SPC Course Material

7/29/2019 SPC Course Material

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Zero Defect ConsultantsStatistical Process Control

Rev No:04, Date: 02.01.2010 1

WELCOME TO ALL


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Training Contents

Day 1:-

Introduction to SPC

Types of Process Controls

Introduction to Statistics

Understanding Mean, Mode, Median, Range, Standard Deviation

Concept of Variation Special cause & common causes

Stable & Unstable Process

Approach towards identification of Special Causes

Histogram An illustration

Normal Distribution

Process Capability


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Training Contents

Day 2:-

Introduction to Control Charts

Types of Control Charts

Understanding application, methodology, interpretations of varioustypes of charts (Variable and Attribute type covered)

Exercises on Control Charts

SPC implementation methodology

Role of Operator in implementing SPC.

Common mistakes done in implementing SPC

Conclusion


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Introduction to SPC

Process:-

Convert input to output using Man, Machine, Material, Method,

Measurement.

Process(Man, M/c, Material,

Method)

Input Output

Measure & give

Feedback


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Process Control:-

Variation in the output of the process is natural. Hence the process needs to

be controlled in order to ensure that output is meeting the customer

requirements.

Tools for Process Control:-

Detection :- A strategy that attempts to identify unacceptable output

after it has been produced and then separate it from the good output.

Prevention :- A future oriented strategy by analysis and action toward

correcting the process itself so that unacceptable parts will not be

produced.


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Need for Process Control

Detection :- Tolerates Waste

Prevention :- Avoids Waste


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Techniques for Process Control

Mistake Proofing :- In this technique 100% process control is achieved by

preventing all types of failures by using modern techniques to get defect

free product. Here causes are prevented from making the effect.

100% Inspection : In this technique 100% checking of all the parameters of

all products has been done to get defect free product. Here only defects are

detected.

Statistical Process Control : In this Statistical technique such as ControlChart, Histogram etc. are used to analyses the process to achieve and

maintain state of statistical control to get defect free product. Causes are

detected and prompting CA before defect occurs


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Statistics

Collection of Data, Analysis and Conclusion

It is a value calculated from or based upon sample data (e.g. a subgroup

average or range) used to make inferences about the process that produces

the output.

E.g. Analysis of rejection data and initiating actions to reduce the rejection

level.


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What is Statistical Process Control

The use of Statistical techniques such as control charts to analyze a process

or its outputs so as to take appropriate actions, to achieve and maintain a

state of statistical control and to improve the process capability.

SPC is

A tool to detect variation

It identifies problems, it does not solve problems


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Introduction to Statistics

Data:

Any facts or numbers or observations made.

Set of observations forms the data.

Types of Data:

Variable data

Attribute data


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Variable DataData generated by

Physically measuring the characteristic using an

instrument

Assigning an unique value to each item

Examples:

Hardness, Strength, Weight, Diameter, etc.


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Attribute DataData generated by

Classifying the items into different groups based on some criteria

No physical measurement is involved

All the items classified into a group will have same value I.e OK

or Not Ok.

Examples:

Sex, Shade Variation, Surface Defects, Go-No GO, etc.


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Statistical Properties of Data

Observations collected needs to be analyzed using various properties.

Statistical properties of data helps in arriving at one value representing

all observations.

Two types of properties

Measure of location

Measure of Dispersion


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Measure of Location

Mean (Average)

Median

Mode

Measure of Dispersion

Range

Standard Deviation


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Mean: Numerical value indicating the central value of data

Sum of all data / Total number of data

Suppose x1

, x2

, - - - xn

be the data, then

Mean = (x1+ x2 + - - -+ xn ) / n = xi /n

Example Hardness Data

Mean:

= (55 + 65 + 59 + 59 + 57 + 61 + 53 + 63 + 59 + 57 + 63 + 55 + 61 + 61 + 57 +

59 + 61 + 57 + 59 + 63) / 20

= 1184 / 20 = 59.2


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Median:

Middle Value

Value which divides data arranged in ascending or descending order

into two equal halves

Case 1: Total number of data is odd

Median: Middle Value

Case 2: Total number of data is even

Median: Average of two middle values


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Median: ExampleProductivity Data

0.97 0.98 0.98 0.99 0.99 0.99 0.99 1.00 1.00 1.00

1.00 1.00 1.01 1.01 1.01 1.01 1.02 1.02 1.02 1.03

Total Number of data: 20 (even)

The middle Values : 1.00 & 1.00 (10th value and 11th value)

Median: Average of 2 middle value

(1.00 + 1.00) / 2 = 1.00


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Mode:

Highest no. of times an observation has occurred (Highest frequency)

Mode: ExampleProductivity Data

0.97 0.98 0.98 0.99 0.99 0.99 0.99 1.00 1.00 1.001.00 1.00 1.01 1.01 1.01 1.01 1.02 1.02 1.02 1.03

0.97 - 1

0.98 - 2

0.99 - 41.00 - 5 - 1.00 is Mode as this occurred more no. of times

1.01 - 4

1.02 - 3

1.03 - 1


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Range: Definition

Range: Maximum value Minimum Value

Example:

5 4 7 3 2

15 9 8 5 2

Maximum Value = 15

Minimum Value = 2

Range = 15 2 = 13

Range: Issues

It depends only on extreme values

Hence affected by outliers


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Range: Issues

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10

Range

f C l


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Standard Deviation: Definition

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10

Square root of the average squared deviation from mean

Indicates On an average how much each value is away from the Mean

Z D f C l


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Below data indicates the Money held by ten students in a class room.

Standard Deviation: Example:

5 4 7 3 2

15 9 8 5 2

Step 1:

Calculate Mean

Mean = 6

Z D f t C lt t


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5 4 7 3 2

15 9 8 5 2

Step 2:

Take deviations from Mean

-1 -2 1 -3 -4

9 3 2 -1 -4

Z D f t C lt t


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Step 2:

Take deviations from Mean

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10

Z D f t C lt t


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Step 3:

Since some values are positive & rest are negative, while

taking sum they will cancel out.So square the values & Sum

1 4 1 9 16

81 9 4 1 16

Sum = 142

Z D f t C lt t


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Step 4:

Standard Deviation = (Sum of Squares / (n -1))

= (142 / (10 -1))

= 15.77 = 3.972

Z D f t C lt t


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Variation No two things are exactly alike

It is impossible to produce or process two items exactly alike

Variation is natural.

Z D f t C lt t


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Example:

Time to reach office : 9:30 am

It is not possible to reach office exactly at 9:30 everyday

Normally there will be a small variation around 9:30 as follows:

9:31 9:33 9:28 9:29 9:25

9:34 9:26 9:27 9:34 9:31

This small variation is difficult to explain.

Zero Defect Consultants


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Generally

Looking at the past values, it is possible to give some rangearound 9:30 am (e.g.: 9:30 5 Minutes) to reach office

Normally it is possible to reach office within this range

SupposeA particular day , there is vehicle break down

that day it may not be possible to reach office at 9:30 5 Minutes

Say, you reach office at 9:50 am

In other words

If you reach office too late (beyond normal range of 9:30 5 minutes),

there will be some special reason for that or

it is easy to find out the reason for such variation



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Assignable Cause of Variation (Special Causes)

Variations of large magnitude

Easy to identify the causes of variation

Easy to eliminate the cause of variation

Common Cause of Variation

Variations of small magnitude

Difficult to identify the causes of variation

Difficult to eliminate the cause of variation



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Local Actions

Are usually required to eliminate special causes of Variation

Can usually taken by the people close to the process

Can correct typically about 15% of process problem

Actions on the System

Are usually required to reduce the variation due to common causes

Almost always require management actions for correction

Are needed to correct typically about 85% of process problems



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Stable Process

No Assignable Causes are present

Process is operating under common causes only

Stable process will be predictable & Statistically under control.

If a process is stable & the data follows normal distribution

Then the variation will be Mean 3 x Standard deviation

Unstable Process

Assignable Causes are present

Process is operating under assignable & common causes.

Unstable process is unpredictable & not under Statistical control.



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Methodology to Identify Assignable Causes

The success of any SPC program is not in our ability to collect data, draw

charts etc., but in effectively identifying and eliminating assignable causes.

Assignable causes are those causes that do not allow one to predict the

behavior of processes.

There is no meaning in calculating Process Capability without having a

predictable process.

Many companies have initiated SPC charts. But the charts do not benefit

them. One of the main reason for this is that they have not stopped theprocess when an assignable cause is indicated and eliminated the cause



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Methodology to Identify Assignable Causes

Before starting the SPC data collection, let us do the following steps:

1. Identify the characteristic for which SPC is to be done.

2. Have a brainstorming to list all the causes that may influence the

variation in this characteristic

3. Prepare a Cause & Effect Diagram

4. Prepare a Master Cause Analysis Table (Annexure 1)

5. Prepare a Why-Why Analysis Table (Annexure 2)

6. Identify factors that may affect Average and those that may affect Range

After completion of the above, plan for data collection & implementation ofSPC.



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Master Cause Analysis (Annexure 1)

Sl.No.

Cause Is therea spec?

If so,what is

thespec?

Basis forthe

spec.

Is itchecked andhow?

What isthe

actual?

Diff.in

Spec.Vs

Actual

Actionplan



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Why Why Analysis (Annexure 2)

Sl.No.

Cause WHY WHY WHY WHY WHY



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HISTOGRAM Histogram is a graphical representation of data and shows the

frequency of data.

Histogram provides the easiest way to understand the distribution of

data. It gives the Birds eye view of the variation in Data set.

Portrays the information on location, spread and shape that enables

the user to interpret the Process behavior.

It indicates whether the process is operating under Normal / stable

conditions.



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DEFINITIONSClass:- Is a category with lower and upper boundary value.

Class Width:- Width of the class.

Frequency:- No. of observations falling in the class.



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STEPS FOR CONSTRUCTING HISTOGRAM

Collect Min 50 no. of readings (N). 50 readings should be continuous

data.

Determine Max value and Min value & Calculate Range.

Range = Max Min.

Record the measurement unit (MU) used. This is usually controlled by

the measuring instrument least count.



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Contd.. Determine No. of classes (k), as below.

No. of Class (k) = N

Determine Class Width (CW), as below

Class Width (CW) = Range / k

Construct the Frequency Distribution Table, as shown in the next

slide.



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Where L1 = Minimum value (1/2*Measurement Unit)

U1 = L1 + Class Width

L2 = U1,

U2 = L2 + Class Width & so on.

Class Tally Frequency

L1 U1

L2 U2

Upto Max value

Total N

Frequency Distribution Table



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Contd.. Determine the axis for the graph. Place Class on X axis and

Frequency on Y axis.

Mark off the classes, and draw rectangles with heights corresponding

to the measurement frequencies in that class. Title the histogram. Give an overall title and identify each axis.



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HISTOGRAM

GRAPHICAL REPRESENTATION.



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HISTOGRAM

INTERPRETATIONS:NORMAL

Depicted by a bell-shaped curve. Most frequent measurement

appears as center of distribution & less frequent measurements taper

gradually at both ends of distribution.

Indicates that a process is running normally (only common causes are

present).



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HISTOGRAM

INTERPRETATIONS:BIMODAL

Distribution appears to have two peaks. May indicate that data from

more than one process are mixed together

Materials may come from 2 separate vendors

Samples may have come from 2 separate machines.



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HISTOGRAM

INTERPRETATIONS:SKEWED

Appears as an uneven curve; values seem to taper to one side.

Can be skewed left side or right side.



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Normal Distribution

Consider the following data on the case depth(mm) of 9 jobs:2.3 2.7 2.4 2.6 2.5

2.5 2.4 2.5 2.6

Plot of the Data:

0

1

2

3

4

2.2 2.3 2.4 2.5 2.6 2.7 2.8



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Plot of the Data:

0

1

2

3

2.3 2.4 2.5 2.6 2.7

Bell Shaped

Symmetric

Total Area under the curve is 1

Then : Normal Curve & Data follows Normal Distribution



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e o e ect Co sulta tsStatistical Process Control

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Standard Normal Distribution:

If

Data follows Normal Distribution then

(Data - Mean) / SD will follow Standard Normal Distribution

For Standard Normal Distribution:

Mean = 0

SD = 1



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Statistical Process Control

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Standard Normal Distribution: Properties

0

1

2

3

4

-3 -2 -1 0 1 2 3

68.26%

95.46%

99.73%



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Normal Distribution: Properties

Between

Mean 1 SD : 68.26 % of Values will lie





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Process Capability

A methodology to check whether a process is capable of meeting customerrequirements

Determined by the variation that comes from common causes

Expressed as Process Capability Indices

This needs to be demonstrated when process is being under statistical control

Process Capability Indices

1. Process Performance Index ( Pp & Ppk )

2. Process Capability Index ( Cp & Cpk )

Process Capability Study

1. Process performance Study (Pp & Ppk)

2. Process Capability Study (Cp & Cpk)



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Process Capability Index (Cp)

A methodology to check whether the process have the potential to meet the

customer requirements

Generally

Customer requirements are given as specification on product characteristics

Example

Specification on Heat Treatment Process:

Hardness should be within 55 5 HRC



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Customer Requirement:

Variation allowed by the customer OrVariation acceptable to customer

Example:

Specification: 55 5 HRC

Meaning:

As long as Hardness of the heat treated jobs are between 50 HRC to 60

HRC, Customer is satisfied

Customer requirements are also expressed as

Lower Specification Limit (LSL) = 50 HRC

Upper Specification Limit (USL) = 60 HRC



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Process Capability Index (Cp):

A process have the potential to meet customer requirement, ifTotal variation in process < Allowed variation

Example:

Specification: 55 5 HRC

Allowed variation = 50 HRC to 60 HRC

Total Variation = 52 HRC to 58 HRC

Total Variation < Allowed variation

Hence

Process have the potential to satisfy customer



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Example:Specification: 55 5 HRC

Allowed variation = 50 HRC to 60 HRC

Total Variation = 48 HRC to 62 HRC

Total Variation > Allowed Variation

Then

Process doesnt have the potential to satisfy customer



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Process capability Index Cp:

If the data is normally distributed, then

Total variation : Mean 3 SD

Example:

Mean = 55 HRC & SD = 1HRC

Total Variation = 55 3 x 1 to 55 + 3 x 1

= 52 HRC to 58 HRC



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Process Capability Index Cp: Definition

Ratio of allowed variation to Total variation

Cp = Allowed variation / total variation

= (USL LSL) / ((Mean + 3 SD) (Mean - 3 SD))

= (USL LSL) / 6 SD

A Process has the potential to meet customer requirements if

total variation < allowed variation

6 SD < (USL LSL)

Cp > 1



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Process Capability Index Cp: Example

20 data on acid content (mm) is given in the table below. If the specification onacid content is 0.70 0.2 mm. Check whether the process has the potential to

meet the customer requirement ?

0.85 0.75 0.80 0.65 0.75 0.60 0.80 0.70 0.75 0.60

0.80 0.75 0.70 0.70 0.75 0.75 0.85 0.60 0.50 0.65

Specification = 0.70 0.2 mm

USL = 0.90 mm

LSL = 0.50 mm

Mean = 0.715

SD = 0.092



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Process Capability Index Cp: Example

Cp = (USL LSL) / 6 SD

= (0.90 0.50) / (6 x 0.092)

= 0.4 / 0.552 = 0.72



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Process Capability Index (Cp): Issues

Cp checks only whether the process has the potential to meet the

requirements

Cp never checks whether the Process is actually meeting requirements



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Process Capability Index (Cpk): Definition

Cpk = Min [Ppl, Ppu]

Cpl = (Mean LSL) / 3 SD

Cpu = (USL - Mean) / 3 SD

Cpk checks whether the process is centered at the middle of the specification



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Process Capability Index Cpk: Graphical Representation

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7

USLLSL

Mean + 3 SD3 SD

ba

c d

Cpl = a / c = (Mean LSL ) / 3 SD

Cpu = b / d = (USL - Mean ) / 3 SD



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0

0.2

0.4

0.6

0.8

1

1.2

5 6 7 8 9 10 11

126

Mean + 3 SD- 3 SD

42

3 3

Example:

USL : 12 LSL: 6

Mean : 8 SD : 1

Cpu = 4 / 3 = 1.33

Cpl = 2 / 3 = 0.66

Cpk = Min [1.33,0.66] = 0.66

Cpk < 1, performance is not OK



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0

0.2

0.4

0.6

0.8

1

1.2

6 7 8 9 10 11 12

126

Mean + 3 SD- 3 SD

33

3 3

Example:

USL : 12 LSL: 6

Mean : 9 SD : 1

Cpu = 3 / 3 = 1

Cpl = 3 / 3 = 1

Cpk = Min [1 , 1] = 1

Cpk = 1

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0

0.2

0.4

0.6

0.8

1

1.2

6 7 8 9 10 11 12

126

Mean + 3 SD- 3 SD

33

3 3

Conclusion:Cpu = 3 / 3 = 1

Cpl = 3 / 3 = 1

Cpk = Min [1 , 1] = 1

Cp = (USL LSL) / 6 SD = 6 /6 = 1When Mean is at middle of

Specification [(USL + LSL) / 2] then

Cpu = Cpl = Cpk = Cp

Otherwise

Cpk < Cp

When Cpk < Cp

Performance is not optimum

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Process Performance Study Is a Short term Study performed during New Product Development.

Indices are represented as Pp & Ppk.

Standard deviation calculated using first principle formulae - Sigma(n-1).

Acceptance value for Pp / Ppk is Min 1.66

Process Capability Study

Is a Long term Study performed to monitor the ongoing Production.

Indices are represented as Cp & Cpk.

Standard deviation calculated using sigma = Rbar/d2

Acceptance value for Cp / Cpk is Min 1.33

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A tool for process control and improvement

A statistical tool to know that process is stable or in control

A statistical tool to detect the presence of Assignable Causes in the process.

PROPERLY USED CONTROL CHARTS CAN : Be used by operators for ongoing control of a process

Help the process perform consistently and predictably

Allow the process to achieve Higher Quality, Lower unit cost, Higher

effective capability

Provide common language for discussing the performance of the process

Distinguish special from common causes of variation, as a guide to local action

or action on the system

CONTROL CHARTS

Zero Defect ConsultantsSt ti ti l P C t l


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For Normally distributed Data

If the process is stable then

Variation will be between Mean 3 x SD

Theory of Control Charts



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A Graphical Tool with three horizontal lines

1. Lower Control Limit (LCL)

2. Center Line (CL)

3. Upper Control Limit (UCL)

Control Charts

UCL

CL

LCL

Control Chart



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UCL & LCL are such that

if the value lies between UCL & LCL then the process is stable or in

control

Control Charts

UCL

CL

LCL

Control Chart



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For Normal Data

UCL =Mean + 3 x SD

CL = Mean

LCL = Mean 3 x SD

Control Charts

UCL

CL

LCL

Control Chart



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1. Calculate the Control Limits from past data

2. Plot the values in the chart

3. If the values are within the limits, the process is stable. Otherwise not.

Control Charts: Working

Control Chart

0

2

4

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15



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Continuous Data

Xbar & R Chart ( or Median R Chart)

Individual X & Moving range Chart

Xbar & S Chart ( or Median S Chart)

Types of Control Charts

Discrete Data

Control Chart for Defectives

p chart

np chart

Control Chart for Defects

c chart

u chart



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Determine

Characteristics to becharted

Are the

data

variable

Is interest inmonitoring %

bad parts

Is it

homogeneou

s in nature

Selection Procedure for Control Charts

Use X-MR Chart

Is interest in

monitoring

nonconformiti

es

Is the sample

size constantIs the sample

size constant

Can sub group

avg. easily

calculated

Is the

subgroup size

9 or more

Is s,

calculated

easily

Use Xbar-S Chart

Use Median Chart

Use Xbar-R Chart

Use Xbar-R Chart

Use U Chart

Use C Chart

Use p ChartUse np Chart

Y

N

N

N

N

N

N

N

N

Y

Y

Y

Y

Y

Y

Y

Y



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Xbar R Chart: Methodology

Conduct initial study :-

Decide on the Total Number of Samples N . (N >19)

Decide on Sub Group Size n. (n > 3)

Decide on Frequency of Sampling. ( eg: Once in a hour, Once in 2 hours,

Once in every 50 items, etc.) Collect Data & Calculate Control Limits

Plot Control Chart

Calculate Process Capability Indices (Pp/Ppk).

If Capable, Set Control Limits for Ongoing study.

Monitor Process through plotting control chart.



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Xbar R Chart: Example

Process: Turning Characteristic: Inner diameter (4.90 5.10)

Sample Size N: 9 Sub Group Size n: 4

Frequency of Sampling: Once in a Hour

Step 1: Collect Data

Sample No. Hour x1 x2 x3 x4

1 8:00 5.00 5.01 4.98 5.00

2 9:00 5.01 4.98 5.00 5.00

3 10:00 5.02 5.01 5.00 5.00

4 11:00 5.00 5.00 5.00 5.00

5 12:00 4.98 4.98 5.01 4.99

6 13:00 5.02 4.99 5.00 4.98

7 14:00 4.99 4.99 4.98 4.98

8 15:00 5.00 5.01 5.02 5.00

9 16:00 4.98 5.00 5.01 4.98



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Step 2: Calculate Sub Group Mean & Range

Sample No. Hour x1 x2 x3 x4 Mean Range

1 8:00 5.00 5.01 4.98 5.00 4.998 0.03

2 9:00 5.01 4.98 5.00 5.00 4.998 0.03

3 10:00 5.02 5.01 5.00 5.00 5.008 0.024 11:00 5.00 5.00 5.00 5.00 5.00 0.00

5 12:00 4.98 4.98 5.01 4.99 4.990 0.03

6 13:00 5.02 4.99 5.00 4.98 4.998 0.04

7 14:00 4.99 4.99 4.98 4.98 4.985 0.01

8 15:00 5.00 5.01 5.02 5.00 5.008 0.02

9 16:00 4.98 5.00 5.01 4.98 4.993 0.03



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Step 3: Calculate Control Limits for R Chart

Center Line

CL = Mean = Rbar = Sum of all Range Values / Total Number

of Values

= 0.21 / 9 = 0.0233

Upper Control Limit

UCL = Mean + 3 SD = D4 Rbar, For n = 4, D4 = 2.282

= 2.282 x 0.0233 = 0.053

Lower Control Limit

LCL = Mean - 3 SD = D3 Rbar, For n = 4, D3 = 0

= 0 x 0.0233 = 0.0



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Step 4: Plot R values in R chart as shown below:

R Chart

0

0.02

0.04

0.06

1 2 3 4 5 6 7 8 9

Step 5: If any value is beyond Control Limits, Do Homogenization

Homogenization:

Remove the out of control value

Recalculate the limits



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Step 6: Calculate Control Limits for Xbar Chart

Center Line

CL = Mean = Xdoublebar = Sum of all Means / Total Number

of Values

= 44.975 / 9 = 4.997

Upper Control Limit

UCL = Mean + 3 SD = xdoublebar + A2Rbar, For n = 4, A2 = 0.729

= 4.997 + 0.729 x 0.0233 = 5.014

Lower Control Limit

LCL = Mean - 3 SD = xdoublebar - A2Rbar, For n = 4, A2 = 0.729

= 4.997 - 0.729 x 0.0233 = 4.98



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Step 7: Plot mean values in xbar chart as shown below:

xbar Chart

4.96

4.98

5

5.02

1 2 3 4 5 6 7 8 9


Step 9: If all values are within limit, Calculate Standard deviation

.

= Rbar/d2 , Where d2 is constant

= 0.023/2.059

= 0.0111



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Step 10: Calculate Process Capability Indices

Cp = Tol / 6 = 0.2 / 6 * 0.0111 = 3.03

Cpk = Min { (Xbar LSL)/3 , (USL-Xbar)/3 }

Cpk = Min { 2.91 , 3.09 } = 2.91.

Process is Capable.

Step 11: If Capable, Set the Control limits for ongoing monitoring.



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Control Chart Constants

n d2 A2 D3 D4 E2

2 1.128 1.880 0 3.268 2.66

3 1.693 1.023 0 2.574 1.77

4 2.059 0.729 0 2.282 1.46

5 2.326 0.577 0 2.114 1.29

6 2.534 0.483 0 2.004 1.18



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Xbar R Chart: Exercise

Sample

Number

x1 x2 x3 Sample

Number

x1 x2 x3

1 6.0 5.8 6.1 11 6.2 6.9 5.0

2 5.2 6.4 6.9 12 6.7 7.1 6.2

3 5.5 5.8 5.2 13 6.1 6.9 7.4

4 5.0 5.7 6.5 14 6.2 5.2 6.8

5 6.7 6.5 5.5 15 4.9 6.6 6.6

6 5.8 5.2 5.0 16 7.0 6.4 6.1

7 5.6 5.1 5.2 17 5.4 6.5 6.7

8 6.0 5.8 6.0 18 6.6 7.0 6.8

9 5.5 4.9 5.7 19 4.7 6.2 7.1

10 4.3 6.4 6.3 20 6.7 5.4 6.7

The following are the data on Time (in Minutes) to Process Transactions in aBPO company. Construct an Xbar R chart to monitor the process



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Individual X & Moving Range Chart: Example

Sample Number Data

1 2.5

2 2.3

3 2.8

4 2.6

5 2.4

6 2.9

7 2.1

8 2.5

For Short Run Process / Bulk Material Processing. Can be used when thetesting method is a destructive type.

Not possible to collect data in Sub Groups

Process: Heat Treatment Characteristic: Case Depth



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Sample Number Date MR

1 2.5

2 2.3 0.23 2.8 0.5

4 2.6 0.2

5 2.4 0.2

6 2.9 0.5

7 2.1 0.8

8 2.5 0.4

Step 2: Calculate Moving Range



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Step 3: Calculate Control Limits for M R Chart

Center Line

CL = Mean = MRbar = Sum of all MR Values / Total Number

of Values

= 2.8 / 7 = 0.4

Upper Control Limit

UCL = Mean + 3 SD = D4 MRbar, For n = 2, D4 = 3.268

= 3.268 x 0.4 = 1.3072

Lower Control Limit

LCL = Mean - 3 SD = D3 MRbar, For n = 2, D3 = 0

= 0 x 0.4 = 0.0



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Step 4: Plot MR values in MR chart as shown below:

MR Chart

0

0.5

1

1.5

1 2 3 4 5 6 7





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Step 6: Calculate Control Limits for Individual X Chart

Center Line

CL = Mean = Xbar = Sum of all Data / Total Number

of Values

= 20.1 / 8 = 2.512

Upper Control Limit

UCL = Mean + 3 SD = xbar + E2MRbar, For n = 2, E2 = 2.66

= 2.512 + 2.66 x 0.4 = 3.58

Lower Control Limit

LCL = Mean - 3 SD = xbar - E2MRbar, For n = 2, E2 = 2.66

= = 2.512 - 2.66 x 0.4 = 1.45




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Step 7: Plot individual values in Individual X chart as shown below:

Individual X Chart

0

1

2

3

4

1 2 3 4 5 6 7 8





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Individual X & Moving Range Chart: Exercise

The data given below are surface Finish values of 30 jobs after chromiumplating. Construct an Individual X & Moving Range chart to monitor the

process?

0.078 0.079 0.077 0.076 0.074 0.072 0.069 0.075 0.078 0.077

0.075 0.078 0.08 0.081 0.08 0.079 0.082 0.073 0.078 0.074

0.072 0.075 0.068 0.073 0.074 0.081 0.076 0.08 0.074 0.07



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Control Charts for Defectives: np Chart

Used when sample size is constant

Used to measure no of nonconforming items in an inspection.

Sample Number Number of Defectives

1 47

2 42

3 48

4 58

5 32

6 38

7 53

8 68

9 45

10 37

Example: Inspection results of video of the month shipment to customers for 10consecutive days are given in table. The number of inspection each day

is constant and is equal to 1000. Construct np chart to control the

defectives?



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np Chart : Calculation of Control Limits

CL = MeanUCL = Mean + 3 SD

LCL = Mean 3 SD

pbar = Sum of Defectives / total Number Inspected

= 468 /(1000*10) = 0.0468

Mean = npbar = 1000 x 0.0468 = 46.8

SD = npbar(1-pbar) = (1000 x (0.0468 x (1-0.0468))) = 6.67

CL = npbar = 1000 x 0.0468 = 46.8

UCL = Mean + 3 SD = 46.8 + 3 x 6.68 = 66.84

LCL = Mean - 3 SD = 46.8 - 3 x 6.68 = 26.76



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Plot the number of defectives in np chart as shown below:

np Chart

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10

If any value is beyond Control Limits, Do Homogenization

np chart: Example



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np Chart: Exercise

Sample

Number

Number of

Defectives

Sample

Number

Number of Defectives

1 3 11 6

2 6 12 9

3 4 13 5

4 6 14 6

5 20 15 7

6 2 16 4

7 6 17 5

8 7 18 7

9 3 19 5

10 0 20 0

The following are the data on defectives in payment of dental insurance

claims. Control the dental insurance payment process with np chart.Sample Size is 300



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Control Charts for Defectives: p Chart

Used when sample size is not constant

Sample Number Number Inspected Number of Defectives

1 500 5

2 550 6

3 700 8

4 625 9

5 700 7

6 550 8

7 450 10

8 600 6

9 475 9

10 650 6

Example: The daily inspection results for electric carving knives are givenbelow. Construct a control chart to monitor the process ?



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p Chart : Calculation of Control Limits

CL = Mean

UCL = Mean + 3 SD

LCL = Mean 3 SD

pbar = Sum of Defectives / Total Number Inspected

= 74 / 5800 = 0.0128

Mean = pbar = 0.0128

SD = pbar(1-pbar) / ni



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p Chart : Calculation of Control Limits

SampleNumber

NumberInspected

Number ofDefectives

p LCL UCL

1 500 5 0.010 0 0.028

2 550 6 0.011 0 0.027

3 700 8 0.011 0 0.026

4 625 9 0.014 0 0.0265 700 7 0.010 0 0.026

6 550 8 0.015 0 0.027

7 450 10 0.022 0 0.029

8 600 6 0.010 0 0.027

9 475 9 0.019 0 0.028

10 650 6 0.009 0 0.026



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Plot the proportion of defectives in p chart as shown below:

p Chart

0

0.01

0.02

0.03

0.04

1 2 3 4 5 6 7 8 9 10


p chart: Example



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p Chart: Exercise

Sample

Number

Number

Inspected

Number of

Defectives

Sample

Number

Number

Inspected

Number of

Defectives

1 171 31 11 181 38

2 167 6 12 115 33

3 170 8 13 165 26

4 135 13 14 189 15

5 137 26 15 165 16

6 170 30 16 170 35

7 45 3 17 175 12

8 155 11 18 167 6

9 195 30 19 141 50

10 180 36 20 159 26

Daily inspection results for the model 305 electric range assembly line are

given in the table. Construct a control chart to monitor the process?



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Control Charts for Defects: c Chart

Used when sample size is constant

Day Number of nonconformities

1 8

2 19

3 14

4 18

5 11

6 16

7 8

8 15

9 21

10 8

Example: A leading bank has compiled the data in the table showing thecount of nonconformities for 100 accounting transactions per

day. Construct a control chart to monitor the process?



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c Chart : Calculation of Control Limits

CL = Mean

UCL = Mean + 3 SD

LCL = Mean 3 SD

cbar = Sum of nonconformities / Total Number Inspected

= 138 /100 = 13.8

Mean = cbar = 13.8

SD = cbar = 13.8 = 3.71

CL = cbar = 13.8

UCL = Mean + 3 SD = 13.8 + 3 x 3.71 = 24.93

LCL = Mean - 3 SD = 13.8 - 3 x 3.71 = 2.67



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Plot the number of nonconformities in c chart as shown below:

c Chart

0

10

20

30

1 2 3 4 5 6 7 8 9 10


c chart: Example



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c Chart: Exercise

Day Number of

Nonconformities

Day Number of Nonconformities

1 22 11 15

2 29 12 10

3 25 13 33

4 17 14 23

5 20 15 27

6 16 16 15

7 34 17 17

8 11 18 17

9 31 19 19

10 29 20 22

100 product labels are inspected every day for surface nonconformities.

The data for the past 20 days is given below. Construct a suitable controlchart to monitor the nonconformities



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Control Charts for Defects: u Chart

Used when sample size is not constant

Lot Number Number Inspected Number of Defects

1 10 45

2 10 51

3 10 36

4 9 48

5 10 42

6 10 5

7 10 33

8 8 27

9 8 31

10 8 22

Example: The inspection results for the surface finish of rolls of whitepaper for 10 lots is given below. Construct a control chart to

monitor the process ?



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u Chart : Calculation of Control Limits

CL = Mean

UCL = Mean + 3 SD

LCL = Mean 3 SD

ubar = Sum of Defects / Total Number Inspected

= 340 / 93 = 3.66

Mean =ubar = 3.66

SD = (ubar / ni)



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u Chart : Calculation of Control Limits

LotNumber

NumberInspected

Number ofDefects

u LCL UCL

1 10 45 4.5 2.80 5.47

2 10 51 5.1 2.86 5.47

3 10 36 3.6 2.70 5.47

4 9 48 5.3 2.83 5.575 10 42 4.2 2.77 5.47

6 10 5 0.5 1.09 5.47

7 10 33 3.3 2.66 5.47

8 8 27 3.4 2.56 5.69

9 8 31 3.9 2.63 5.69

10 8 22 2.8 2.44 5.69



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Plot the defects / unit (u) of in u chart as shown below:

u Chart

0

2

4

6

1 2 3 4 5 6 7 8 9 10


u chart: Example



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u Chart: Exercise

SampleNumber

Number ofbottles

inspected

Number ofDefects

SampleNumber

Number ofbottles

Inspected

Number of Defects

1 40 45 11 52 55

2 40 40 12 52 74

3 40 33 13 52 43

4 40 43 14 52 61

5 40 62 15 40 43

6 52 79 16 40 32

7 52 60 17 40 45

8 52 50 18 40 33

9 52 73 19 40 50

10 52 54 20 52 28

Construct a suitable control chart for the data in the table for empty bottle

inspections of a soft drink manufacturer?



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Select the

characteristics &

Process for SPC

Plan for Data

Collection

Is Process

Capable

Is Process

Stable

Establish Control

Limits

Improve the Process

Find

Assignable

Cause & Fix it

N

N

Y

Y

Perform MSA Study

Collect Data & Plot

Control Chart

Prepare Reaction PlanOngoing Process

Control

SPC Implementation:-



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Collect Data

Is Process in

Control (I.e no

special cause)

Refer Reaction Plan

N

Y

Plot on the Control

Chart

Take Corrective Action

Take Disposition

action, if required

Operator Role in SPC:-



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REACTION PLAN

Process:-

Parameter:-

Doc No.:-

Rev. No./Date:-

Chart Condition Possible

Causes

Corrective

Action

Disposition Action



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Common Mistakes in SPC Implementation

SPC Chart plotting is just a show put up to customers and outsiders. No realanalysis is done.

Companies do Fill SPC Charts, even though 100% inspection is being done.

Hi we are implementing SPC charts Hence we are going to reduce

Rejection. Just by plotting charts, rejection level doesnt reduce.

Charts are plotted at the end of the shift & analyzed.

Inspection frequency & the SPC chart plotting frequency is different.

Management involvement is very less. It is just to meet the customer /

certification requirement.

Charts & Capability indices show positive sign. But rejections/reworks are

increasing????



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Common Mistakes in SPC Implementation

Reaction plans are not prepared. Even if available, not referred / used.

Corrective actions are not initiated even if the process is not stable / not

capable.

Process Capability results are not considered as feedback for new product

development.

Poor awareness at Operator level on usage of SPC charts & Its interpretation

So would you like to avoid above mistakes????

&

Get Maximum benefit of SPC???



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Any Questions



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