Statistical Process Control SPC Attributes Charts Outline Attributes Charts

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					       Statistical Process Control (SPC)                                          Outline
                Attributes Charts
                                                                                   Attributes Charts
                                                                                   Managerial Decisions for SPC
                                      MGNT 3430                                    Process Capability

                                                                                   Acceptance Sampling

                                                                                   Homework

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     Control Chart Types                                                          Control Chart Types
    Continuous                    Control           Categorical or Discrete                             Control           Categorical or Discrete
    Numerical Data                Charts            Numerical Data                                      Charts            Numerical Data


              Variables                             Attributes                                                            Attributes
               Charts                                Charts                                                                Charts


       R                    X                 P                   C                                                 p                   c
      Chart               Chart             Chart                Chart                                            Chart                Chart


3                                                                             4
    p Chart (p: percent or proportion)                              Calculating p Chart Control Limits

     Type of attributes control chart                                z=2             95.45% limits; z = 3   99.73% limits
          Categorize as defective or nondefective
                                                                                     =    p + zσ
     –
                                                                                                              Mean of sample
                                                                    UCL          p                 p
                                                                                                              proportions
     Measures % of nonconforming items
     –    Example: Count # defective chairs & divide by total       LCL          p   =    p − zσ   p
          chairs inspected; Plot
            Chair is either defective or not defective
                                                                            p (1 − p )
     Relies on Binomial distribution (or normal)                    σ   p    =
                                                                                n
     Like x-bar chart approach
     –    Based on Central Limit Theorem                            n = sample size
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    Example: p Chart                                                See excel file: SPC p c charts

     Audit of order accuracy at Pea Bar & Grill                      Tabs
      –   Enter hundreds of orders each week into the                   –   p chart fill-in
          computerized point-of sale (POS) system
                                                                        –   p chart data
      –   Randomly choose 10 wait staff (# of samples)
                                                                        –   p chart
      –   Randomly choose 50 orders entered by each
      –   Determines # of incorrect orders by each
     Tool to track variation in the ordering process
      –   Compare each server against the average server
      –   Use a z = 3 or 99.73% control limits

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                                                                         c Chart
     c Chart                                                             Control Limits

     Type of attributes control chart                                    UCL     c       = c + 3   c
      –       Discrete quantitative data                                                                Use 3 for 99.7%
     Shows number of nonconformities (defects) in                                                       limits
     a unit                                                              LCL     c       = c − 3   c
      –       Unit may be chair, steel sheet, car, fabric, etc.
      –       Size of unit must be constant
                                                                                                        # Defects in
              Example: Count # defects (scratches, chips etc.) in                    k
      –                                                                                                 Unit i
              each chair of a sample of 100 chairs; Plot                          ∑ c        i

     Relies on Poisson distribution
                                                                         c =      i= 1
                                                                                                       # Units Sampled
                                                                                         k
9     Mean = Variance                                               10




     Example: c Chart                                                    See excel file: SPC p c charts

      Out of control sports program                                       Tabs
          –    A sports reporter is trying to evaluate the                 –   c chart fill-in
               criminality of five targeted teams                          –   c chart data
          –    Takes random sample of players                              –   c chart
          –    # of recorded criminal offenses per team
      Tool to track variation in criminal records
          –    A single player sampled may have > 1 offense
          –    Use a z = 3 or 99.73% control limits

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     Outline                              SPC Decisions

      Attributes Charts                    Which parts are critical to success?

      Managerial Decisions for SPC         Which process steps tend to become OC?
      Process Capability
                                           Which control chart is appropriate?
      Acceptance Sampling
                                           When do we decide to stop the process?
      Homework
                                            –   Run test: rules for check for nonrandom variation

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     Signals in Control Charts            Outline

                                           Attributes Charts

                                           Managerial Decisions for SPC

                                           Process Capability
                                           Acceptance Sampling

                                           Homework

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     Process Capability                                                     Process Capability Ratio, Cp

        SPC                                                                  Capable process has Cp >= 1.0
         –   Keep a process in control
         –   Natural process variation narrow enough to meet quality         Relates spread of process output to tolerance
             standards
                                                                                    (x-bar + or – 3σ)
        Design specifications
         –   Upper (USL) and Lower (LSL) limits)                             Six sigma initiatives           Cp = 2.0
         –   From engineers or customers
             Is a process capable of meeting specs
                                                                                    Upper Specificat ion − Lower Specificat ion
         –
        Process capability measures                                         Cp =
         –
         –
             Process Capability Ratio (Cp)
             Process Capability Index (Cpk)
                                                                                                        6σ

17                                                                     18   σ = standard deviation of the process




     Process Capability Index, Cpk                                          Example of Cp and Cpk

        Proportion of natural variation between                              Honda wants us to machine an engine part
        centerline and nearest spec. limit (USL,LSL)                          –   Our process produces this part with an average
                                                                                  diameter of 15.01 cm and σ = .01 cm
        Cpk=Cp: Process is centered in USL & LSL                              –   They specify a USL=15.03 cm and LCL=14.97 cm
                      ⎡ Upper Specificat ion Limit − x                        –   Is our current process capable of meeting
   C pk = minimum of ⎢                                 , or                       Honda’s specification requirements?
                      ⎣              3σ                                             Cp = USL – LSL / 6σ       .06 / .06 = 1.0
                         x − Lower Specificat ion Limit ⎤                           Cpk = min [USL – x_bar / 3σ , x_bar – LSL / 3σ]

                                      3σ                ⎥                                = min [.02 / .03 , .04 / .03 ]
                                                        ⎦                                = .67
   where x = process mean
19        σ = standard deviation of the process population             20
     Outline                              Acceptance Sampling

      Attributes Charts                   Form of quality statistical testing used for
                                          incoming materials or finished goods
      Managerial Decisions for SPC         –   e.g., purchased material & components
      Process Capability                  Procedure
                                           –   Take one or more samples at random from a lot
                                               (shipment) of items
      Acceptance Sampling                  –   Inspect each of the items in the sample
                                           –   Decide whether to reject the whole lot based on
      Homework                                 the inspection results

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     Outline                              Homework

      Attributes Charts                    Supplement to Ch. 6
      Managerial Decisions for SPC
                                           Discussion Questions: 9, 11
      Process Capability

      Acceptance Sampling                  Problems: s6.15, s6.24, s6.27, s6.30

      Homework
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