Statistical Process Control by zhouwenjuan

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									       IE 405
QUALITY MANAGEMENT

    RECITAITON FIVE:

   REVIEW SESSION




       FALL 2002
     BASIC CONCEPTS OF QUALITY
• Traditional definition: ‘FITNESS FOR USE’
QUALITY DIMENSIONS: Performance, Reliability,
  Durability, Serviceability, aesthetics, features, perceived
  quality and conformance to standards.

QUALITY CONTROL: Operational techniques and the
  activities which sustain a quality of product or services
  that will satisfy given needs.
 e.g. inspection at the end of production, in-
  receiving inspection

QUALITY ASSURANCE: All plant and systematic activities
  to provide adequate confidence that a product or
  service will satisfy a quality dimension.
  e.g. training the people, statistical process
  control, preventive maintenance programs for
  bottleneck machines
QUALITY IMPROVEMENT: Reduction of variability in
  processes and products.
 STATISTICAL METHODS FOR QUALITY
    CONTROL AND IMPROVEMENT

THREE MAJOR AREAS:


1. Statistical Process Control
i.e Control charts for process monitoring

2. Design of Experiments
i.e. Factorial Experiments

3. Acceptance Sampling
           CUSTOMER TYPES


1. Internal customer

2. External customer

Possible questions:
 Who is the customer?
 Who are my customers?
 What do they need?
 What are their measures and
  expectations?
         Customer types continued…

• INTERNAL CUSTOMER: Person within the company
  who receives the work of another and then adds his or
  her contribution to the product or service before passing
  it on to someone else.
EXAMPLES:
 In manufacturing, the internal customer is the
  next person down the line who builds the
  product.
 In a restaurant, the chef has the waiters and
  waitresses as internal customers and the chef
  must meet their requirements if they are all to
  please their guests.
 Sand Muller Operator to Mold Machine
  Operator
 Shipping Supervisor to Billing Clerk
          Customer types continued…

• EXTERNAL CUSTOMER:People outside who are the
  end user’s of a firm’s products and services.


EXAMPLES:
• Manufacturer of the nozzle for a gasoline
  pump has the oil company, the service station
  owner and you as the users as external
  customers.
• An auto insurance company has brokers,
  customer service representatives and the
  insured as the external customers.
            QUALITY COSTS

Four Types of Costs:

1.   Prevention
2.   Appraisal
3.   Internal Failure
4.   External Failure costs
           QUALITY COSTS


1. Prevention Costs: All costs incurred in
    an effort to ‘make it right the first
    time’.
 i.e Training
2. Appraisal Costs: These are costs to
     determine conformance with quality
     standards.
 i.e. Inspection, Auditing
      QUALITY COSTS continued..

3.Internal Failure Costs: Incurred when
   products, components, materials and services
   fail to meet quality requirements and this
   failure is discovered prior to the delivery of the
   product to the customer.
 i.e. scrap, yield losses
4.External Failure Costs: Occur when the product
   does not perform satisfactorily after it is
   supplied to the customer.
i.e. complaint adjustment, returned
   product/material
QUALITY COSTS MATRIX
 STATISTICAL PROCESS CONTROL TOOLS

• HISTOGRAMS, CHECK SHEETS, SCATTER
  DIAGRAMS, DEFECT CONCENTRATION
  DIAGRAMS

• PARETO CHART

• CAUSE AND EFFECT DIAGRAM

• CONTROL CHARTS
                                                                                            Pareto Chart for Defects
                 Cause-and-Effect Diagram
                                                                                                                                                                                 100
Measurements   Materials     Personnel              400

                                                                                                                                                                                 80
                                                    300




                                                                                                                                                                                       Percent
                                                                                                                                                                                 60




                                            Count
                                                    200
                                                                                                                                                                                 40

                                                    100
                                                                                                                                                                                 20


                                                      0                                                                                                                          0
                                                                             s                                      t                        i                  rt
                                                                        r ew                     ps              ske                      us                  Pa
                                                                     Sc                       Cli              Ga                  e   Ho              lete                 rs
                                                                                                                                                                         he
                                            Defect              sin
                                                                   g
                                                                                 Mis
                                                                                     s   in g
                                                                                                          ea
                                                                                                            ky
                                                                                                                          f ec
                                                                                                                               tiv
                                                                                                                                                   co
                                                                                                                                                     mp                Ot
Environment    Methods       Machines                     Mis                                         L                 De                       In

                                             Count          274                     59                      43               19                     10                 18
                                            Percent         64,8                  13,9                    10,2              4,5                     2,4                4,3
                                            Cum %           64,8                  78,7                    88,9             93,4                    95,7              100,0
          Why do we use STATISTICAL PROCESS
                   CONTROL TOOLS?

3 SIGMA
           2 SIGMA   1 SIGMA   1 SIGMA   2 SIGMA   3 SIGMA   IN ANY PRODUCTION
                                                                PROCESS, REGARDLESS OF
                                                                HOW WELL DESIGNED OR
                                                                CAREFULLY MAINTAINED IT
                                                                IS, A CERTAIN AMOUNT OF
                                                                INHERENT OR NATURAL
                                                                VARIABILITY WILL ALWAYS
                                                                EXIST.
                                                             .
Chance and Assignable causes of Quality
              Variation

• A process that is      • Sources of variability
  operating with only      that are not part of
  chance causes of         the chance
  variation present is     cause,pattern as
  said to be IN            ‘assignable causes’.
  STATISTICAL              A process that is
  CONTROL.                 operating in the
                           presence of
                           assignable causes is
                           said to be OUT OF
                           CONTROL.
      TYPES OF CONTROL CHARTS
• VARIABLE CONTROL CHARTS: Data are
  usually continuous measurements, such
  as length, voltage or viscosity
Exp. X chart, R chart, S chart

• ATTRIBUTE CONTROL CHARTS: Are for
  discrete data often taking the form of
  counts.
• Exp. P chart, np chart, c and u charts.

CHART CONSIDERATIONS INCLUDE
 SAMPLE SIZE AND FREQUENCY
 Analysis of Patterns on Control Charts
 A control chart may indicate and out-of-control
  condition either when one or more points fall beyond
  the control limits or when the plotted points exhibit
  some nonrandom pattern of behavior.


 Therefore, the problem is one of pattern recognition,
  that is recognizing systematic or nonrandom patterns
  on the control chart and identifying the reasons for this
  behavior.
THUS use SENSITIZING RULES.
LOOK for CYCLING PATTERNS, TRENDS, SHIFTS IN
  PROCESS LEVEL AND STRATIFICATION
            SUMMARY OF SHEWART CONTROL CHARTS


 CATEGORY TYPE OF CHART                           PURPOSE
                X                         Controls process average
                R                         Controls spread of process
VARIABLE        S              Controls spread of process (large subgroup size)

                  p                       Fraction nonconforming
ATTRIBUTE        np                       Number nonconforming
                  u       Number of nonconformities per unit (usually variable sample
                  c                      Number of nonconfomities
      ADVANTAGES AND DISADVANTAGES OF
              CONTROL CHARTS

• Attributes control charts have the advantage that several
  quality characteristics can be considered jointly an the unit
  classified as nonconforming if it fails to meet the specification
  on any one characteristic
• Variable control charts provide much more useful information
  about process performance than does an attributes control
  chart. Specific information about the process mean and
  variability is obtained directly.
 The most important advantage of X and R chartss is that they
  often provide an indication of impending trouble and allow
  operating personnel to take corrective action BEFORE any
  defectives are actually produced. Thus, X and R charts are
  leading indicators of trouble.
 P charts (or c and u charts) will not react unless the process
  has already changed so that MORE NONCONFORMING UNITS
  are produced.
Recitation 5 Q1
SERIAL N0.        COUNT OF NON-CONFORMITIES
  MY102                       7
  MY113                       6
  MY121                       6
  MY125                       3
  MY132                      20
  MY143                       8
  MY150                       6
  MY152                       1
  MY164                       0
  MY166                       5
  MY172                      14
  MY184                       3
  MY185                       1
  MY198                       3
  MY208                       2
  MY222                       7
  MY235                       5
  MY241                       7
  MY258                       2
  MY259                       8
  MY264                       0
  MY267                       4
  MY278                      14
  MY281                       4
  MY288                       5
Recitation 5 Q1


                               Control chart for count of
                               nonconformities (c chart)
                                 1
                      20


                                              1              1
       Sample Count




                                                                      UCL=12,76

                      10


                                                                      C=5,64



                       0                                              LCL=0


                           0     5       10       15    20       25
                                       Sample Number
• C: count of nonconformities
• Cbar=x/n= 141/25=5.64
• UCL=12,76
• LCL=-1,4 approximately 0
• Remember in this chart low values that do not
  have an assignable cause represent
  exceptionally good quality.
• CANOE NO 132,172 AND 278 are out of
  control. Since canoes 132 and 278 have an
  assignable cause, they are dicarded, however
  canoe 172 maybe due to chance cause and
  not discarded in this case.
• Revised c =141-20-14/25-2=4.65

• UCL=11.1            LCL=1.82 APPROX. 0
Recitation 5 Q1


                               Revised control cart for count of
                               non-conformities
                                    1
                      20


                                                1                  1
       Sample Count




                                                                              Revised
                      10                                                      UCL=11,1
                                                                            Revised
                                                                            c= 4,65

                                                                              Revised
                       0                                                    LCL=1,82


                           0        5      10       15     20          25
                                          Sample Number
Recitation 5 Q2
  Sample   Sample size   No. of defects per Sample   Avg. No. of Defects per Unit   LCL    UCL
     1        16                     23                          1,44               0,49   2,25
     2        20                     30                           1,5               0,59   2,16
     3        26                     35                          1,35               0,68   2,06
     4         8                     12                           1,5               0,13   2,61
     5        22                     29                          1,32               0,62   2,12
     6        29                     35                          1,21               0,72   2,02
     7        31                     50                          1,61               0,74     2
     8        13                     15                          1,15                0,4   2,35
     9        28                     36                          1,29               0,71   2,04
    10        23                     38                          1,65               0,64    2,1
    11        19                     24                          1,26               0,57   2,18
    12        23                     32                          1,39               0,64    2,1
    13        14                     24                          1,71               0,43   2,31
    14        29                     34                          1,17               0,72   0,72
    15        27                     38                          1,41                0,7   2,05
    16        15                     25                          1,67               0,46   2,28
    17        22                     26                          1,18               0,62   2,12
    18        22                     24                          1,09               0,62   2,12
    19        14                     22                          1,57               0,43   2,31
    20        16                     17                          1,06               0,49   2,25
    21        22                     33                           1,5               0,62   2,12
    22        16                     21                          1,31               0,49   2,25
    23        14                     18                          1,29               0,43   2,31
    24         5                      9                           1,8                 0    2,94
    25        13                     18                          1,38                0,4   2,35
    26        19                     26                          1,37               0,57   2,18
    27        10                     12                           1,2               0,26   2,48
Recitation 5 Q2


                                   U chart for the
                                   Moonroof Installation

                         1,5                                    UCL
      Defects per Unit




                         1,0

                                                                U=1,37

                         0,5



                         0,0                                    LCL


                               0    10          20         30
                                    Sample
N: sample size
C: number of defects per sample
U: Avg. No of Defects per unit
u bar= c/n 706/516=1.37
• U bar=Centerline
• UCL= 2.25 LCL=0,49
• Although it seems in statistical
  control the defect rate is high,
  almost 1.4 defects per unit.
• Therefore, the company has
  decided to investigate the causes
  of the large number of defects
Recitation 5 Q2

 Sample Sample size No. of defects per Sample Avg. No. of Defects per Unit   LCL    UCL

  28         10                  8                          0,8              0,26   2,48
  29         14                  14                          1               0,43   2,31
  30         11                  8                         0,73              0,31   2,43
  31         29                  14                        0,48              0,72   2,02
  32         19                  7                         0,37              0,57   2,18
  33         19                  12                        0,63              0,57   2,18
  34         45                  25                        0,56              0,85    1,9
Recitation 5 Q2



                   u chart for the moonroof example after
                   implementing the new seal
              3




              2
                                                                 UCL
      Defect per




                                                                 U=1,372
              1
      Unit




                                                                 LCL



              0


                     0    5    10      15    20   25   30   35
                                    Sample
• It is clear that the process has
  changed, in particular that the
  average number of defects per
  unit has been significantly
  reduced. The values are in the
  range of 0.4 and 0.7, previously
  being 1.4.

								
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