean – 3 Standard Deviations

UCL

LCL

±3σ

→ 99.7% of

process values should

be in this range

time

Special Cause of Variation:

Using Control Charts

Control Charts are used to check for process control

In-control Process



_{A process is said to be in control when the}

control chart does not indicate any

out-of-control condition



_{Contains only common causes of variation}



_{If the common causes of variation is small, then}

control chart can be used to monitor the process



_{If the common causes of variation is too large, you}

Process In Control



_{Process in control: points are randomly}

distributed around the center line and all

points are within the control limits

UCL

LCL

time

Process Not in Control

Out of control conditions:



_{One or more points outside control limits}



_{8 or more points in a row on one side of the}

center line



_{8 or more points in a row moving in the same}

Process Not in Control

One or more points outside

control limits

UCL

LCL

Eight or more points in a row on one

side of the center line

UCL

LCL

Eight or more points in a row

moving in the same direction

UCL

LCL

Process

Average

Process

Average

Out-of-control Processes



_{When the control chart indicates an}

out-of-control condition (a point outside the out-of-control

limits or exhibiting trend, for example)



_{Contains both common causes of variation and}

assignable causes of variation



_{The assignable causes of variation must be}

identified



_{If detrimental to the quality, assignable causes of}

variation must be removed

Control Chart for the

Proportion: p Chart



_{Control chart for proportions}



_{Is an attribute chart}



_{Shows proportion of nonconforming items}



_{Example -- Computer chips: Count the number}

of defective chips and divide by total chips

inspected



_{Chip is either defective or not defective}

Control Chart for the

Proportion: p Chart



_{Used with equal or unequal sample sizes}

(subgroups) over time



_{Unequal sizes should not differ by more than}

±25% from average sample sizes

Creating a p Chart



_{Calculate subgroup proportions}



_{Graph subgroup proportions}



_{Compute mean proportion}

Average of Subgroup

Proportions

The average of subgroup proportions =

p

where:

If equal sample sizes:

If unequal sample sizes:

Computing Control Limits



_{The upper and lower control limits for a p chart are}



_{The standard deviation for the subgroup proportions}

is

UCL = Average Proportion + 3 Standard Deviations

LCL = Average Proportion – 3 Standard Deviations

n

)

p

)(1

p

(

_

where:

Computing Control Limits



_{The upper and lower control limits for the p}

chart are

n

Proportions are never

negative, so if the

calculated lower

control limit is

p Chart Example

You are the manager of a 500-room hotel.

You want to achieve the highest level of

p Chart Example

# Not

Day

# Rooms

Ready

Proportion

1

200

16

0.080

2

200

7

0.035

3

200

21

0.105

4

200

17

0.085

5

200

25

0.125

6

200

19

0.095

p Chart Example

p = .0864

UCL = .1460

LCL = .0268

0.00

0.05

0.10

0.15

1

2

3

4

5

6

7

P

Day

Individual points are distributed around p without any pattern. Any

improvement in the process must come from reduction of

common-cause variation, which is the responsibility of management.

_

Understanding Process Variability:

Red Bead Experiment

The experiment:



_{From a box with 20% red beads and 80% white}

beads, have “workers” scoop out 50 beads



_{Tell the workers their job is to get white beads}



_{Some workers will get better over time, some will}

Morals of the

Red Bead Experiment

1.

Variation is an inherent part of any process.

2.

The system is primarily responsible for worker performance.

3.

Only management can change the system.

4.

Some workers will always be above average, and some will

be below.

5.

Setting unrealistic goals is detrimental to a firm’s

R chart and X chart



_{Used for measured numeric data from a}

process



_{Start with at least 20 subgroups of observed}

values



_{Subgroups usually contain 3 to 6}

observations each



_{For the process to be in control, both the R}

Example: Subgroups

Process measurements:

Subgroup measures

Subgroup

number

Individual measurements

(subgroup size = 4)

Mean, X

Range, R

1

Average

subgroup

mean

=

Average

subgroup

range =

R

The R Chart



_{Monitors variability in a process}



_{The characteristic of interest is measured on a}

numerical scale



_{Is a variables control}

_chart



_{Shows the sample range over time}



_{Range = difference between smallest and}

The R Chart

1.

Find the mean of the subgroup ranges (the

center line of the R chart)

2.

Compute the upper and lower control limits

for the R chart

3.

Use lines to show the center and control

limits on the R chart

4.

Plot the successive subgroup ranges as a

Average of Subgroup Ranges

k

R

R

_



i

Average of subgroup ranges:

where:

R

_i

= i

th

_{subgroup range}

R Chart Control Limits

The upper and lower control limits for an R chart are

)

R

(

D

LCL

)

R

(

D

UCL

3

4





where:

D

₄

and D

₃

are taken from the table

R Chart Example

You are the manager of a 500-room hotel.

You want to analyze the time it takes to

R Chart Example

Day

Subgroup

R Chart

Control Chart Solution

UCL = 8.232

0

2

4

6

8

1

2

3

4

5

6

7

Minutes

Day

LCL = 0

R = 3.894

_

The X Chart



_{Shows the means of successive subgroups}

over time



_{Monitors process average}



_{Must be preceded by examination of the R}

The X Chart



_{Compute the mean of the subgroup means (the}

center line of the X chart)



_{Compute the upper and lower control limits for}

the X chart



_{Graph the subgroup means}

Average of Subgroup

Means

k

X

X

_



i

Average of subgroup means:

where:

X

_i

= i

th

_{subgroup average}

Computing Control Limits



_{The upper and lower control limits for an X chart are}

generally defined as



_{Use to estimate the standard deviation of the}

process average, where d

2

is from appendix Table E.11

UCL = Process Average + 3 Standard Deviations

LCL = Process Average – 3 Standard Deviations

n

d

R

Computing Control Limits



_{The upper and lower control limits for an X chart are}

generally defined as



_so

UCL = Process Average + 3 Standard Deviations

LCL = Process Average – 3 Standard Deviations

Computing Control Limits

Simplify the control limit calculations by using

X Chart Example

You are the manager of a 500-room hotel.

You want to analyze the time it takes to

X Chart Example

Day

Subgroup

X Chart

Control Limits Solution

X Chart

Control Chart Solution

UCL = 8.061

LCL = 3.567

0

2

4

6

8

1

2

3

4

5

6

7

Minutes

Day

X = 5.814

__

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 customers’ expectations



_{The upper specification limit (USL) is the largest}

value that can be obtained and still conform to

customers’ expectations



_{The lower specification limit (LSL) is the smallest}

Estimating Process Capability



_{Must first have an in-control process}



_{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

Estimating Process Capability

For a characteristic with a LSL and a USL

Where

Z

is a standardized normal random variable



within

be

Estimating Process Capability

For a characteristic with only an USL

Where

Z

is a standardized normal random variable



within

be

Estimating Process Capability

For a characteristic with only a LSL

Where

Z

is a standardized normal random variable



within

be

will

P(outcome

Process Capability

Example

You are the manager of a 500-room hotel.

You have instituted a policy that 99% of all

luggage deliveries must be completed within

ten minutes or less. For seven days, you

Process Capability

Example

Day

Subgroup

Process Capability

Example

Therefore, we estimate that 99.38% of the luggage deliveries will

be made within the ten minutes or less specification. The process is

capable of meeting the 99% goal.

Capability Indices



_{A process capability index is an aggregate}

measure of a process’s ability to meet

specification limits



_{The larger the value, the more capable a}

C

_p

Index

A measure of potential process performance is the

Cp index

C

p

> 1 implies a process has the potential of having

more than 99.73% of outcomes within specifications

C

p

> 2 implies a process has the potential of meeting the

expectations set forth in six sigma management

spread

spread

ion

specificat

)

/

(

6

R

d

₂

process

LSL

USL

CPL and CPU

To measure capability in terms of actual process

performance:

CPL (CPU)

> 1 implies that the process mean is more

than 3 standard deviation away from the lower

(upper) specification limit

CPL and CPU



_{Used for one-sided specification limits}



_{Use CPU when a characteristic only has a UCL}



_{Use CPL when a characteristic only has an}

C

_pk

Index



_{The most commonly used capability index is the C}

_pk

_index



_{Measures actual process performance for characteristics with}

two-sided specification limits

C

pk

= min(CPL, CPU)



_C

_pk

_{= 1 indicates that the process average is 3 standard}

deviation away from the closest specification limit



_{Larger C}

_pk

_{indicates greater capability of meeting the}

Process Capability

Example

You are the manager of a 500-room hotel.

You have instituted a policy that all luggage

deliveries must be completed within ten

Process Capability

Chapter Summary



_{Reviewed the philosophy of quality management}



_{Deming’s 14 points}



_{Discussed Six Sigma}

®

Management



_{Reduce defects to no more than 3.4 per million}



_{Uses DMAIC model for process improvement}



_{Discussed the theory of control charts}



_{Common cause variation vs. special cause}

variation

Chapter Summary



_{Constructed and interpreted p charts}



_{Constructed and interpreted}

_{X and R charts}



_{Obtained and interpreted process capability}

measures