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Statistical Process Control

Reminder…

• The final exam is in two weeks
• We will be posting a study guide and exam breakdown later this week
• NOW is the time to start seriously preparing for the OM Exam

Only Two More Ideas…

• Process Control
• Process Capability

Statistical Process Control

• Concepts
• Driven by process data
• Common Cause vs. Special Cause
• Hypothesis testing and UCL/LCL
• Tools
• xbar Chart – continuous data, question is “are we close to the target/nominal value?” (“centered”)
• R Chart – continuous data, question is “are our values close together?” (“tight”)
• p Chart – categorical data, question is “is there special cause in our defect rate?”

Control Charts

• A control chart is a graphical tool, that uses actual variation in observed data to determine if a process is “in control” (just regular or common cause variation) or “out of control” (special cause variation).
• There are several types of control charts based on the kind of data that is being collected.

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Common Cause Variation

Common causes are the process inputs and conditions that contribute to the regular, everyday variation in a process.

• Common causes are a part of the process
• They contribute to output variation because they themselves vary
• Each common cause contributes a small part of the total variation by looking at a process over time, we know how much variation to expect from common causes
• The process is stable, or predictable, when all the variation is due to common causes

Special Cause Variation

Special causes are factors that are not always present in a process but that appear because of some particular circumstance.

• Special causes are not usually present
• They may come and go sporadically; may be temporary or long-term
• A special cause is something special or specific that has a pronounced effect on the process
• We can’t predict when a special cause will occur or how it will affect the process
• The process is unstable, or unpredictable, when special causes contribute to the variation
• Also called “assignable cause” variation

Addressing Common & Special

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Wastes Time

Increases Variation

Under-stand the system better

Reduce Variation

Gain useful information

Reduce Variation

Wastes time not responding to problem

Lost pro-ductivity may increase variation

ACTION

Look for differences between individual points

Common

Special

CAUSE

Take action based on the reported differences

Study all the data

Make basic changes to the process

What are Control Limits?

• A control limit defines the bounds of common cause variation in the process
• A control limit is a tool we use to help us take the right actions:
• If all points are between the limits, assume only common cause variation is present (unless one of the other Signals of a Special Cause is present)
• If a point falls outside the limit, you treat it as a special cause
• Otherwise, you do not investigate individual data points, but instead study the common cause variation in all data points

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Characteristics of Control Charts

• Center line – average (central tendency)
• Upper control limit: + 3 standard dev
• Lower control limit: - 3 standard dev
• Data – collected through sampling

Interpreting Control Charts

• The purpose of control charting is to give us an objective, statistically based tool to judge if a process is in control or out of control
• In Control – functioning as it has historically, exhibiting only common causes of variation (sampling error)
• Out of Control – process is not functioning as it has in the past, exhibiting evidence that a special or attributable cause of variation has entered the process.
• Consider it a type of hypothesis test:
• H0: The system is in control
• Ha: The system is out of control

Processes and Sampling Distributions

• What is a sample?
• How many samples are possible from a given population? (nCr)
• What does the distribution look like?
• A normal curve
• Variation
• Much around the mean; a little at the tails
• Would you expect any trends? (hopefully not)
• Would you believe the process was “stable”?

• The application of these sampling distribution principles to production processes is the basis for statistical process control! (SPC)
• In Control
• A process is “in control” when the process variation is random and within the limits of the normal curve. Or, variation is due to chance or sampling error.
• The process needs no adjustment.
• Out of Control
• A process is deemed “out of control” when the process variation is non-random or outside of the limits of the normal curve. This variation is due to some assignable or special cause.
• The process needs some type of attention or adjustment.