SPC

4

Basics• SPC, Control, Process• SPC Tools e.g. histogram, Pareto charts,

control charts• Variations (Long Term vs Short Term,

Common Cause vs Special Cause)Details• Sampling, Normal Distribution, Central Limit

Theorem• Mean & Range Charts, Process Stability, i-

charts/ Run Charts, Zone Control, Pre Control, Mean & Range Charts, Short Term SPC

Going Practical• Process Maturity vs effort, Protection

layers concept, Amplitude 1.1• CPU, Wafers, Steam P, TDS, % oxygen,

Fuel gas flow, Steam flow, Flow Process Values

To be followed by conclusion and bibliography

CONTENTS

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The theme of SPC is the Process: Everything we do in any

type of organization is a process, which:

Requires UNDERSTANDING

has VARIATION

must be properly CONTROLLED

has a CAPABILITY

needs IMPROVEMENT

6

Control: What & Why

To maintain desired conditions in a system by adjusting the values of

some physical parameters for:

Suppressing the effect of external disturbances

Ensuring the stability of the process

Optimization of performance

7Taken from Presentation: How to Streamline, Integrate and Synergize Project Management and Six Sigma Techniques for Optimal Results, by Candace G. Medina, CGM Associates, LLC, 2006

8

Taken from Six Sigma Certification Training Program Course Material

9

SPC is not really about statistics or control, it is about

competitiveness. Organizations, whatever their nature, compete on

three issues:

Quality

Delivery

price

10

What is quality?

The word ‘quality’ is often used to signify ‘excellence’ of a product or

service. In some manufacturing companies, quality may be used to

indicate that a product conforms to certain physical characteristics

set down with a particularly ‘tight’ specification. But in general:

Quality is defined simply as meeting the requirements of the

customer.

11Taken from Statistical Process Control, 5th Ed by John S. Oakland

12

Some basic SPC tools are: process flowcharting (what is done); check

sheets/tally charts (how often it is done); histograms (pictures of

variation); graphs (pictures of variation with time); Pareto analysis

(prioritizing); cause and effect analysis (what causes the problems);

scatter diagrams (exploring relationships); control charts (monitoring

variation over time). An understanding of the tools and how to use

them requires no prior knowledge of statistics.

13Taken from Six Sigma for Dummies , by Craig Gygi At All, Wiley Publishers, 2005

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15


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Histogram Purpose

A histogram is used to graphically summarize and display the distribution of a process data set.

What questions does it answer?- What is the systems most common response?- What distribution (center, variation & shape) does the data have?- Does the data look symmetric or is it skewed to the left or right?- Does the data contain outliers?


17

Pareto Chart: (80:20 rule)It’s a vertical bar chart that relates non-

numerical or qualitative categories to their respective frequency or cost.

It charts the causes in descending order of frequency or cost from left to right.

A Pareto chart is used to graphically summarize and display the relative importance of the differences between groups of data.

Land Owners In Pakistan

0

20

40

60

80

100

120

Series2 55 25 9 6 4 1

Series1 55 80 89 95 99 100

FeudalsArmed Forces /

Government

Private Industrial Sector

Business Tycoons Employed Labour

18

19

Cause & Effect Diagram

Measurements Material Personnel

Environment Methods Machines

Safety Related

Incidents


20Taken from Six Sigma for Dummies , by Craig Gygi At All, Wiley Publishers, 2005

21

And of course:

1. Bar Charts2. Graphs

Taken from Statistical Process Control, 5th Ed by John S. Oakland

22

Control charts are simply run charts or plot of data in real time.

This plot enables us to see wood rather than tree which is not the

case in most of the other data recording and measuring methods.

25

This is rather like a set of traffic lights which signal: ‘stop’, ‘caution’ or ‘go’.


26

The control chart has 3 zones and the action required depends on the

zone in which the results fall. The possibilities are:

1 Carry on (stable zone – common causes of variation only).

2 Be careful and seek more information, since the process may be

showing special causes of variation (warning zone).

3 Take action, investigate or, where appropriate, adjust the process

(action zone – special causes of variation present).

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Questions to be asked

1 ‘Is the process stable, or in-control?’ In other words, are there

present any special causes of variation, or is the process variability

due to common causes only?

2 ‘What is the extent of the process variability?’ or what is the

natural capability of the process when only common causes of

variation are present?

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This approach may be applied to both variables

and attribute data, and provides a systematic

methodology for process examination, control and

investigation.

32

The run chart becomes a control chart if decision lines are added

and this and helps to distinguish between:

common cause variation – inherent in the process

special cause variation – due to real changes.

Good organizations do not blame people but examine processes

to identify the causes of variation.

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Some variation is just natural and cannot be eliminated. The natural forces of nature naturally work to mix up things for us because human created processes are nature manipulation. For example heads and tails variation in coin toss is natural. If the mail man arrival is 11:30 am daily. But he comes (5 days of week) at 11:30:21, 11:29:45, 11:31:00, 11:30:10 and 11:29:59 am. This is perfectly natural. But he some day comes at 12:30 pm or 10:30 it is special cause variation. It may be due to schedule change or flat tire.

We can act to reduce common cause variation but cannot eliminate it but we can eliminate special cause variation.

Effort spent on identifying common and special cause variation certainly repays later.

34

Long Term Variation (Shift)

Taken from Six Sigma for Dummies , by Craig Gygi At All, Wiley Publishers, 2005

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Short Term Variation


36


38

About Sampling:

You typically can't check every single member of the target

population. There is no time or money to do that. The best you can

do is select a sample (a subset of individuals from the population)

and get the information. Because this sample of individuals is your

only link to the entire target population, you want that sample to be

really good.

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A good sample represents the target population. The sample doesn't

systematically favor certain groups within the target population, and

it doesn't systematically exclude certain groups, either. That is get a

sampling frame and select a sample from it. The sample is to be

randomly selected from the target population. Randomly means

that every member of the target population has an equal chance of

being included in the sample. In other words, the process you use

for selecting your sample can't be biased. Also, sampling should be

appropriate and well timed.

40

"Less good information is better than more bad information, but

more good information is better."

If you have a large sample size, and the sample is representative of

the target population (meaning randomly selected), you can count

on that information to be pretty accurate. How accurate depends on

the sample size, but the bigger the sample size, the more accurate

the information will be. Selecting a smaller initial sample and

following up later is better than selecting a bigger sample. It is

known to reduce bias.

41

A quick and dirty formula to calculate the accuracy of a survey is to

divide by the square root of the sample size. For example, a survey

of 1,000 (randomly selected) people is accurate to within, 1/(sq

root of 1000) which is 0.032 or 3.2%. This percentage is called the

margin of error.

42

Normal Distribution Curve


43

The Central Limit Theorem

If we draw samples of size n from a population with a mean μ and a

SD, then as n increases in size, distribution of sample means

approaches a normal distribution with a mean μ and standard error

so even if individual values are not normally distributed, distribution

of means will tend to have a normal distribution. Larger the sample

size, the greater will be this tendency. Also, Grand or Process Mean

will be very good estimate of true mean of the population μ.

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47


48

Steps in assessing process stability

1 Select a series of random samples of size n (greater than 4 but less

than 12) to give a total number of individual results between 50 and

100.

2 Measure the variable x for each individual item.

3 Calculate X (sample mean) & R( sample range) for each sample.

4 Calculate the Process Mean X – the average value of X and the Mean

Range R – the average value of R

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5 Plot all the values of X and R and examine the charts for any

possible miscalculations.

6 Calculate the values for the action and warning lines for the

mean and range charts

7 Draw the limits on the mean and range charts.

8 Examine charts again – is the process in statistical control?

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Some Terms

Mean and Range

Grand Mean

Precision and Accuracy

Deviation, Variance , SD & bias corrected/estimated SD

Shewhart Charts, Hartley’s Constant

State of Control

Process Capability

51

Total number of readings should be at least 50 and:

NO Mean or Range values which lie outside the Action LimitsNO more than about 1 in 40 values between the Warning and Action Limits (Zone 2)NO incidence of two consecutive Mean or Range values which lie outside the same Warning Limit on either the mean or the range chart (Zone 2) NO runs of more than six sample Means which lie either above or below the Grand Mean (Zone 1)NO trends of more than six values of the sample Means which are either rising or falling (Zone 1)

52

Charts for individuals or run charts

The individuals or run chart is often used with one-at-a-time data

and the individual values, not means of samples, are plotted. The

centerline is usually placed at: the centre of the specification, or

the mean of past performance, or some other, suitable – perhaps

target value. The action lines (UAL and LAL) or control limits (UCL

and LCL) are placed 3 standard deviations from the centerline.

Warning lines (upper and lower) may be placed at two standard

deviations from the centerline.

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When plotting the individual results on the i-chart, the rules for out

of control situations are:

1. any points outside the 3 SD limits;

2. two out of three successive points outside the 2 SD limits;

3. eight points in a run on one side of the mean.

Owing to the relative insensitivity of i-charts, horizontal lines at ±1

either side of the mean are usually drawn, and action taken if four

out of five points plot outside these limits.

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The zone control chart

The so-called ‘zone control chart’ is simply an adaptation of

the individuals chart, or the mean chart. In addition to the

action and warning lines, two lines are placed at one standard

error from the mean. Each point is given a score of 1, 2, 4 or

8, depending on which band it falls into. It is concluded that

the process has changed if the cumulative score exceeds 7.

The cumulative score is reset to zero whenever the plot

crosses the centerline.

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Pre-control

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Other Control Charts

Median & Mode(Constant)

Median & Mode (Moving)

Techniques for Short Term SPC

Difference Charts

Z Charts

59

Going Practical

60Taken from Statistical Methods for Industrial Process Control by David Drain, CRC Press

61Taken from Modern Control Engineering, 2003, Lecture Notes

62Taken from Modern Control Engineering, 2003, Lecture Notes

67

All following figures, tables and graphs are based on Practical industrial data. Either reproduced or copied as such from industrial presentations.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29568

570

572

574

576

578

580

582

584

586

588

Natural gas PressurePr

essu

re in

psi

g

70

% oxygen in furnace flue gases

71

Fuel Gas Flow in KSCFH to two cells of furnace

Pressure Variability LimitsTAG Nor

malUPPE

RLIMIT

LOWER

LIMIT

UPPER LIMIT CONTROLPHILOSPHY

LOWER LIMIT CONTROL

PHILOSPHY

PRC-101

505# 595# 490% On low load or other plant tripping to control battery limit press. According to load

To control load

PRC-102

589# 650/650 550 To avoid design limits of vessel D-2503 A/B

PRC-103

479# 488/490 - To avoid design limit of vessel D-2510

PRC-104

459# 460/465 - To avoid design limit of vessel D-2513

PRC-131

418# 420/430 - To avoid damage of internals of C-2519

PRC-132

On high pressure P-2503 may trip on O/L amps.

Anti surge of K-2502 may open

PRC-319

94# 100# 60# May damage burners, coil temp increase May burners Extinguish.

PRC-306

240# 250# 160# May pop PSV - 929 Process air reduce.KGT rpm may decrease

Six Sigma and (continued)

Case Study – 3

Reduction in efficiency of Thermo-compressor

Before PI

Thermo-compressor would have been sent to workshop for its opening for internals’ inspection. Activity would have taken a minimum of two days, resulting in low-pressure steam venting.

After PI

Motive steam flow trends from PI showed that the drop in efficiency happened over a period of two months, contributed by scaling on the motive steam path. This was confirmed by boroscopy. Thermo-compressor was back in service after four hours of downtime required for cleaning.

“Right analysis leads to right decisions”

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SPC is a set of tools for managing processes, and

determining and monitoring the quality of the outputs of

an organization. It is also a strategy for reducing variation

in products, deliveries, processes, materials, attitudes and

equipment. The question which needs to be asked

continually is ‘Could we do the job better?’

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BIBLIOGRAPHY:

Statistical Process Control, Fifth Edition by John S. Oakland, , Published by Butterworth-

Heinemann Publishers in 2003

Statistical process control: theory and practice by G. Barrie Wetherill and Don W.

Brown, Published by Chapman and Hall in 1991

Statistical process control by Charles L. Mamzic, Published by Instrument Society of

America in 1995

Statistical Process Control by DI (FH) Andreas Leitner, Published by GRIN Verlag in 2007

Statistical process control:, a guide for implementation by Roger W. Berger, Thomas

Hart, Published by CRC Press in 1986

Modern Control Engineering, 2003, Lecture Notes

77

BIBLIOGRAPHY:

Statistical process control by Leonard A. Doty, Published by Industrial Press Inc. in 1996

Statistical process control by Sven Knoth, Published by Sonder for schungsbereich in

2002

Statistical process control: a guide to the use of statistical process control techniques to

improve quality and productivity, Copyrights: Ford Motor Company, 1986

Statistical process control in manufacturing practice by Fred W. Kear, Published by CRC

Press in 1998

Statistical methods for industrial process control by David Drain, Published by CRC

Press in 1997

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BIBLIOGRAPHY:Statistical Methods for Industrial Process Control by David Drain, , Published by CRC

Press

Six Sigma Certification Training Program Course Material( Orientation & yellow belt)

Six Sigma for Dummies, by Craig Gygi, Neil De Carlo and Bruce Williams Published by

Wiley Publishers in 2005

Statistical engineering: an algorithm for reducing variation in manufacturing

processes by Stefan H. Steiner, R. Jock MacKay, Published by American Society for

Quality in 2005

Statistics for Dummies by Deborah Rumsey, Published by John Wiley & Sons in 2003

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Thank You

SPC

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