Statistical Process Control
Out of control
-a single sample statistic that is outside of the control limit -two consecutive sample statistics near the control limits -five consecutive points above or below the central line -a trend of five consecutive points -very erratic behavior
Nominal Value
=Target value
Control Charts
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) Several types of control charts based on the kind of data that is being collected
Variance
Better to have tight ____ and target be off than for target to be on and ____ to be off
Lower control limit
D3
Upper control limit
D4
Out of Control
Erratic behavior (very low, very high, very low, very high)... Investigate
Hypothesis test
Ho: the system is in control (null) Ha: the system is out of control * Can't prove system is in control, only can disprove. Reject null, then system is out of control
Treat as a special cause
If a point falls outside the limit
Only common cause variation is present
If all points are between the limits
Out-of-Control
Improving in-control is different that controlling _________. If you improve them in the same way, you make things worse
In Control
Just regular or common cause variation
x bar
LCL =x-dbl-bar - A2 (R-bar)
Okay
Out of control limit but in specification limit
Bad
Out of specification limit but in control
Range
Reducing is a good thing... Close to LCL is a good thing
Out of control
Run of five above central line. Investigate for cause of sustained poor performance
Out of control
Run of five below central line. Investigate for cause of sustained poor performance
Out of control
Special cause variation
Special Cause variation
Special causes are factors that are not always present in a process but 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
Process Capability
Specification limits
Out of control
The process variation is non-random or outside 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.
Z Score
To find a z score that will yield a 93% control limit... divide .93 in half= .465. Look up closet value to .465, z = 1.81
The purpose of control charting
To give us an objective, statistically based tool to judge if a process is in control or out of control
Out of control
Trend in either direction five plots. Investigate for cause of progressive change
Why 3 standard deviations
Type I and Type II errors are equal and combined total risk is minimized -Minimizes the sum of both errors -There is the possibility that 1% of the samples will fall outside of the control limits--this is a Type I error. To reduce probability you widen the control limits -As you increase the limits, it increases the chance of a Type 2 error (As you widen the control limits, Type 1 goes down, Type 2 goes up.
x bar
UCL = x-dbl-bar + A2(R-Bar)
Type II Error
We don't think we have a problem but we do... Avoid the most. -When a system that is out of control is judged to be in control is judged to be in control, and we fail to intervene in the system... "False negative" or "Consumers risk"--the risk a consumer takes when buying a product from a control process.
Type I Error
We think we have a problem but we don't -When a system that is in control is judged to be out of control and adjustments are made... "False positive" or "Producers Risk"--the risk a producer takes when "Adjusting" a system
X double bar
average of all averages
R bar
average of range
P bar
average of the sample percentages
Characteristics of control charts
center line--average (central tendency) Upper control limit is + 3 standard deviations above Lower control limit is - 3 standard deviations below Data- collected through sampling
Process Control
control limits statistically generated
X bar
for changes in process mean
R chart
for changes in process variance center line (average) = the average of the sample range (r bar) UCL = D4 * R bar LCL = D3 * R bar
X bar
for changes in the process mean center line (average) = the average of the sample averages (x-double-bar) UCL= x-dbl-bar + A2(R-Bar)
P bar
for data that is NOT on a continuous scale (typically defective vs non-defective) Center line = p-bar (average of the sample percentages) 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 causes of variation (sampling error)
Out of control
one plot out above-investigate for cause of poor performance
Out of control
one plot out below. investigate for cause of low value
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
Out of Control
sudden change in level/there is a pattern... investigate for cause
x bar
the average of one sample
Common cause variation
the process inputs and conditions that contribute to the regular, everyday variation in a process -part of the process -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
Out of control
two plots near lower control. investigate for cause
Out of control
two plots near upper control. investigate for cause of poor performance
In control
variation is random and within the limits of the normal curve. Or when it is due to chance or sampling error. The process needs no adjustment.