Statistical Process Control

Unlikely Data Patterns -> System out of Control?

1) Single sample statistic is outside control limits 2) 2 consecutive sample statistics near control limits 3) 5 consecutive points above/below central line 4) Trend of 5 consecutive points 5) Very erratic behavior

Center Line

Average or central tendency

Why Change the Width or Control Chart

Cost of quality -Sometimes it's not worth it to have such strict control limits -Eg: Rubber band width is not a big deal, whereas the elasticity is.

Control Limit

Defines the bounds for common cause variation in the process. -UCL, Center Line, and LCL -Purpose is to give us an objective, statically based tool to judge if a process is in control or out of control

Special Cause Variation

Factors that are not always present in a process but that appear because of some particular circumstance. -Assignable cause -If a point falls outside the control limits, treat it this. -May come and go sporadically; may be temporary or long-term -Has a pronounced effect on a process -Unpredictable when it will occur on its affect on the process -Process is unstable and unpredictable when this variation exists

X-bar Control Chart

For changes in the process mean. Individual observations to be plotted are the sample averages. -Center Line = X-bar-bar (average of the averages) -UCL = X-bar-bar + A2*R-bar -LCL = X-bar-bar - A2*R-bar

R Control Chart

For changes in the process variance. -Center Line = R-bar -UCL = R-bar*D4 -LCL = R-Bar*D3

P Control Chart

For data that is not on a continuous scale. Also for changes in attributes. -Center Line = P-bar -UCL = P-bar + z*Sp -LCL = P-bar - z*Sp -Z is usually 3 (3 standard deviations)

In Control

Functioning as it has historically, exhibiting only common cause variation, or sampling error. -Inherent or natural to the process

Control Charts

Graphical tool that uses actual variation in observed data to determine if a process is 'in control' or 'out of control'. -Variation is the enemy; reduce it to improve the process

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. -Not inherent or natural to the process

Type II Error

The control chart tells us that the process is in control, when it is out of control. -False Negative -Consumer's Risk

Type I Error

The control chart tells us that the process is out of control, when it is in control. -False Positive -Producer's Risk

Type I and Type II Errors

Typically only focus on type I Errors. -Use 3 standard deviations because at these limits, we are minimizing the total risk of type I and II combine. -There is an indirect relationship between these two: if the control limits are increased, type I decreases while type II increases

Types of Control Charts

X-bar, R, and P Charts

Standard Deviation of P (Sp)

[(P-bar(1 - P-bar))/n]^1/2

Upper Control Limit (UCL)

+3 standard deviations

Lower Control Limit (LCL)

-3 standard deviations

Statistical Process Control (SPC)

A method of quality control that uses statistical methods in order to monitor and control a process.

Common Cause Variation

The process inputs and conditions that contribute to the regular, everyday variation in a process. -If all points are within the control limits, assume only this variation is present (unless other signals exist) -Part of the process -Can determine how much of this variation to expect by looking at a process over time -Stable when all variation comes from these causes

Consumer's Risk

The risk a consumer takes when buying a product from an out of control process. -Type II Error

Producer's Risk

The risk a producer takes when 'adjusting' a system. -Type 1 Error

H(o)

The system is in control

H(1 or a)

The system is out of control