qctool- charts training

8/12/2019 QCtool- Charts Training

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Seven QC Tools for ProcessQuality Improvement


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Seven Major Tools1) Flowchart or process mapping

2) Check Sheet

3) Histogram4) Pareto Chart

5) Cause and Effect Diagram

6) Scatter Diagram

7) Control Chart


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Flowcharts or Run chart Used to explore if there is aprocess

A Flow Diagram, also known as a flow chart,is a diagramatic technique to document aprocedure, within a role or department."Structured" flow diagrams are created using

a single entry (with inputs), a single exit (withoutputs), and a combination of three buildingstructures:


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Building structures

sequence- any series of 1-n sequentialsteps can be represented as a singlestep

choice- a decision between two or morepaths (structured subpaths) [e.g., if-then, case/select]

loop- a structured subpath (single entryand single exit) that is executed 0-ntimes


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Check Sheets Also called: defect concentration

diagram

A check sheet is a structured, preparedform for collecting and analyzing data. This

is a generic tool that can be adapted for awide variety of purposes.


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Source:

http://www.hci.com.au/hcisite3/tool

kit/data.htm

Example :

The figure below shows a check sheet used to collect data

on telephone interruptions. The tick marks were added as

data was collected over several weeks.


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Data organizing tools

Once collected, raw data is typicallysummarized (reduced, or compacted)

this can be done in several ways

Histograms


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The Frequency Distributionand HistogramA frequency distribution shows how often each

different value in a set of data occurs.

A histogram is the most commonly used graphto show frequency distributions.

It looks very much like a bar chart, but thereare important differences between them.


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Parts of a HistogramHistogram

100

80

60

40

20

0

0

F

R

E

QU

E

N

CY5 10 15 20 25 30 35 40 45 50 55 60

Days of operation prior to

failure for an HF receiver1

3

2

4

1. Title , 2. Horizontal / X -axis , 3. Bars, 4. Vertical / Y -axis


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Histogram

Recorded are the percentages of code defects for 80 personnel

during development of s/w application.These are the data collected:

EXERCISE 1:

The source of data for the first exercise is the following scenario.A

list of the data collected follows this description


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HistogramEXERCISE 1:

PERCENT defects RECORDED

11 22 15 7 13 20 25 12 16 19

4 14 11 16 18 32 10 16 17 10

8 11 23 14 16 10 5 21 26 10

23 12 10 16 17 24 11 20 9 13

24 10 16 18 22 15 13 19 15 24

11 20 15 13 9 18 22 16 18 9

14 20 11 19 10 17 15 12 17 11

17 11 15 11 15 16 12 28 14 13


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Histogram

Step 1 -Count number of data points ANS : Total - 80

Step2 -Summarize on a tally sheet

Step3 -Compute the range

Largest value = XY Percent defect

Smallest value = XY Percent defect

Range of values = xyz Percent defect


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HistogramEXERCISE 1:

Step 1 Count number of data points

PERCENT Defects RECORDED

11 22 15 7 13 20 25 12 16 19

4 14 11 16 18 32 10 16 17 10

8 11 23 14 16 10 5 21 26 10

23 12 10 16 17 24 11 20 9 13

24 10 16 18 22 15 13 19 15 24

11 20 15 13 9 18 22 16 18 9

14 20 11 19 10 17 15 12 17 11

17 11 15 11 15 16 12 28 14 13

ANS : Total - 80


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EXERCISE 1:

Step 1 Summarize the data on a tally sheet

%Deft No.Of.Pers %Deft No.Of.Pers %Deft No.Of.Pers

0 0 11 9 22 3

1 0 12 4 23 2

2 0 13 5 24 3

3 0 14 4 25 1

4 1 15 7 26 1

5 1 16 8 27 0

6 0 17 5 28 1

7 1 18 4 29 0

8 1 19 3 30 0

9 3 20 4 31 0

10 7 21 1 32 1


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Histogram

Step3 -Compute the range

Largest value = 32 Percent Defects

Smallest value = 4 Percent Defects

Range of values = 28 Percent Defects


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Histogram

Step 4 -Determine number of intervals

IF YOU HAVE THIS

MANY DATA POINTS

USE THIS NUMBER OF

INTERVALS:

Less than 50 5 to 7 intervals

50 to 99 6 to 10 intervals

100 to 250 7 to 12 intervals

More than 250 10 to 20 intervals

ANS : Select 6 to 10 intervals - 8


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Histogram

Step 5 -Compute interval width

Interval

Width=

Range

Number of Intervals

= 3.5=

Round up to next

whole number

28

8

Use 8 for the number

of intervals


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Histogram

Step6 -Determine the starting point of each interval

Step7 -Count the number of points in each interval

INTERVAL

NUMBER

1

2

3

4

5

6

7

8

STARTING

VALUE

4

8

12

16

20

24

28

32

INTERVAL

WIDTH

+4

+4

+4

+4

+4

+4

+4

+4

ENDING

VALUE

8

12

16

20

24

28

32

36

NUMBER

OF COUNTS

3

20

20

20

10

5

1

1


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Histogram

Step8 -Plot the data

Step9 -Add the title and legend

18

14

10

4

0

0 4 8 12 16 20 24 28 32 36

20

16

12

8

2

6

Critical Defects

PERCENT Defect


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The Frequency Distributionand HistogramFrequency Distribution

Arrangement of data by magnitudeMore compact than a stem-and-leaf

display

Graphs of observed frequencies arecalled histograms.


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Pareto Chart A Pareto chart is a bar graph. The

lengths of the bars represent

frequency or cost (time or money), and

are arranged with longest bars on the

left and the shortest to the right. In this

way the chart visually depicts which

situations are more significant.


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Pareto Chart The Pareto chartis a frequency

distribution (or histogram) of attribute dataarranged by category.

Plot the frequency of occurrence of eachdefect type against the various defect types.

Also called: Pareto diagram, Pareto analysis

Variations: weighted Pareto chart,

comparative Pareto charts


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Why use Pareto chart Breaks big problem into smaller pieces

Identifies most significant factors

Shows where to focus efforts

Allows better use of limited resources

Pareto


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Pareto

Example

Pareto

40

28

1512

838.83

66.0280.58

92.23 100.00

05

1015202530

354045

Documents

Product

Quality

Packages

Delivery

Others

Category of Cost

CostAmoun

t$$

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Cumluative

Cost

Individual category

Cumulative Cost

E l


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ParetoExample

Figure 2 takes the largest category, documents, from Figure 1, breaks it down into

six categories of document-related complaints, and shows cumulative values.

If all complaints cause equal distress to the customer, working on eliminating

document-related complaints would have the most impact, and of those, working onquality certificates should be most fruitful..

Pareto

32

21

15

10837.21

61.63

79.07

90.70100.00

05

10

15

20

25

30

35

ODerrors

PMPerror

not

approved

Version

problem

Training

Category of Cause

Valuesincost

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Cumuvalueof

Costs

Individual cause

Cum cause


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Cause and Effect Diagram A Cause-and-Effect Diagram is a tool that helps

dentify,sort,and display possible causes of a specific problem

or quality characteristic (Viewgraph 1).It graphically illustrates

the relationship between a given outcome and all the factorsthat influence the outcome.

This type of diagram is sometimes called an "Ishikawa

diagram because it was invented by Kaoru Ishikawa,or a

"fishbone diagram"because of the way it looks.


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Cause and Effect Diagram

Variations: cause enumeration diagram, process

fishbone, time-delay fishbone, CEDAC (cause-and-

effect diagram with the addition of cards), desired-

result fishbone, reverse fishbone diagram

The fishbone diagram identifies many possible

causes for an effect or problem. It can be used to

structure a brainstorming session. It immediately

sorts ideas into useful categories.

Cause and Effect


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When should a team use a Cause-And-Effect

Diagram?

Identify the possible root causes ,the basic

reasons,for a specific effect, problem,or condition.

Sort out and relate some of the interactions among

the factors affecting a particular process or effect.

Analyze existing problems so that corrective action

can be taken.

Cause and Effect


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Why should we use a Cause-and-Effect

Diagram?

Helps determine the root causes of a problem or quality

characteristic using a structured approach.

Encourages group participation and utilizes group

knowledge of the process.

Uses an orderly,easy-to-read format to diagram cause-and-

effect relationships.

Indicates possible causes of variation in a process.

Increases knowledge of the process by helping everyone tolearn more about the factors at work and how they relate.

Identifies areas where data should be collected for further

study.

Cause and Effect


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Benefits of Using a Cause-and-Effect

Diagram

Helps determine root causes

Encourages group participation

Uses an orderly,easy-to-read format

Indicates possible causes of variation

Increases process knowledge Identifies areas for collecting data

Cause and Effect


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Step 1 Identify and Define the Effect Decide on the effect to examine

Use Operational Definitions

Phrase effect as

>positive (an objective)or

>negative (a problem)

Cause and Effect


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Step 21. Brainstorm the major categories of causes of the

problem. If this is difficult use generic headings:

Methods Machines (equipment)

People (manpower)

Materials

Measurement

Environment

Cause and Effect


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Step 31. Write the categories of causes as branches from the main

arrow.

Cause and Effect

EFFORT

CAUSE B CAUSE D

CAUSE A CAUSE C

Library-functionI/O and fileHardwareComputational


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ExceptionFailure

Standard libraries

not available

Standard libraries

modified

Incorrect return code

from external function

Incorrect parameters

passed to external

function

problem

File does not exist

File permissions

incorrect

File corrupted

problems

File moved

Invalid

filename

File locked by

another

program

Output file

already exists

Insufficient disk

space

Power outage

Spurious

interrupts

problems

Disconnected /

dismounted

Timeout

Transient errors

Corrupt memory

Crash

Divide by zero

Uninitialized

variable

Square root of a

negative number

problem

Type mismatch

Insufficient

precision

Over flow /

underflow

Null pointer and

memory problems

External user /

client problem

Return-value problem

function/procedure call

Data-input

problem

Incorrect delimiters

Non-numeric in

numeric field

Non-ASCII

Extraneous data

Missing data

Empty data file

Data values outside

of range

Missing end of File

Values of arguments

invalid

Wrong number of

argument

Failure to handle

error return code

Wrong type of

arguments

Erroneous

response to

prompt

Later response

to prompt

Incorrect

command line

arguments

No response to

prompt

Buffer overflow

Corrupt memory

Non- allocated

memory accessed

Insufficient memory

Memory allocation error

Illegal access

Array boundary violation

Invalid pointer dereferenced


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Scatter Diagram The scatter diagramis a plot of two variables that can be

used to identify any potential relationship between thevariables

The shape of the scatter diagram often indicates what typeof relationship may exist

The scatter diagram graphs pairs of numerical data, with one

variable on each axis, to look for a relationship betweenthem. If the variables are correlated, the points will fall alonga line or curve. The better the correlation, the tighter thepoints will hug the line.

Also called: scatter plot, X

Y graph


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ScatterScatter plot for relationship between apartment

size and its rent (n=25)

500700

900

1100

1300

1500

1700

1900

2100

2300

2500

500 700 900 1100 1300 1500 1700 1900 2100

Size

Rent

Scatter plot suggests that there is a positive, linear relationship between Rent and Size


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Example

If there are 24 data points.

To test for a relationship, they calculate:A = points in upper left + points in lower right = 8 + 9 = 17

B = points in upper right + points in lower left = 4 + 3 = 7Q = the smaller of A and B = the smaller of 7 and 17 = 7N = A + B = 7 + 17 = 24

Then they look up the limit for N on the trend test table. For N =24, the limit is 6.

Q is greater than the limit. Therefore, the pattern could haveoccurred from random chance, and no relationship is demonstrated.

Scatter


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Control Chart The control chart is a graph used to study how a process changes

over time. Data are plotted in time order. A control chart always hasa central line for the average, an upper line for the upper controllimit and a lower line for the lower control limit. These lines are

determined from historical data. By comparing current data to theselines, you can draw conclusions about whether the process variationis consistent (in control) or is unpredictable (out of control, affectedby special causes of variation).

Control charts for variable data are used in pairs. The top chartmonitors the average, or the centering of the distribution of datafrom the process. The bottom chart monitors the range, or thewidth of the distribution. If your data were shots in target practice,the average is where the shots are clustering, and the range is howtightly they are clustered. Control charts for attribute data are used

singly.


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What is control chartA statistical tool used to distinguish

between process variation resulting

from common causes and variation

resulting from special causes.

Control Chart


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Analyzing Process Performance

Why Control Charts?

Notice what the control charts dothey seek to identify if

the process is behaving one way or another. This, in

effect, is the same as asking if the process exists as awell-defined entity, where the past can be used to predict

the future, or if the process is so ill-defined and

unpredictable that the past gives little clue to the future.

Donald J. Wheeler, 1995


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Variations Different types of control charts can be used, depending upon the

type of data. The two broadest groupings are for variable data andattribute data.

Variable dataare measured on a continuous scale. Forexample: time, weight, distance or temperature can bemeasured in fractions or decimals. The possibility ofmeasuring to greater precision defines variable data.

Attribute dataare counted and cannot have fractions ordecimals. Attribute data arise when you are determining onlythe presence or absence of something: success or failure,accept or reject, correct or not correct. For example, areport can have four errors or five errors, but it cannot havefour and a half errors.

Control Chart


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Variables charts X and R chart (also called averages and range chart)

X and s chart

chart of individuals (also called X chart, X-R chart, IX-

MR chart, Xm R chart, moving range chart) moving averagemoving range chart (also called MA

MR chart)

target charts (also called difference charts, deviationcharts and nominal charts)

CUSUM (also called cumulative sum chart) EWMA (also called exponentially weighted moving

average chart)

multivariate chart (also called Hotelling T2)

Control Chart


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Attributes charts p chart (also called proportion chart)

np chart

c chart (also called count chart)

u chart

Control Chart

Charts for either kind of data

short run charts (also called stabilized chartsor Z charts)

group charts (also called multiplecharacteristic charts)


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Why should teams use Control

Charts? Monitor process variation over time.

Differentiate between special cause

and common cause variation.

Assess the effectiveness of changes

to improve a process.

Communicate how a processperformed during a specific period.

Control Chart


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Why to use Monitor process variation over time

Differentiate between special cause and common cause variation

Assess effectiveness of changes

Communicate process performance

When controlling ongoing processes by finding and correcting problems asthey occur.

When predicting the expected range of outcomes from a process.

When determining whether a process is stable (in statistical control).

When analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process).

When determining whether your quality improvement project should aim toprevent specific problems or to make fundamental changes to the process

Control Chart


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What are the types of Control Charts?

There are two main categories of Control Charts,those that

display attribute data ,and those that display variables

data .

While these two categories encompass a number of different types of Control

Charts,

there are three types that will work for the majority of the data analysis cases

you will encounter.In this module,we will study the construction and application in these three

types of Control Charts:

X-Bar and R Chart

Individual X and Moving Range Chart for Variables Data

Individual X and Moving Range Chart for Attribute Data

Control Chart


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Chart types studied in this module:

X-Bar and R Chart

Individual X and Moving Range Chart

-For Variables Data

-For Attribute Data

Other Control Chart types:

X-Bar and S Chart u Chart

Median X and R Chart p Chart

c Chart np Chart

Control Chart


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Detecting Signals

The simplest rule for detecting a signal (possible

assignable cause): a point outside the 3-sigma control

limits.

Many other sets of detection rules proposed.

makes the control chart more sensitive to signals

also leads to more false alarms decision on detection

rules should be based on economic trade-offs


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Stability Concepts

Stable process = Process In Statistical

Control

= Sources of Variability

Due to CommonCauses only


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Control Charts

Two broad classes of control charts

variable data, which is continuous

attribute data, which is discrete

Choice of what control chart to use should be based on

knowing the right assumptions!

Use the correct formulas for the kind of control

chart selected!


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The Distinction Between Variables Data and Attributes

Data

Variables data (sometimes called measu rement data)

are usual ly measurements of cont inuous phenomena.

Examples: measurements of length, weight, height,

volume, voltage, horsepower, torque, efficiency,

speed, and viscosity.

Software examples: elapsed time, effort expended,

years of experience, memory utilization, CPU

utilization, and cost of rework.


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The Distinction Between Variables Data and Attributes Data

Attributes data occur when information is recorded only

about whether an item conforms or fails to conform to a

specified criterion or set of criteria.

Attributes data almost always originate as counts.

Examples: the number of defects found, the number of

defective items found, the number of source statements ofa given type, the number of lines of comments in a module

of n lines, the number of people with certain skills or

experience on a project or team, and the percent of

projects using formal code inspections.


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Average - Range Control Charts

where X =X

number of samples

R =R

number of sample

D R and D R3 4

Control Limits for Mean:X A R2

Control Limits for Range:


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Sample

Size d2 A 2 D3 D4------------------------------------------------------------------

2 1.128 1.880 0 3.267

3 1.693 1.023 0 2.575

4 2.059 0.729 0 2.2825 2.326 0.577 0 2.116

6 2.534 0.483 0 2.004

10 3.078 0.308 0.233 1.777

15 3.472 0.223 0.348 1.65220 3.735 0.180 0.414 1.586

25 3.931 0.153 0.459 1.541


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0 1 2 3 4 5 6 7 8 9 10

Sample Number

MEAN

S

R

ANGES

UCL

CL

LCL

UCL

CL

LCL


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Detecting Instabilities and Out-of-Control Situations

To test for instabilities in processes, we examine

control charts for instances and patterns that signalnonrandom behavior.

Values falling outside the control limits and unusual

patterns within the running record suggest thatassignable causes exist.


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Detecting Instabilities and Out-of-Control SituationsTest 1: A single point falls outside the 3-sigma control

limits.

Test 2: At least two of three successive values fall on thesame side of, and more than two sigma units away from,

the center line.

Test 3: At least four out of five successive values fall on

the same side of, and more than one sigma unit awayfrom, the center line.

Test 4: At least eight successive values fall on the same

side of the center line.


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Useful Control Charts

Most likely to be of value for software processes

u-chart

XmR chart


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XmR Chart

When measurements are spaced widely in time orwhen each measurement is used by itself to

evaluate or control a process, a time-sequenced

plot of individual values, rather than averages,

may be all that is possible.


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XmR Chart

Control limits for Individuals Chart:

X-bar 3(MR-bar/d2)

Upper limit for Moving Range Chart:

D4MR-bar


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Week

First Quarter

Second Quarter

Third quarter

19 27 20 16 18 25 22 24 17 25 15 17

20 22 19 16 22 19 25 22 18 20 16 17

20 15 27 25 17 19 28

1 2 3 4 5 6 7 8 9 10 11 12

Each week, a system test organization reports the

number of critical problems that remain unresolved.

There is concern that week 31 value of 28 is higher than

would have been expected.

A control chart is constructed to investigate this possibility.


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