Statistical Process Control

1
Statistical Process Control

• Goal is to establish when a process is in
  statistical control (in-control).
• An in-control process has parameters (mean, std
  dev, etc.) which are unchanged over time.
• SPC is a statistical approach for determining if
  some parameter in the process has changed. It
  does not indicate directly what has changed.

2
Process Variation

• Assignable (Special, Controllable)
• the cause of the variation can be identified
• identify cause of variation
• eliminate cause of variation
• prevent variation from reoccurring
• Unassignable (Common, Uncontrollable)
• the cause of the variation is unknown
• document the variation
• obtain management involvement
• improve the process by removing variation

3
Statistical Process Control

• Statistical Process Control is established
  through the use of control charts
• A process is in-control when there is no
  assignable variation present
• A process is out-of-control when assignable
  variation is present
• There will always be unassignable variation in
  the process

4
Control Charts

• Applicable to any process
• Used to measure both variables and attributes
• The type of control chart used depends on what is
  being measured
• For variables, X and R-charts are used
• For attributes c or p charts are used

5
Constructing X and R Charts

• Take a series of samples from the process
• Calculate the mean and range for each sample
• Calculate upper and lower control limits
• central limit theorem
• Factors for calculating 3s control limits can be
  obtained from tables

6
Calculations

• Upper 3s Control Limits (UCL) and Lower 3s
  Control Limits (LCL) limits for an X-Chart are
• Upper Control Limit for the R-Chart is
• Lower Control Limit for the R-Chart is

7
Sample Data
8
Means and Ranges
9
Calculations

• Sample Data
• grand mean 8.53
• range mean 0.40
• From Table for n5
• A2 0.58
• D3 0
• D4 2.11
• For X-Chart the Upper (UCL) and Lower (LCL)
  Control Limits are 8.53 /- (0.58)(0.40)
• UCL 8.76
• LCL 8.30
• For R-Chart the limits are
• UCL (2.11)(0.40) 0.85
• LCL (0)(0.40) 0

10
Attribute Control Charts

• p charts
• used for monitoring the percentage defective
  produced
• sample should be sufficiently large to include at
  least one defective unit
• c charts
• used for monitoring the number of defects when
  potential defects are unknown
• based on Poisson arrivals

11
Attribute Control Charts
For a p chart, 3s control limits are given by
For a c chart, 3s control limits are given by
12
Monitoring Control Charts

• Take a sample of n observations
• Plot the mean/range of sample on control chart
• Identify values/trends which indicate loss of
  control
• Take necessary corrective action
• When variation has been reduced adjust mean,
  UCL, and LCL accordingly

13
What does it mean when a process is in-control?

• When a process is in-control, all assignable
  variation has been removed from the process
• Continue to look for methods for improving the
  process and tightening the control limits
• Continuous improvement implies that we are always
  trying to either
• Bring a process back in control by eliminating
  assignable variation
• Improve a process by identifying and eliminating
  random variation

14
SPC Issues

• Sample Size
• Central Limit Theorem
• Generally, samples of size 4 or 5 are usually
  sufficient
• Problems with Large Samples
• Cost
• Bridge changes

15
SPC Issues

• Why use Range instead of standard deviation?
• ???
• When should control limits be updated?
• When a process has been improved.

16
SPC Issues

• Where should inspections be done?
• After a suspect operation (one that frequently
  shifts)
• Before a costly operation (labor or materials)
• Before an irreversible process
• Before a covering process
• Raw materials / Finished goods

17
SPC Issues

• How should samples be taken?
• Inspect products produced from natural portions
  of the production process, such as the product
  from one production line for one shift, product
  produced from one batch of raw material, and so
  forth.
• Do not combine product produced from different
  batches of raw material or from component parts
  obtained from different sources
• Do not combine product from different production
  lines or produced by different methods
• Do not combine product of different shifts
• Do not combine product produced from different
  sets of molds, patterns, or dies

18
Okay. The process is in-control.Now what?

• Are the design specifications being met?
• Not necessarily
• Can defective units be produced?
• Yes
• What does in-control mean?
• The process is stable (not changing over time
  no assignable variation )
• How likely is the process to meet design
  specifications?
• Process capability (and six-sigma quality)
  addresses this issue