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. To learn more about SPC software to generate control charts and calculate statistics, visit https://www.pqsystems.com/.

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 high-powered 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 5-15% 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 down-time (plant shut-down...), 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 X-Bar & 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 Non-Random 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

	The. Deming PDCA Cycle	QMS Implementation	FMEA Information	APQP Information
Auditing Information	8-D Problem Solving	Statistics	Error Proofing (Poka Yoke)	Brainstorming
Identifying Waste	Pull Systems	Lead Time Reduction	Planned Maintenance	Quick Setup
Discovering Change	Process Capability - Cp vs. Cpk	Histogram. Animation	Process Loop Animation	Taguchi Loss Function
		Fishbone / Cause and Effects Animation

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Thoughts about Statistics and Statistical Process Control (SPC) in Business Systems

Circa 2000

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