Docstoc

Statistical Process Control Template

Document Sample
Statistical Process Control Template Powered By Docstoc
					Statistical Process Control



      Douglas M. Stewart, Ph.D.
 The Anderson Schools of Management
    The University of New Mexico
      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
    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
   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
    Inspection/Testing Points
Receiving inspection
In-process inspection
Final inspection




                                5
      Receiving Inspection
Spot check procedures
100 percent inspection
Acceptance sampling




                             6
      Acceptance Sampling
          Lot received for inspection


         Sample selected and analyzed


    Results compared with acceptance criteria


 Accept the lot                  Reject the lot


Send to production            Decide on disposition
 or to customer
                                             7
          Pros and Cons
      of Acceptance Sampling
 Arguments for:                 Arguments against:
    Provides an assessment         Does not make sense for
     of risk                         stable processes
    Inexpensive and suited         Only detects poor quality;
     for destructive testing         does not help to prevent it
    Requires less time than        Is non-value-added
     other approaches               Does not help suppliers
    Requires less handling          improve
    Reduces inspector fatigue
       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

                                                  9
          Economic Model
C1 = cost of inspection and removal of
     nonconforming item
C2 = cost of repair
p = true fraction nonconforming

Breakeven Analysis: p*C2 = C1

    If p > C1 / C2 , use 100% inspection

         If p < C1 / C2 , do nothing
                                         10
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.
           Gauges and
       Measuring Instruments
Variable gauges
Fixed gauges
Coordinate measuring machine
Vision systems



                                12
Examples of Gauges
  Metrology - Science of Measurement

Accuracy - closeness of agreement
between an observed value and a
standard
Precision - closeness of agreement
between randomly selected individual
measurements
         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
       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
Reliability and Reproducibility
           Studies(2)
 Measurement (M) made by
 Operators (i from1 to m) on
 Parts (j from1 to n) in
 Trials (k from1 to r)
                 
        M ijk 
                 
 xi   j k        average for each operator
          nr
 xD  max( xi )  min ( xi ) difference(range) of operator averages
         i          i

 R ij  max( M ijk )  min ( M ijk ) range for each part for each operator
         k              k

             
        Rij 
             
 Ri   j      average range for each operator
          n
            
        Ri 
 R  i       average range of all
         m
  Reliability and Reproducibility
             Studies(3)
Control limit of ranges Rij  D4  R
             als
Use number tri (r) for n in table. Check
for randomnessof errors.
Repeatability or Equipment Variation
EV  K1  R                     ied
               K1 is a constant t to # of trials
Reproducibility or operator (appraisal) variation
                    EV 2 
AV  K 2  xD   
                    n  r  K 2 is a constant t to # of operators
                  2
                                              ied
                          
Repeatability and Reproducibility
R&R      EV 2   AV 2

Results are in actual units measured. Customary to express
as percentages.
Under 10% - Acceptable
10 - 30% - ? based on importanceand repair cost
Over 30% - Unacceptable
     R&R Constants

Number of    2    3    4    5
Trials
K1          4.56 3.05 2.50 2.21
Number of    2    3    4    5
Operators
K2          3.65 2.70 2.30 2.08
        R&R Evaluation
Under 10% error - OK
10-30% error - may be OK
over 30% error - unacceptable
                 R&R Example
 R&R 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.
    x1  0.830
    x2  0.774
    x3  0.829




    R1  0.037
    R2  0.034
    R3  0.017
             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
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




                                         24
Common
Causes




Special
Causes
Histograms do not
take into account
changes over time.



                     Control charts
                     can tell us
                     when a process
                     changes
  Control Chart Applications
Establish state of statistical
 control
Monitor a process and signal
 when it goes out of control
Determine process capability

                                  27
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)

                                          28
     Developing Control Charts
1. Prepare
   Choose measurement
   Determine how to collect data, sample size,
    and frequency of sampling
   Set up an initial control chart
2. Collect Data
   Record data
   Calculate appropriate statistics
   Plot statistics on chart
              Next Steps
3. Determine trial control limits
   Center line (process average)
   Compute UCL, LCL
4. Analyze and interpret results
   Determine if in control
   Eliminate out-of-control points
   Recompute control limits as
    necessary
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

                                   36
Shift in Process Average
Identifying Potential Shifts
Cycles
Trend
            Final Steps

5. Use as a problem-solving tool
   Continue to collect and plot data
   Take corrective action when
    necessary
6. Compute process capability
               Process Capability
 Capability Indices

           UTL  LTL
    Cp 
               6
    if C p  1 is defined as capable (1.5 more often the minimum)


    Example : Part specification is 10.75mm  .25mm   0.0868mm


                          11.00  10.50
                     Cp                 0.96
                           6  0.0868
           Process Capability (2)
       UTL                                 11.0  10.7171
C pu 
          3                        C pu                    1.086
                                               3  0.0868
         LTL
C pl 
         3                                  10.7171 10.5
                                    C pl                   0.834
C pk  min C pl , C pu                       3  0.0868
                                  2  T
C pk  C p 1  K  whereK 
                          Tolerance
Example : same as above, but assumeprocessis centered at 10.7171mm

                    Cp
  C pm                           T is the Target
              1
                     T    2


                      2
                      0.960
  C pm                                   0.8977
             1
                  10.7171 10.75   2


                         0.8682
     Capability Versus Control

                     Control
Capability    In Control   Out of Control

   Capable      IDEAL


Not Capable


                                        44
Process Capability Calculations
Excel Template
   Special Variables Control Charts

x-bar and s charts
x-chart for individuals
         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
                Control Chart Selection
                  Quality Characteristic
 variable                                       attribute
                                defective                       defect
           no
  n>1?           x and MR
                                            yes                 constant
yes                             constant
                                                  p or          sampling
                                 sample
                                                  np              unit?
n>=10 or no                       size?
                    x and R
computer?                                                yes            no
                                     no
yes
                              p-chart with                  c            u
 x and s                      variable sample
                              size
                                                                   64
  Control Chart Design Issues
Basis for sampling
Sample size
Frequency of sampling
Location of control limits



                                65
         Pre-Control
   LTL                  UTL


Red                       Red
Zone      Green Zone      Zone


           nominal
            value


         Yellow Zones         67
      SPC Implementation
        Requirements
Top management commitment
Project champion
Initial workable project
Employee education and training
Accurate measurement system

                                   68

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:30
posted:8/18/2011
language:English
pages:68
Description: Statistical Process Control Template document sample