Business statistics a decision making approach 6th edition ch17ppln

Introduction to Control Charts  Control Charts are used to monitor variation in a measured value from a process  Exhibits trend  Can make correction before process is out of control

Chapter Goals

After completing this chapter, you should be able to:

 Use the seven basic tools of quality

 Construct and interpret x-bar and R-charts

 Construct and interpret p-charts

 Construct and interpret c-charts

Chapter Overview

Quality Management and Tools for Improvement

Deming’s 14 Points

Themes of Quality

Management

 Primary focus is on process improvement

 Most variations in process are due to systems

 Teamwork is integral to quality management

 Customer satisfaction is a primary goal

 Organization transformation is necessary

 It is important to remove fear

 Higher quality costs less

 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

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.

 9 Break down barriers between departments so

(continued)

Deming’s 14 Points

 10 Eliminate slogans and targets for the

workforce

 They can create adversarial relationships

 11 Eliminate quotas and management by

objectives

 12 Remove barriers to pride of workmanship

 13 Institute a vigorous program of education

and self-improvement

(continued)

Deming’s 14 Points

Juran’s 10 Steps to Quality

Improvement

 1 Build awareness of both the need for

improvement and the opportunity for improvement

 2 Set goals for improvement

 3 Organize to meet the goals that have been set

 4 Provide training

 5 Implement projects aimed at solving

problems

Juran’s 10 Steps to Quality

 10 Maintain momentum by building

improvement into the company’s regular systems

(continued)

The Deming Cycle

The Deming Cycle

The key is a continuous cycle of

Act

Plan

Do

The Basic 7 Tools

The Basic 7 Tools

The Basic 7 Tools

Cause 2 Cause 1

The Basic 7 Tools

The Basic 7 Tools

Examine the performance

of a process over time

time

(continued)

Introduction to Control

Charts

 Control Charts are used to monitor variation in

a measured value from a process

 Exhibits trend

 Can make correction before process is out of control

 A process is a repeatable series of steps

leading to a specific goal

 Inherent variation refers to process variation

that exists naturally This variation can be reduced but not eliminated

Common Cause Variation

Common cause variation

 naturally occurring and expected

 the result of normal variation in materials, tools, machines, operators, and the environment

Special Cause Variation

Special cause variation

 abnormal or unexpected variation

 has an assignable cause

 variation beyond what is considered inherent to the process

Statistical Process Control

Charts

 Show when changes in data are due to:

 Special or assignable causes

 Fluctuations not inherent to a process

 Represents problems to be corrected

 Data outside control limits or trend

 Common causes or chance

 Inherent random variations

 Consist of numerous small causes of random

Process Average

Control Chart Basics

UCL = Process Average + 3 Standard Deviations

Special Cause Variation:

Range of unexpected variability

time

Special Cause of Variation:

A measurement this far from the process average

is very unlikely if only expected variation is present

Statistical Process Control

Charts

Statistical Process Control Charts

X-bar charts and R-charts c-charts

Used for measured numeric data

Used for proportions (attribute data)

Used for number of attributes per sampling unit

p-charts

x-bar chart and R-chart

 Used for measured numeric data from a

Steps to create an x-chart

and an R-chart

 Calculate subgroup means and ranges

 Compute the average of the subgroup means and the average range value

 Prepare graphs of the subgroup means and ranges as a line chart

Steps to create an x-chart

17 16 21

…

15 9 18

…

11 15 20

…

14.5 13.0 19.0

…

6 7 4

…

Average subgroup

Average subgroup

Average of Subgroup Means and Ranges

where:

Computing Control Limits

 The upper and lower control limits for an x-chart are generally defined as

LCL

x UCL

Computing Control Limits

 Since control charts were developed before it

was easy to calculate σ, the interval was formed using R instead

 The value A 2 R is used to estimate 3σ , where

A 2 is from Appendix Q

 The upper and lower control limits are

) R ( A x

(continued)

where A 2 = Shewhart

Example: R-chart

 The upper and lower control limits for an R-chart are

) R ( D LCL

) R ( D UCL

x-chart and R-chart

UCL

LCL time

Using Control Charts

 Control Charts are used to check for process

control

H 0 : The process is in control

i.e., variation is only due to common causes

H A : The process is out of control

i.e., special cause variation exists

 If the process is found to be out of control,

steps should be taken to find and eliminate the special causes of variation

Process In Control

 Process in control: points are randomly distributed around the center line and all points are within the control limits

UCL

LCL

x

x

Process Not in Control

Out of control conditions:

 One or more points outside control limits

 Nine or more points in a row on one side of the center line

 Six or more points moving in the same direction

 14 or more points alternating above and below the center line

Process Not in Control

 One or more points outside

control limits

UCL

LCL

x

 Nine or more points in a row

on one side of the center line

UCL

LCL

x

 Six or more points moving in

the same direction

UCL

 14 or more points alternating above and below the center line

UCL

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

 If increases quality, assignable causes must be incorporated into the process design

 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

 Finding a defective chip can be classified a

 Used with equal or unequal sample sizes

(subgroups) over time

 Unequal sizes should not differ by more than ±25% from average sample sizes

 Easier to develop with equal sample sizes

 Should have np > 5 and n(1-p) > 5

(continued)

Creating a p-Chart

 Calculate subgroup proportions

 Compute the average of the subgroup proportions

 Prepare graphs of the subgroup proportions as a line chart

 Compute the upper and lower control limits

 Use lines to show the control limits on the

p-Chart Example

Subgroup number

Sample size

Number of successes Proportion, p

1 2 3

…

150 150 150

15 12 17

…

10.00 8.00 11.33

…

Average subgroup proportion = p

Computing Control Limits

 The upper and lower control limits for an p-chart are

LCL

p UCL

Standard Deviation of Subgroup Proportions

 The estimate of the standard deviation for

the subgroup proportions is

n

) p )(1

sample size

p

s

Computing Control Limits

 The upper and lower control limits for the

p-chart are

(continued)

) p )(1 p (

n

) p )(1 p

( p

LCL

) s ( p

if the calculated lower control limit

is negative, set LCL = 0

 Control chart for number of nonconformities

(occurrences) per sampling unit (an area of opportunity)

 Also a type of attribute chart

 Shows total number of nonconforming items

Mean and Standard Deviation

c-Chart Control Limits

c c

LCL

c c

Process Control

Determine process control for p-chars and c-charts using the same rules as for x-bar and R-charts

Out of control conditions:

 One or more points outside control limits

 Nine or more points in a row on one side of the center line

 Six or more points moving in the same direction

 14 or more points alternating above and below the center

c-Chart Example

 A weaving machine makes

cloth in a standard width

Random samples of 10 meters

of cloth are examined for flaws

Is the process in control?

Sample number 1 2 3 4 5 6 7 Flaws found 2 1 3 0 5 1 0

Constructing the c-Chart

 The mean and standard deviation are:

1.7143 7

0 1

5 0

3 1

2 k

x

c   i        

1.3093 1.7143

c

s   

2.214 3(1.3093)

1.7143 c

3 c

LCL

5.642 3(1.3093)

1.7143 c

3 c

The completed c-Chart

The process is in control Individual points are distributed around

0

Chapter Summary

 Reviewed the philosophy of quality management

 Demings 14 points

 Juran’s 10 steps

 Described the seven basic tools of quality

 Discussed the theory of control charts

 Common cause variation vs special cause variation

 Constructed and interpreted x-bar and R-charts

 Constructed and interpreted p-charts