1. Statistical Process Control
Chapter 14
Statistical
Process
Control

2. Statistical Quality Control
Acceptance sampling
Process Control
Attributes
Variables
Attributes
Variables
Statistical Quality Control for Acceptance Sampling and for Process Control.

3. Statistical Process Control
Statistical process control is the application of statistical techniques to determine whether a process is delivering what the customer wants.
Acceptance sampling is the application of statistical techniques to determine whether a quantity of material should be accepted or rejected based on the inspection or test of a sample.

4. Types of Variations Common Cause Special Cause Random Situational
Chronic
Small
System problems
Mgt controllable
Process improvement
Process capability
Special Cause
Situational
Sporadic
Large
Local problems
Locally controllable
Process control
Process stability

6. Variation from Common Causes

7. Variation from Special Causes

8. Causes of Variation
Two basic categories of variation in output include common causes and assignable causes.
Common causes are the purely random, unidentifiable sources of variation that are unavoidable with the current process.
If process variability results solely from common causes of variation, a typical assumption is that the distribution is symmetric, with most observations near the center.
Assignable causes of variation are any variation-causing factors that can be identified and eliminated, such as a machine needing repair.

9. Assignable Causes
The red distribution line below indicates that the process produced a preponderance of the tests in less than average time. Such a distribution is skewed, or no longer symmetric to the average value.
A process is said to be in statistical control when the location, spread, or shape of its distribution does not change over time.
After the process is in statistical control, managers use SPC procedures to detect the onset of assignable causes so that they can be eliminated.
Location
Spread
Shape
© 2007 Pearson Education

10. Statistical Process Control (SPC)
A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate
SPC relies on control charts

11. Control Chart Applications
Establish state of statistical control
Monitor a process and signal when it goes out of control
Determine process capability

12. Key Idea Capability and Control
Process capability calculations make little sense if the process is not in statistical control because the data are confounded by special causes that do not represent the inherent capability of the process.

13. Capability Versus Control
Capable
Not Capable
In Control Out of Control
IDEAL

14. Commonly Used Control Charts
Variables data
x-bar and R-charts
x-bar and s-charts
Charts for individuals (x-charts)
Attribute data
For “defectives” (p-chart, np-chart)
For “defects” (c-chart, u-chart)

15. Developing Control Charts
Prepare
Choose measurement
Determine how to collect data, sample size, and frequency of sampling
Set up an initial control chart
Collect Data
Record data
Calculate appropriate statistics
Plot statistics on chart

17. Next Steps Determine trial control limits
Center line (process average)
Compute UCL, LCL
Analyze and interpret results
Determine if in control
Eliminate out-of-control points
Recompute control limits as necessary

22. Key Idea Interpreting Control Charts
When a process is in statistical control, the points on a control chart fluctuate randomly between the control limits with no recognizable pattern.

23. Typical Out-of-Control Patterns
Point outside control limits
Sudden shift in process average
Cycles
Trends
Hugging the center line
Hugging the control limits
Instability

24. Shift in Process Average

25. Identifying Potential Shifts

26. Cycles

27. Trend

28. Final Steps Use as a problem-solving tool Compute process capability
Continue to collect and plot data
Take corrective action when necessary
Compute process capability

29. Key Idea Process Monitoring and Control
Control charts indicate when to take action, and more importantly, when to leave a process alone.

30. Spreadsheet Template

32. Special Variables Control Charts
x-chart for individuals

33. Key Idea Charts for Individuals
Control charts for individuals offer the advantage of being able to draw specifications on the chart for direct comparison with the control limits.

34. Charts for Attributes Fraction nonconforming (p-chart)
Fixed sample size
Variable sample size
np-chart for number nonconforming
Charts for defects
c-chart
u-chart

35. Key Idea Choosing between C- & U-charts
Confusion often exists over which chart is appropriate for a specific application, because the c- and u-charts apply to situations in which the quality characteristics inspected do not necessarily come from discrete units.

36. Control Chart Formulas

37. Control Chart Selection
Quality Characteristic
variable
attribute
defective
defect no
n>1?
x and MR
constant
sampling
unit?
yes
constant
sample
size?
yes
p or np no
n>=10 or
computer?
x and R
yes no no
yes
p-chart with
variable sample
size
c u
x and s

38. Control Chart Design Issues
Basis for sampling
Sample size
Frequency of sampling
Location of control limits

39. Key Idea
In determining the method of sampling, samples should be chosen to be as homogeneous as possible so that each sample reflects the system of common causes or assignable causes that may be present at that point in time.

40. Key Idea
In practice, samples of about five have been found to work well in detecting process shifts of two standard deviations or larger. To detect smaller shifts in the process mean, larger sample sizes of 15 to 25 must be used.

42. Economic Tradeoffs

43. Pre-Control
nominal
value
Green Zone
Yellow Zones
Red
Zone
LTL
UTL

44. Key Idea
Pre-control is not an adequate substitute for control charts and should only be used when process capability is no greater than 88 percent of the tolerance, or equivalently, when Cp is at least If the process mean tends to drift, then Cp should be higher.