Statistical Process Control

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Statistical Process Control

• Douglas M. Stewart, Ph.D.
• The Anderson Schools of Management
• The University of New Mexico

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Quality Control (QC)

• Control the activity of ensuring conformance to
  requirements and taking corrective action when
  necessary to correct problems
• Importance
• Daily management of processes
• Prerequisite to longer-term improvements

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Designing the QC System

• Quality Policy and Quality Manual
• Contract management, design control and
  purchasing
• Process control, inspection and testing
• Corrective action and continual improvement
• Controlling inspection, measuring and test
  equipment (metrology, measurement system analysis
  and calibration)
• Records, documentation and audits

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Example of QC HACCP System

1. Hazard analysis
2. Critical control points
3. Preventive measures with critical limits for each
   control point
4. Procedures to monitor the critical control points
5. Corrective actions when critical limits are not
   met
6. Verification procedures
7. Effective record keeping and documentation

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Inspection/Testing Points

• Receiving inspection
• In-process inspection
• Final inspection

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Receiving Inspection

• Spot check procedures
• 100 percent inspection
• Acceptance sampling

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Acceptance Sampling
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Pros and Cons of Acceptance Sampling

• Arguments for
• Provides an assessment of risk
• Inexpensive and suited for destructive testing
• Requires less time than other approaches
• Requires less handling
• Reduces inspector fatigue

• Arguments against
• Does not make sense for stable processes
• Only detects poor quality does not help to
  prevent it
• Is non-value-added
• Does not help suppliers improve

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In-Process Inspection

• What to inspect?
• Key quality characteristics that are related to
  cost or quality (customer requirements)
• Where to inspect?
• Key processes, especially high-cost and
  value-added
• How much to inspect?
• All, nothing, or a sample

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Economic Model
C1 cost of inspection and removal of
nonconforming item C2 cost of repair p true
fraction nonconforming Breakeven Analysis
pC2 C1 If p gt C1 / C2 , use 100
inspection If p lt C1 / C2 , do nothing
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Human Factors in Inspection
complexity defect rate repeated
inspections inspection rate
Inspection should never be a means of assuring
quality. The purpose of inspection should be to
gather information to understand and improve the
processes that produce products and services.
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Gauges and Measuring Instruments

• Variable gauges
• Fixed gauges
• Coordinate measuring machine
• Vision systems

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Examples of Gauges
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Metrology - Science of Measurement
Accuracy - closeness of agreement between an
observed value and a standard Precision -
closeness of agreement between randomly selected
individual measurements
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Repeatability and Reproducibility

• Repeatability (equipment variation) variation
  in multiple measurements by an individual using
  the same instrument.
• Reproducibility (operator variation) - variation
  in the same measuring instrument used by
  different individuals

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Repeatability and Reproducibility Studies

• Quantify and evaluate the capability of a
  measurement system
• Select m operators and n parts
• Calibrate the measuring instrument
• Randomly measure each part by each operator for r
  trials
• Compute key statistics to quantify repeatability
  and reproducibility

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Reliability and Reproducibility Studies(2)
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Reliability and Reproducibility Studies(3)
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RR Constants
Number of Trials 2 3 4 5
K1 4.56 3.05 2.50 2.21
Number of Operators 2 3 4 5
K2 3.65 2.70 2.30 2.08
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RR Evaluation

• Under 10 error - OK
• 10-30 error - may be OK
• over 30 error - unacceptable

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RR Example

• RR Study is to be conducted on a gauge being
  used to measure the thickness of a gasket having
  specification of 0.50 to 1.00 mm. We have three
  operators, each taking measurement on 10 parts in
  2 separate trials.

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Calibration

• Calibration - comparing a measurement device or
  system to one having a known relationship to
  national standards
• Traceability to national standards maintained by
  NIST, National Institute of Standards and
  Technology

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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

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Common Causes
Special Causes
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Histograms do not take into account changes over
time.
Control charts can tell us when a process changes
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Control Chart Applications

• Establish state of statistical control
• Monitor a process and signal when it goes out of
  control
• Determine process capability

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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)

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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

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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

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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

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Shift in Process Average
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Identifying Potential Shifts
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Cycles
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Trend
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Final Steps

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

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Process Capability

• Capability Indices

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Process Capability (2)
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Capability Versus Control
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Process Capability Calculations
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Excel Template
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Special Variables Control Charts

• x-bar and s charts
• x-chart for individuals

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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

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Control Chart Selection
Quality Characteristic
variable
attribute
defective
defect
no
ngt1?
x and MR
constant sampling unit?
yes
constant sample size?
yes
p or np
no
ngt10 or computer?
x and R
yes
no
no
yes
p-chart with variable sample size
c u
x and s
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Control Chart Design Issues

• Basis for sampling
• Sample size
• Frequency of sampling
• Location of control limits

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Pre-Control
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SPC Implementation Requirements

• Top management commitment
• Project champion
• Initial workable project
• Employee education and training
• Accurate measurement system