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					       Module-1
Six Sigma Introduction
                 History of Six Sigma

• Established by Motorola in the 1980’s and still being
  developed. Seen as a cornerstone to the company’s
  culture.

• Companies adopting 6 Sigma include General Electric,
  Allied Signal, ABB, Sony, Lockheed Martin, Ford,
  Nissan and many others

• It is essential for companies to take responsibility for
  their own (unique) programme.
                   What is Six Sigma?

                                                    LSL   USL

• A systematic approach to process
  improvement.
• Processes can be related to design,
  manufacturing or administrative functions.
• It involves the use of statistical tools and      LSL   USL
  techniques to analyse & improve processes.
• The relentless pursuit of variability reduction
  and defect elimination.
      Where can Six Sigma be applied?



• Six Sigma can be applied to all company processes
• A distinction is often made between:
  • Design applications (Design for Six Sigma)
  • Manufacturing applications (Operational Six Sigma)
  • Administrative and Service applications (Transactional
    Six Sigma)
            The Six Sigma Metric


          σ       =      Sigma
 Used in statistics as a measure of variation

               Standard Deviation

The central philosophy of 6 Sigma is the reduction
      of variation in all our work processes
                The Normal Distribution


Lower                             Upper
Spec.                             Spec.
Limit                             Limit         y ± 1σ = 68.26%
                                                     σ
                                                y ± 2σ = 95.44%
                                                     σ
                                                y ± 3σ = 99.73%
                                                     σ

 -3σ
   σ    -2σ
          σ   -1σ y
                σ         +1σ +2σ +3σ
                            σ   σ   σ
                 (Target)

   The 3 Sigma mentality means 2700 defectives per million!
                 The 6 Sigma Metric
                       Normal Distribution
   Lower               Centred on Target                    Upper
Specification                                            Specification
   Limit                                                    Limit




    -6σ -5σ -4σ -3σ
      σ   σ   σ   σ   -2σ
                        σ     -1σ
                                σ   y    +1σ +2σ +3σ +4σ +5σ +6σ
                                           σ   σ   σ   σ   σ   σ

 Specification     Percent within Specification         Defects Per Million
    Limit            (Centred Distribution)           (Centred Distribution)

     ±3σ
       σ                       99.73                         2700
     ±4σ
       σ                      99.9937                         63
     ±5σ
       σ                      99.99994                       0.6
     ±6σ
       σ                    99.999999999                    0.002
        From 3 Sigma to 6 Sigma

Lower            Upper    Defects per Million
Spec.            Spec.
Limit            Limit

                               2700

Lower            Upper
Spec.            Spec.
Limit            Limit        0.002
        Motorola’s 6 Sigma Metric


                        ±1.5σ Shift
                            σ




Lower                                              Upper
Spec.                                              Spec.
Limit                                              Limit




 -6σ -5σ -4σ -3σ -2σ
   σ σ     σ   σ   σ   -1σ
                         σ   y   +1σ +2σ +3σ +4σ +5σ +6σ
                                   σ   σ   σ   σ   σ   σ
                      Motorola’s 6 Sigma Metric

                   Percent within   Percent within    Defects       Defects
Specification      Specification    Specification    per million   per million
   Limit             (Centred)       (1.5 σ shift)   (Centred)     (1.5σ shift)
                                                                       σ

      ± 1σ             68.26           30.23          317400        697700
      ± 2σ
         σ              95.44          69.13           45600         308700
      ± 3σ             99.73           93.32           2700          66810
      ± 4σ
         σ            99.9937          99.38            63            6210
      ± 5σ
         σ            99.99994         99.98            0.6           233
      ± 6σ           99.9999998       99.9997          0.002          3.4


                Motorola’s definition of a 6 Sigma process is one
                 which achieves 3.4 defects per million or less.
                6 Sigma & Defect Rates

                   A Process with 10 Steps

   Each Process Step has a 3σ Quality Level = 93.32% Yield
                            σ
The probability of success (non-defective) at each step = 0.9332
     The probability of overall success = 0.933210 = 0.5008
       Overall Process Yield = 50.08% (499200 dpm)
                 6 Sigma & Defect Rates

                 Another Process with 10 Steps

  Each Process Step has a 6σ Quality Level = 99.99966% Yield
                           σ
The probability of success (non-defective) at each step = 0.9999966
    The probability of overall success = 0.999996610 = 0.999966
           Overall Process Yield = 99.9966% (34 dpm)
                      The Hidden Factory

• To produce a defect uses production time, production capacity,
  energy, raw material….
• This all takes time, people, material, energy, floor space....
• It must be identified by testing and/or inspection,
  transported, stored, re-tested….
• It must be reworked and then checked or scrapped and disposed
  of…
• Often this non-value added activity is not shown within the factory
  metrics - the “hidden” factory
                        Process Yield


 Raw                                                Finished
               Mixing       Forming      Cooling
Materials                                           Product



This process has 100% yield. Our                      Final
                                      0% Fail      Inspection
customers would be very pleased.
Should we be just as happy?

                                                   100% Pass
                    Rolled Throughput Yield

 Raw                                                          Finished
               Mixing           Forming         Cooling
Materials                                                     Product


              Rework
              & Repair                                          Final
                                                             Inspection   0% Fail
                                                                          0%
                                Rework
            7.5% of Units       & Repair
                                                 Rework
                            6% of Units          & Repair
                                               5% of Units   100% Pass



  RTY = 0.925               x    0.94      x      0.95 = 0.826 = 82.6%
              DMAIC Improvement Process

Define

               Measure
 Identify
Opportunity                      Analyse
              Identify Key y’s
                 (Outputs)                      Improve
                                  Identify
                                 Critical x’s
                                                           Control

y = f(x)                          (Inputs)      Optimise
                                                  x’s
                                                           Control
                                                             x’s
                      DMAIC Improvement Process
   Define               Measure                           Analyse                           Improve                               Control
Select Project        Define Measures (y’s)           Identify Potential x’s           Characterise x’s                       Control Critical x’s
Define Project

                                                                                               .. .. .
                                                     C1 C2 C3                                                          10.2
Objective                                                                              y                                                    Upper Control Limit



Form the Team
                      Evaluate Measurement
                      System
                                                                              Effect         .. .
                                                                                           . ..
                                                                                                                       10.0



                                                                                                                        9.8                 Lower Control Limit
                                                                                                       x
                                                     C4 C5 C6                              y=f(x1,x2,..)                9.6
                                                                                                                              1    5   10        15        20


                                                      Analyse x’s                      Optimise x’s                           Monitor y’s
                                                     Run 1    2   3   4   5   6   7
Map the Process
                      Determine Process               1
                                                      2
                                                          1
                                                          1
                                                              1
                                                              1
                                                                  1
                                                                  1
                                                                      1
                                                                      2
                                                                          1
                                                                          2
                                                                              1
                                                                              2
                                                                                  1
                                                                                  2
Identify Customer     Stability                       3   1   2   2   1   1   2   2
                                                      4   1   2   2   2   2   1   1
Requirements                                          5   2   1   2   1   2   1   2                                                           y
                      Determine Process               6   2   1   2   2   1   2   1
                                                      7   2   2   1   1   2   2   1
                      Capability                      8   2   2   1   2   1   1   2


                                                                                       Set Tolerances for x’s                 Validate Control
                               LSL        USL         Select Critical x’s
                                                                                       Verify Improvement                     Plan
                                                              xx
                                                                   x x
                                                              x x                                LSL        USL
                          15    20   25   30    35
                                                                x x
Identify Priorities                                               x
                      Set Targets for                            x
Update Project File   Measures                                                                                                Close Project
                                                                  x
                                                                                            15    20   25   30    35




  Phase Review           Phase Review                     Phase Review                       Phase Review                         Phase Review
                                  1. Define the Problem

    8. Standardise and Future Actions                            2. Interim Actions


                          Problem Solving
7. Verify the Results
                              Process                            3. Acquire and Analyse Data




      6. Action Plan and Implement                           4. Determine Root Cause
                                5. Evaluate Possible Solutions
                       A Few of the Six Sigma Tools!
                             Review                                                                                                                                                           Accuracy                        Analysis of Variance
Cause & Effect
                            Templates                                                                                                                                                                         Calibration
   Diagram                                                                                                              Measurement                                                           Stability
                            M
                                                                                                                          System
    Man Machine              A                                                                                                                                                              Reproducibility
                                                                                                                         Variation
                              I                                                                                                                                                                               Gauge R&R

                  Effect       C                                                                                                                                                             Repeatability                           A1 A2

                                       Minitab Software                                                                                                                                                                                Customer
Maint. Method                                                                  D e s c rip tive S ta tis tic s                                                                               Process                                     Focus
                                                                                                                                        V a ria b le : S A T

                                                                                                                              A n d e r s o n - D a r lin g N o r m a lity T e s t
                                                                                                                                    A- S q u a r e d :
                                                                                                                                    P - V a lu e :
                                                                                                                                                                        0 .3 2 9
                                                                                                                                                                        0 .5 1 2
                                                                                                                                                                                            Validation                      Flow
                                                                                                                                    M ea n                          5 9 0 .2 4 0
                                                                                                                                    S tD e v                          6 5 .1 0 1



                                                                                                                                                                                                                            Chart
                                                                                                                                    Va r ia n c e                   4 2 3 8 .0 8
                                                                                                                                    Sk ew n e ss                  2 .6 3 E - 0 2
                                                                                                                                    K u r to s is                  - 4 .0 E - 0 1
                                                                                                                                    N                                      10 0
                                       44 0      5 00            5 60           620            6 80       74 0



     Regression                                  9 5 % C o n fid e n c e In te r v a l fo r M u
                                                                                                                                    M in im u m
                                                                                                                                    1 s t Q u a r tile
                                                                                                                                    M e d ia n
                                                                                                                                    3 r d Q u a r tile
                                                                                                                                    M a x im u m
                                                                                                                                                                   4 2 6 .0 0 0
                                                                                                                                                                   5 4 2 .2 5 0
                                                                                                                                                                   5 9 8 .0 0 0
                                                                                                                                                                   6 4 0 .0 0 0
                                                                                                                                                                   7 4 0 .0 0 0




      Analysis
                                                                                                                               9 5 % C o n fid e n c e In te r v a l fo r M u
                                                                                                                                    5 7 7 .3 2 3                   6 0 3 .1 5 7
                                 568           5 78                     5 88                59 8                 60 8       9 5 % C o n fid e n c e In te rv a l fo r S ig m a
                                                                                                                                    5 7 .1 5 9                       7 5 .6 2 6
                                                                                                                            9 5 % C o n fid e n c e In te r v a l fo r M e d ia n
                                              9 5 % C o n fid e n c e In te r v a l fo r M e d ia n
                                                                                                                                    5 7 0 .7 1 1                   6 0 5 .0 0 0




y      y=f(x)
                           Design of Experiments                                                                                                                                          Robust Design
                           Run            A                B                    C                     D                 E          F                     G                           y   Tolerance Design
                           1              1                1                    1                     1                 1         1                      1                   y1
                           2              1                1                    1                     2                 2         2                      2                   y2
                           3              1                2                    2                     1                 1         2                      2                   y3
                   x
                           4              1                2                    2                     2                 2         1                      1                   y4
                                                                                                                                                                                                                   Scatter             FMEA
                           5              2                1                    2                     1                 2         1                      2                   y5
                           6              2                1                    2                     2                 1         2                      1                   y6                                    Diagram
                           7              2                2                    1                     1                 2         2                      1                   y7
                           8              2                2                    1                     2                 1         1                      2                   y8
     Process                                                                                                                                                                                                               x
                                                                                                                                                                                                Mistake                 x x
    Capability
                                  Pareto                                                                                    Histogram                                                           Proofing            x
                                                                                                                                                                                                                     x x x
                                                                                                                                                                                                                         x
                                                                                                                                                                                                                        x x
                                                                                                                                                                                                                    x x

				
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posted:5/13/2011
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Description: BSI: Standards, Training, Testing, Assessment & Certification