Table of Contents
Statistics
Recommended Statistical Course Attendance
Basic Definitions
Universe, Populations & Samples
Statistical Methodology  Statistical
methods are procedures for drawing conclusions about populations
utilizing information provided by random samples.
Classification of Statistics:
Four Levels of Measurements
SPC is Concerned With:
Data Collection
Venn Diagrams
Events
Putting it all Together
SPC
Variation
Causes of Variation
Causes of Variation
Distribution
A ‘Normal’ Distribution
Normal Distribution (Bell Curve)
Standard Deviation
Standard Deviation
Basic Terms
More On Standard Deviation
Dispersion Revisited
Population vs Sample
Samples
Samples
Samples
Samples
So What?
A Square Root?
A Shift in the Center
Control Chart
Control Charts
Control Charts
Control Chart Construction
Control Chart Construction
Chart the Data
Figuring Control Limits
A1, D3 and D4 Table
Attribute Control Charts
Interpreting Control Charts
Interpreting Control Charts
Interpreting Control Charts
Interpreting Control Charts
Interpreting Control Charts
Interpreting Control Charts
Interpreting Control Charts
Interpreting Control Charts
Interpreting Control Charts
Analysis Reaction
Analysis Reaction

Email: Marc Smith
Editable Powerpoint file available. Details HERE.
Also see this LIST.
Summary Information:
This file is a brief presentation with some thoughts about Statistics
and Statistical Process Control (SPC) in Business Systems including some
basic Statistical Process Control and Control Charts.
Statistics
Statistical Process Control & Control Charting
Basic Definitions
Statistics:
the science of collecting, analyzing, interpreting and presenting data.
Universe, Populations & Samples
Statistical Methodology
Statistical methods are procedures for drawing conclusions about populations
utilizing information provided by random samples.
Classification of Statistics:
Four Levels of Measurements
Nominal: Objects are classified into simple attributable categories
with no quantitative difference between them, (Yes/No, Good/Bad).
Ordinal: Objects are able to be arranged, ranked, or ordered into a meaningful
attributable arrangement with no real measurement. (Yellow/Blue/Green, Square/Round/Triangle)
Interval: observations are able to be ranked into exact differences between
any two observations, measurements with no natural origin or zero, 80 degrees
is
not twice as hot as 40 degrees. A one unit scale change corresponds to a
one unit change on the object being studied.
Ratio: contains all the properties of interval but has a natural origin.
Having a natural origin allows 25 to behalf of 50.
Note that each successive level has all the properties of the previous.
SPC is Concerned With:
Data Collection
Venn Diagrams
Events
SPC
Statistical Process Control
The development and use of statistics and statistical theories about
distributions and how they vary has become the corner stone of process
improvement. Statistical
process control allows the user to continuously monitor, analyze, and
control the process.
SPC is based on the understanding of variation and how it effects the
output of any process. Variation is the amount of deviation from a
design nominal
value. Not every product that is produced will exactly match it's design
nominal values.
That's why we have tolerances on the nominal values to judge whether
a product is acceptable or not. But the closer we are to the nominal
value
the better
the product is. Control charts are one SPC tool that enables us to
monitor and control
process variation.
Variation
The greatest obstacle to the use of modern quality control methods
is the mistaken belief that the math involved is too difficult for
the 'ordinary'
person to
understand. While the Theories on which many statistical methods are
based involve some highpowered
mathematics, you don't have to be a mathematician to use many of these
modern methods nor do you have to fully understand them.
Causes of Variation
Special Causes of Variation
Special causes are problems that arise in a periodic fashion. They
are somewhat unpredictable and can be dealt with at the machine or
operator
level. Examples
of special causes are operator error, broken tools, and machine setting
drift. This type of variation is not critical and only represents a
small fraction
of the variation found in a process.
Special Causes of Variation
Accounts for 515% of quality problems.
Is due to a factor that has "slipped" into the process causing
unstable or unpredictable variation.
Are unpredictable variations that are abnormal to the process including
human error, equipment failure, defective/changed raw materials, acid
spills, power
failures, etc.; failure to remove them can result is corrosion, scale,
metal fatigue, lower equipment efficiency, increased maintenance costs,
unsafe
working conditions, wasted chemicals, increased downtime (plant shutdown...),
etc.
Removal of all special causes of variation yields a process that is
in statistical control.
Correctable by local personnel.
Distribution
Sometimes you can look at two slices of pie and tell which is bigger.
Sometimes you cannot. Slice a pie up into what you think are equal
sized pieces and
line them up according to size. Many look the same. If we want to arrange
the pieces
according to size, we need another way to tell how big each piece is.
A weight scale will do quite well. Now  lets look at what we would
find
if we weighed
each piece.
There are big and little pieces, but you can see that the number of
pieces in each step of the graph (weight group) varies from the largest
piece
to the smallest
piece in a fairly regular and symmetrical pattern. This is the Distribution
of the weights. The curve is what we would expect if the Distribution
was a 'Normal'
distribution.
Imagine doing this with 100 pies!
A 'Normal' Distribution
Normal Distribution (Bell Curve)
This is a pattern which repeats itself endlessly not only with pieces
of pie but in manufactured products and in nature. There is always
an inherent
Variability.
Sometimes it's a matter of finding a measurement device sensitive enough
to measure it.
Measurements may be in volts, millimeters, amperes, hours, minutes,
inches or one of many other units of measure.
It you take a sample of a population (such as height) and you chart
their distribution, you will end up with a curve that looks like a
bell.
A Distribution which looks like a bell is a Normal Distribution. Normal
Distributions are the most common type of distribution found in nature
 but they are not
the ONLY type of distribution.
Standard Deviation
Mean
Basic Terms
]
More On Standard Deviation
Dispersion Revisited
Population vs Sample
Samples
So What?
A Square Root?
A Shift in the Center
Control Charts
Control Charts Serve 2 Basic Purposes
Control Charts provide information for decision making with respect
to a manufacturing process. When a random pattern of variation
occurs and
process
capability has
been established, the process should be left alone. When an unstable
(nonrandom) pattern of variation is occurring, action should be
taken to find and eliminate
the disturbing or assignable causes.
Control Charts provide information for decision making with respect
to recently produced product. The Control Chart can be used as
one source
of information
in the determination of whether product should be released to the
customer or some alternate disposition made.
The most common type of Control Chart is the XBar & R
Chart
Control Chart Construction
1. Take measurements of the characteristic being studied.
Control Chart Construction
Chart the Data
Figuring Control Limits
A1, D3 and D4 Table
Attribute Control Charts
Interpreting Control Charts
Control Charts provide information as to whether a process is being
influenced by Chance causes or Special causes. A process is said
to be in Statistical
Control when all Special causes of variation have been removed
and only Common causes
remain. This is evidenced on a Control Chart by the absence of
points beyond the Control Limits and by the absence of NonRandom
Patterns
or Trends
within the Control Limits. A process in Statistical Control indicates
that production
is representative of the best the process can achieve with the
materials, tools and equipment provided. Further process improvement
can only
be made by reducing
variation due to Common causes, which generally means management
taking action to improve the system.
When Special causes of variation are affecting a process and
making it unstable and unreliable, the process is said to be
Out Of Control.
Special
causes
of variation can be identified and eliminated thus improving
the capability of
the process
and quality of the product. Generally, Special causes can be
eliminated by action from someone directly connected with the
process.
Analysis Reaction 