SPC Module_BW

Statistical Process Control (SPC)
Training

Delegate Name :

Prepared by:
EFR CERTIFICATION SDN BHD
2909B (Level 2), Jalan Merbau 3
Bandar Putra
81000 Kulai, Johor
www.efrcert.com

Welcome to EFR Training

With a warm welcome, it is our pleasure to share the knowledge with you.

EFR offers a wide selection of comprehensive courses and training solutions to support continual
improvement in productivity and quality that impact on business performance included customized
course to suit your esteem organization needs. EFR also work closely with local universities, Malaysia
Productivity Corporation and other major education and training provider to enhance the knowledge
provide to you. Courses are designed to be stimulating and enjoyable, and we hope that this course
meets with your expectations.

EFR was founded by renowned consultant Ts. Dr. Edly Ferdin Ramly which conducted various high
impact, quality, productivity, occupational health and safety and environmental training and
consultation for various organizations. EFR Certification offers expert resources for quality &
productivity improvement through training, consultancy, publication, and audio video production.
Currently, the focus of EFR in consultancy and training while the research for publications and audio
video productions are still ongoing.

For consultancy, EFR provide the most efficient way to certify to various management system
certification i.e., ISO9001, ISO14001, ISO45001 & IATF16949. EFR also work as associate for many other
organizations and EFR work closely with major certification body.

In Malaysia EFR shared best practice and EFR understand the local culture very well and all the EFR
services are adaptable to local customer needs, cultures and customs. EFR look forward to sharing the
world class best practice with you.

If you do have any comments, suggestions for improvement or criticisms, then please raise these with
the Trainer or contact us via email [email protected] or fax to 07-5987331. Alternatively,
you will have the opportunity to express your views from our website www.efrcert.com

Enjoyed and Excel with us.

Thank you

Ts. Dr. Edly Ferdin Ramly
Certification Director
EFRCert (EFR Certification Sdn Bhd)
Professional Technologist
PhD Mechanical Engineering (Operation Management)
Fellow Industrial Engineering and Operation Management International
International Automotive Task Force Lead Auditor

● Excellence ● Forward ● Resourceful ●

Welcome to EFR
Training

Statistical Process Control

50

45 UCL

40

35

30

25 Presented by:
20

15

10 Ts. Dr. Edly Ramly

5 LCL

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© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Course Objectives – Module 1

 Module 1

 What is SPC?
 Why SPC?
 Where SPC commonly apply?
 Common concept in SPC

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Course Objectives – Module 2

 Module 2

 2.1 Data and Quality Characteristics
 2.2 Planning for data collection
 2.3 Analysis of chart pattern
 2.4 Variable control chart

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Course Objectives – Module 3

 Module 3

 SPC – Cpk : Study of process capability
 Cp - Cpk
 Pp - Ppk

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What is SPC
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© EFR Certification Objective: Revison 0006
Understanding what is SPC?

•QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC)

What Is Statistics ?

 Scientific method of:

 Collection,
 Organization,
 Presentation,
 Analysis and
 Interpretation of data

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What Is A Process?

 A set of interrelated resources & activities which transforms inputs into
outputs.
(ISO 9000 definition)

resources may include personnel, equipment, raw material, technology,
methodology, & facilities.

Input in-process output
(resources) activities (product
/ service)

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

What Is Statistical Process Control (SPC) ?

 SPC is a collection of problem solving techniques to collect or analyse data
so that we can understand & act to reduce variability in a process so as to
stabilize the process and improve its capability.

 The ‘main’ tool of SPC is the statistical control chart. (The focus in this
course).

 Other SPC tools, also commonly known as ‘QC tools’ are the Pareto chart,
histogram, checksheet, process flow chart, cause & effect diagram, scatter
diagram.

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50 UCL
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40

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10 LCL
5

Module 1.2 0
Why SPC?
12 3 45 67 89

© EFR Certification Objective: Revison 0006
Understanding why we need SPC?

•QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC)

To prevent defect

 THE NEED FOR PROCESS CONTROL
 Detection – Tolerates Waste
 Prevention – Avoids Waste

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50 UCL
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Application of SPC?

© EFR Certification Objective: Revison 0006
Where can we apply SPC?

•QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC)

Where SPC apply

 A graphical tool used to monitor the stability and capability of a process
indicate when corrective or preventive actions need to be taken to
improve a process, and when not to (avoid over-adjustment).

Used during :
new product / process introduction
engineering changes
as an on-going QA monitor

implementation of SPC requires understanding of
principle and theory ofSPC (technical), &
managing an organization’s resources to sustain the activity (managerial).

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IATF16949:2016 requirements

9.1.1.2 Identification of statistical tools

The organization shall determine the appropriate use of statistical tools. The organization shall
verify that appropriate statistical tools are included as part of the advanced product quality
planning (or equivalent) process and included in the design risk analysis (such as DFMEA) (where
applicable), the process risk analysis (such as PFMEA), and the control plan.

9.1.1.3 Application of statistical concepts

Statistical concepts, such as variation, control (stability), process capability, and the consequences
of over-adjustment shall be understood and used by employees involved in the collection,
analysis, and management of statistical data.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

9.1.1.1 Monitoring and measurement of
manufacturing processes

The organization shall perform process studies on all new manufacturing
(including assembly or sequencing) processes to verify process capability and
to provide additional input for process control, including those for special
characteristics.

The organization shall maintain manufacturing process capability or
performance results as specified by the customer's part approval process
requirements. The organization shall verify that the process flow diagram,
PFMEA, and control plan are implemented ….

A corrective action plan shall be developed and implemented by the
organization indicating specific actions, timing, and assigned responsibilities
to ensure that the process becomes stable and statistically capable.

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8.3.5.2 Manufacturing process design output

The manufacturing process design output shall include but is not limited to the
following:

d) tooling and equipment for production and control, including capability
studies of equipment and process(es);

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

50 UCL
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10 LCL
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Module 1.4 0

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Common concept SPC?

© EFR Certification Objective: Revison 0006
Understand principle of variation
Page 8
•QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC)

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Section 3
PRINCIPLES OF VARIATION

© EFR Certification Objective : Revison 0006
Understand the Concept of Variation in a Process and

What Should Be Done to Improve Its Stability &
Capability.

•QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC)

Ten Principles of Variation

1. Everything Varies.
Variation is the norm, not the exception.

2. All variation is caused
Some are obvious, while others are more obscure.

3. Not all causes of variation are equally important.
Causes follow the Pareto principle (80/20 rule)

4. Most causes of process variation can be
categorized into one of these groups:
• method
• material
• machine
• personnel
• measurement
• environment

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Ten Principles of Variation (cont’d)

5. Stable processes produce consistent patterns of variation over time.
This means we can predict the process performance within certain
boundary.

6. The variation in a stable process comes from common causes which
are part of the normal process.

Common Cause is also known as ‘random’ or ‘system’ cause.
Common cause variation can be associated with the natural variation in

• traffic flow
• raw material quality
• environmental stability (e.g. vibration, electrical fluctuation, weather)
• worker’s different processing speed
• workmanship standard (due to unspecific standards / instructions/

training)

However, when any of these common cause becomes too excessive, it
becomes an assignable cause.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Graphical Illustration of a Process in Control

If only common cause of variation are prediction
present in a process, the output forms a
stable distribution over time
and is predictable.

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Ten Principles of Variation (cont’d)

7. Variation that comes from special (‘assignable’) causes results in
the process being unstable, or “out-of-control”.
These are unpredictable occurrences that can result in a large
variation.

Special causes of variation can be associated with

• a new operator put to work without proper training
• process parameters setting error
• data entry error
• power outage (affecting computer system integrity, machine

stability)
• gauges out of calibration
• machine parts wear-out
• a batch of contaminated raw material

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Graphical illustration of a process out of control

Prediction ???

quality characteristics

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Ten Principles of Variation (cont’d)

8. To understand the causes of variation, stratify the data into various
sensible ways and compare.
For example,
stratify the length of equipment service time by the service technicians
stratify production defect rates by shifts and by lines.

9. Major causes of process variation can be discovered by simple
statistical plots
(e.g., histogram, normal probability plot, scatter plot, boxplot, &
control charts)

10. Reducing process variation produces lower cost and improves
quality.

Reducing variation helps to improve on our ability to predict and
plan the ‘operation’ for realistic quality / quantity targets
Ad-hoc ways of over / under adjusting a process is undesirable.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Graphical illustration :
Bringing an out-of-control process back in control

Special cause present

Special cause eliminated

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VARIATION, STABILITY, & CAPABILITY

If variation due to then the
process is
special common said to be

cause cause out-of-control (unstable) & NOT capable
in control (stable) but NOT capable
high low / high in control (stable) & capable
low high
low low

It is not valid to speak of a process’ capability when its state of control cannot
be ascertained.

The exact quantification of process capability depends also on the
specification limits

The key result in a process improvement is to move from an
out-of-control state to a stable & capable state

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Specification vs. Control Limits

specification limits - given by customer, or product / process
development group.
control limits - determined only by the process’ inherent variability.

Control limits have no relation with spec limits

However, process capability is indicated through a
comparison of the control vs. spec limits.
Product development group may therefore set the spec
after reviewing control limits, so as not to ‘over-commit’.

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Graphical illustration:
Improving an incapable process towards a

capable state

lower specification

stable but not capable

upper
specification

stable & capable

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

MANAGING VARIATION

Special cause
• Can be handled by the ‘shop-floor’ level personnel doing the day-to-

day work.
• Solution may be specific to preventing the recurrence of the particular

cause.
• Do not look for fundamental system change.
• Short term solution in general.

Common cause
• To be handled by those with sufficient management / technical

knowledge, possibly through a cross functional team.
• Required fundamental system changes to the way we do business or

run an operation to improve process capability.
• Solution may be medium to long term.

W. E. Deming claimed that 80% of the process variation in industry is
due to common cause, while 20% is due to special cause!

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What Can Statistical Techniques Do ?

 Determine appropriate managerial action in response to the value of a
data point from a particular process.
» To see if high or low points are due to special causes

 Understand and predict process capability (expected range of future
values) for planning purposes.

 Identify root causes (vital few Xs) of variation by differentiating between
special and common causes of variation in the data.

 See whether intentional changes in a process had the desired result.
 Monitor key processes and identify shifts or changes quickly to help hold

the gains made from an improvement project.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Milestones In Development Of SPC

 1920’s - Walter Shewart developed control chart method for bell lab, USA.
 1940’s (WW II) - US dept. Of Defence used statistical control chart and sampling

plans to help ensure product quality of suppliers. (Japan defeated in WW II and its
economy in ruin.).
 1950’s - W. Edward Deming invited by Japan to deliver lectures on applying SPC to
improve industrial product quality.
JUSE established national ‘Deming prize’ awarded to companies who practiced
Deming’s teaching effectively.
K. Ishikawa introduced ‘7QC tools’ for shop-floor personnel to analyse and improve
quality problems.
Proliferation of QC circles in Japanese industries utilizing ‘7 QC tools’.
 1970’s - effective management, QC circles, & SPC propelled Japan to recover from
WW II ruin into world class industrial leader of quality product.
1980’s U.S. And others follow the footstep of Japan in applying SPC methodology,
form QC teams, etc.
Motorola issued a “six sigma challenge” to improve its company wide process
capabiltiy through SPC.
 QS9000 standard was established with a requirement on ‘statistical techniques’

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MODULE 2
SPC Online learning

SPC – Control Chart

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10 Studies of Stability

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Course content – Module 2

 Module 2

 2.1 Data and Quality Characteristics
 2.2 Planning for data collection
 2.3 Analysis of chart pattern
 2.4 Variable control chart

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Module 2.1
DATA & QUALITY
CHARACTERISTICS

Objective :
Understand the Type & Characteristics of Data Used for SPC

Purpose.

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Attribute Data

Non-measurable parameters where each outcome are logged in one of two
possibilities, e.g.,

 Head or tail
 Accept or reject
 Yes or no

 The analysis of attribute data is through counting the occurrence, and
express the

 Result as
number of occurrence, or
proportion or percentage of occurrence.

 With attribute data, the criteria used for classifying an outcome must be
clear. Without adequate clarification, the attribute data collected may not
be reliable and accordingly cannot contribute towards SPC use.

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Variable Data

 Variable data are those obtained as a result of measurement.
Measurement can be with physical instruments….

EXAMPLES
electrical parameters (e. G. Voltage, current, resistance)
dimensions
weight
pressure
time

… OR assignment of numerical indicators based on certain index scheme..
Examples
the KLSE composite index
the intelligent quotient (IQ)

with variable data, the issue of gauge capability needs to be addressed.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Simple Statistics From Variable Data

 If we have data X1, X2, ..., Xn , and.

 Then.
 Mean (X bar or m) = S Xi / n.
 Range (R) = Xmax - Xmin.

 Standard deviation (S or s) =.

 The mean is used to represent the “location” or center of the data.

 The range or std deviation is used to represent the spread or variability of
the data.

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Range vs. Std Deviation

 Advantage of range :

 Simple to calculate

 Indicate the absolute spread of the data

 Disadvantage of range:

 The statistical theory is not so well understood and applied

 Very prone to outliers

 Does not make good use of all available data (only the min and max)
example:

 Data1: 4,5,5,6,6,6,7,7,7,7,8,8,8,9,9,10

mean= range =

data2: 4, 6.5, 6.6, 6.7, 6.7, 6.7, 7,7,7,7, 7.3,7.3, 7.3, 7.4, 7.5, 10

mean= range =

do you think data1 and data2 are ‘equivalent’, that they represent the
same process?

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Quality Characteristics

 Those properties of a process that are deemed indicative of the process’
quality.

 Should be expressed in terms of either attribute or variable data.

 Can be taken from the process input, the in-process activities, or the process
output.

Example: (baking a batch of pound cake)

process stage attribute data variable data
input appearance of egg weight of egg
in-process smoothness of mixture oven temperature
output [a] texture of cake [a] weight of cake
[b] no. Of surface voids [b] chef’s ranking
.© EFR Certification
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Page 19

Types Of Control Charts

 For variable data, 50
_
X - R (mean & range) chart 45 UCL
_
X - s (mean & standard deviation) chart 40
35
X - MR (individual & moving range) chart 30
25
20
15
10

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 For attribute data,

Np chart (for counts of non-conformance)
p chart (for proportion of non-conformance)
c chart (for counts of non-conformities)
u chart (for proportion of non-conformities, on per unit basis)

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Section 2.2
PLANNING FOR DATA

COLLECTION

© EFR Certification Objective : Revison 0006
To Appreciate the Various Aspects of Planning Needed
Page 20
in Order to Obtain an Appropriate Data Collection
Scheme.

•QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC)

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SUBGROUP

One or more events or measurement sampled at a given time,
and used to calculate the quality characteristics of a process
at that point in time.

SUBGROUP SIZE

Number of observations within one sampling of the subgroup

Larger subgroup size will
- have narrower control limits
- be more sensitive to detect small process drift.

But the benefit needs to be weighed against the cost of
sampling.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Subgroup size consideration

For variable control charts
If sampling is very costly, or negligible within-group variation, then

use s.s = 1 (X-MR chart)

If cost of sampling is acceptable, within-group variation not negligible, &
easy to calculate std dev., then

use s.s = 5-20 ( -s chart)

If within-group variation not negligible, not easy to calculate std dev., not
necessary or cost effective to sample many, then

use s.s = 2-4 ( -R chart)

For attribute control charts
- Large enough to detect at least 5 occurrences per subgroup
- Vary by no more than approximately + 25% of the average subgroup size

Generally it is better to sample a small subgroup but more frequently
rather than a big subgroup but less frequently.

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Sampling Method

Generally, sampling should be done in a random manner so that every unit
in the pupulation has an equal chance of being sampled.

Further consideration:
If the objective is to
- maximize the contrast of any process drift between 2 sampling period, use
method A below
- obtain representative sample during the sampling period for verifying
conformance, use method B below.

Method A : Instantaneous time x = one or more sampling units

[…...xxx] […...xxx] […...xxx] […...xxx] […...xxx] […...xxx] […...xxx]

one sampling period

Method B: Period-of-time e.g. every shift

[x..x...x] […x..x..x] [.x...x..x] [x..x….x] […x..x..x] [.x….x.x] [..x..x..x]

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Choice of setting control limits

Usually the control limits are set at +/- 3 std. deviation (sigma) from
the mean level of the quality characteristcs.
Reason ?
- from convention (historical)
- gives good practical protection against reacting to false alarm.

However the down side is that this does not give very good
protection against small process drift.

Hence there is a ‘sensitizing’ rule of responding to ‘2-out-of-3’ points
beyond the 2-sigma limits (see next section).

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

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SECTION 2.3
ANALYSIS OF CHART

PATTERNS

Objective:

To recognize the sign of
process instability on the
control chart, so that
corrective / preventive
action may be taken.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Components Of A Control Chart

 X axis - sub-group sequence, in time order
 Y axis - sub-group quality characteristic
 Center line (solid)

 Average value of the quality characteristic corresponding to the

 In- control state
 Control limits (dashed)

 Are probability limits that a process is in statistical control

Y X
UCL
1 23 123 123 12
CL Jan 2 Jan 3 Jan 4 Jan 5

LCL

shift
day

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Review: Causes (Common –stable, special – not stable)

 ________ These causes of variation are a part of the process.

 ________ These causes of variation are not usually present.

 ________ Each cause contributes a small part of the total variation.

 ________ They may come and go sporadically; may be temporary or long-
term.

 ________ If these causes are present, the process is unstable, or unpredictable.

 ________ If all the variation is due to these causes, the process is stable, or
predictable.

 ________ This type of variation results from something specific that has a
pronounced effect on the process.

 ________ We can’t predict when this type of cause will occur or how it will
affect the process.

 ________ By looking at a process over time, we know how much variation to
expect from these causes.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

READING OUT-OF-CONTROL SIGNS

A process may be in an out of control state when the
control chart indicates

• one or more points fall beyond the control limits or

• the plotted points exhibit some nonrandom pattern
of behavior, e.g.,

– Trends
– Shifts
– Cycles
– Mixture
– Stratification
– Systematic pattern

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Points beyond control limits

1. If any one point is outside the 3 sigma control limits

2. If any 2 out of 3 consecutive points are within the 2- and 3-sigma
zone.

m+3s

m+2s
m+1s
m

m-1s
m-2s

m-3s

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

TRENDS

Trend is the continuous movement in one direction, usually due to a
gradual wearing out or deterioration of critical process component e.g.
operator fatigue
• heat or stress
• machine parts
• material shelf life

Common rule of detection : a run of 7 points in one direction

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SHIFT

A Shift is seen when the consecutive points depart sharply from those
points in the previous sampling period.

Shift can result from introduction of significant changes (planned or
unplanned) in the process, e.g., new operator, service / assembly /
inspection procedure, new raw material, better equipment.

Common rule of detection : a run of 7 points above or below the
center line.

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CYCLE

Cycle is regular movements from systematic environmental changes, e.g.,
• temperature change throughout the day,
• rotation of shift or machines, or
• fluctuation in voltage or pressure

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MIXTURE

Mixture is when the plotted points tend to fall near or slightly outside the
limits, with relatively few points near the centre line.
Mixture can be due to
• Material from two different suppliers
• Two different typesof machines, operators, or operating methods in use
• Over adjustment of the process by operators (often responding to random

variation in the output rather than systematic causes)
The severity of the mixture depends upon the extent to which the distribution
overlap.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

50

45 UCL

40
35
30
25
20
15
10

5 LCL

0
12345 6789

Section 2.4
VARIABLE CONTROL CHARTS

Xbar R chart

© EFR Certification Objective : Revison 0006
To Understand the Construction & Formula of
Page 27
Variable Control Charts.

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PROCEDURE: CONTROL CHART PREPARATION

1. Select the quality characteristic for control chart application.
2. Select the appropriate type of control chart.
3. Decide on the sampling plan, subgroup size, and frequency of

sampling.
4. Collect and record data on at least 20 to 25 subgroups, or use

previously recorded data.
5. Calculate statistics for the quality characteristics of each subgroup.
6. Calculate center line and control limits based on the statistics from

subgroup samples
7. Construct a chart and plot the subgroup statistics
8. Examine the plot for points outside control limits and for patterns

indicating presence of assignable causes
9. If there are,

- investigate for root cause, & provide corrective actions,
- omit those points in (8), continue data collection to make up for the

‘lost’ data.
- go back to (5)
10. Examine the plot

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VARIABLE CONTROL CHARTS

For variable data, the charts are usually plotted in pairs, e.g.
_

• X - R (mean & range) chart
_

• X - s (mean & standard deviation) chart
• X - MR (individual & moving average) chart
This is so that we can compare within-subgroup variation vs. between-
subgroup variation -
between subgroup : represents special cause variation (monitored by or X chart)
within-subgroup : represents common cause variation (monitored by R or s chart)
A process is considered out-of-control when
• between-subgroup variation is excessive relative to within-group

variation.
• within-subgroup variation becomes unstable over time.

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USES OF VARIABLE CONTROL CHART

stage of process use

input monitor supplier product quality
in-process monitor process parameters & intermediate
product quality
output monitor final product quality

…. For both conformance to spec and stability

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

WHICH VARIABLE CONTROL CHART TO USE

Chart type use when ...
_
•X - R chart subgroup size is small e.g. < 10 ;
difficult to calculate std dev.
_
•X - s chart subgroup size is > 10 ;
not difficult to calculate std dev.

•X - MR chart within-subgroup variation is negligible ;
data very costly to obtain

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APPROPRIATE INITIAL SCALE ON THE CHARTS

The X or chart
choose lower limit and upper limit such that the distance of each
from the mean is approx. the difference between the highest and the
lowest statistics observed in the initial data gathered.

The R or s chart
lower limit : 0
upper limit: about twice the largest statistics observed in the initial
data gathered.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

STATISTICAL BASIS OF THE CHARTS

The formula used to derive the control limits for the variable
control charts are based on the assumption the mean is normally
distributed.

This is frequently justified by the CENTRAL LIMIT THEOREM which
states:

“Regardless of the distribution of the underlying population,
the distribution of the averages ( ’s) of samples drawn from
that population will approximate a normal distribution as the
sample size increases”

A subgroup size of 5 or above will generally satisfy this
requirement.

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NORMAL DISTRIBUTION

1. Bell shaped and single peak at its mean
2. Symmetrical about its mean
3. approximately 68 % lie within 1 sigma of the mean

approximately 95 % lie within 2 sigma of the mean
approximately 99 % lie within 3 sigma of the mean

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95.46%
99.73%
-3 -2 -1 u 1 2 3

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Formula for variable control chart parameters

_ (m = no. of subg_roups)
1. X-R chart 2. X-s chart
_ _
X: X:
centre line centre line

UCL UCL
LCL LCL

R: s:
centre line centre line

UCL UCL
LCL LCL

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Formula for variable control chart parameters

3. X-MR chart note:
X MR is defined as follows:
centre line
X MR
UCL X1 MR1 = undefined
X2 MR2 = | X2-X1 |
LCL X3 MR2 = | X3-X2 |
….
MR: Xm MRm = | Xm-Xm-1 |
centre line

UCL
LCL

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

MODULE 3
PROCESS CAPABILITY ANALYSIS

Objective:

To understand how the capability of a process in
meeting specification is quantified.

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What is Process Capability Analysis ?

Analysis of the process variability relative to product requirements
or specifications

Applied to the input / in-process / output quality characteristics of a
process.

Provides an index to assess the capability of a process in meeting
the customer / designer ‘s requirement

Applies to variable data where measurement of actual performance
is made, against specification.

One index for one variable characteristics

(For attribute data, we can only check the defect rate directly.)

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

What determines the Process Capability ?

• Specification limits
• Process width or spread
• Process location
• assumption of a stable process
• assumption of a normal process distribution

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Process Capability Indices

The basic and most commonly used indices are:

Cp : Measures the spread (variability) of a process relative to specification

limits.

Cpk : Measures the spread (variability) of a process relative to specification

limits, also taking into account the location (centre) of process
distribution.

Formula for Cp / Cpk

Cp: Cpk:

2-sided min ( , )
spec

1-sided spec not defined use Cpu or Cpl as appropriate

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Procedure for Process Capability Analysis

1. Identify the important quality characteristics & collect data

2. Plot control chart & determine control limits

3. Assess STABILITY

4. Validate normality of process distribution

5. Estimate population standard deviation using or

6. Calculate Cp/ Cpk
7. Improve Process Capability if not acceptable

8. Analyze revised process

9. Continuous monitor through SPC

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Process Performance Indices

Another set of related indices, advocated primarily by the U.S.
automotive industries, are the Pp and Ppk :
Their formula are same as with Cp and Cpk, except the s is replaced by

s=

where the Xi ‘s are the individual measurements.
These indices intend to capture ALL (common & assignable) sources
of variation occurring in a process.

© EFR Certification •QUALITY PLANNING & CONTROL : STATISTICAL PROCESS CONTROL (SPC) Revison 0006

Targets for Process Capability Indices

There are no hard & fixed target for the indices, but the higher the
better.

However, current industry standard will expect somewhat the
following

indices inferior good excellent
Pp < 1.33 1.67 --
Ppk < 1.33 1.5 --
Cp < 1 1.5 2
Cpk < 1 1.33 1.5
(used as a guide only)

Your customer’s expectation will determine what target is needed.

Continuous improvement spirit means that over time, all targets will
be raised to increase the quality expectation.

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THANK YOU FOR ATTENDING THIS COURSE

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