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Ch 4 - Statistical Process Control

  1. Introduction (Items preceded with an * are most appropriate for class participation.) 
    1. Classes of Quality Control Techniques
      1. Statistical Process Control (SPC) - techniques used to ensure that processes are meeting standards DURING production.  (p133)
      2. Acceptance Sampling - techniques used to make accept-or-reject decision on a batch of products AFTER production. (Chapter 4 Supplement, page 172)
    2. Variations  (p133)
      1. Assignable Variations - can be traced to a specific factor, such as machine wear, fatigued worker, new raw materials.
      2. Natural Variations – random.
    3. A process is operating in statistical control when the only source of variation is natural.
    4. Types of Quality Measures
      1. Inspection by Attributes - characteristic is either present or not. (Light bulb burns or it doesn't)  (p134)
      2. Inspection by Variables - characteristic is measured in varying degrees. (Light bulb uses 94 watts)
  2. Statistical Process Control Applied to Services (p134)
    1. Historically, SPC has been used to control quality in manufacturing.
    2. Presently, SPC is being used to control quality in services.  Some important characteristics to be controlled in services are:
      1. Financial organizations - employee availability and response time, correctness and timeliness of following procedures, billing accuracy
      2. Medical organizations - correctness and timeliness of physician diagnosis, correctness and timeliness of nursing care, accuracy of lab tests, cleanliness
      3. Retail organizations - correctness and timeliness of check out, stockouts, cleanliness (stored price of sale items above advertised price)
      4. Transportation organizations - (flight) delays, lost luggage, timeliness of check in, passenger cabin air cleanliness
      5. Restaurants - waiting time for seating, order accuracy, cleanliness, employee courtesy
  3. Control Charts (p135)
    1. Def - Control chart - chart used for plotting sample statistics to determine if process is in control.
      1. Chart has upper and lower control limits established from previous data.
      2. If current data falls within upper and lower control limits and no inappropriate pattern is present, then process is considered in control. See Fig 4.1 p136, Fig 4.3 p149.
    2. Types of Control Charts.  (Use Section II.B above for ideas about applying control charts for a CPAI.) 
      1. *Control Charts for Attributes.  (p137) 
        p-Chart - proportion defective items in a sample - proportion of defective (at least 1 typo) documents in a sample of 5 documents.
        c-Chart - number of defective items in a sample - number of typos in a sample of 5 documents.
      2. Control Charts for Variables.  (p142)
         X-Chart - process mean.
        R-Chart - process range.
  4. *Control Charts for Variables (p142)
    1. Definitions
      1. µ - process mean
      2. X - sample mean
      3. R - sample range (largest - smallest)
    2. X-Chart
      1. If X < LCLX Lower Control Limit
        or         X > UCLX Upper Control Limit
        or there is an inappropriate pattern (see Fig 4.1 p136, Fig 4.3 p149)
        then process is considered out of control.
      2. Determination of LCLX , UCLX
        UCLX = mean(         X ) + A2 R
        LCLX = mean(         X ) - A2 R
      3. Example 4.3 Slip-ring bearings - page 143
        n=5,  mean(         X ) = 5.01,  R = 0.115
        From Table 4.1 A2 = 0.58
        UCLX = mean(         X ) + A2 R = 5.01 + .58(.115) = 5.08
        LCLX = mean(         X ) - A2 R = 5.01 - .58(.115) = 4.94
    3. R-Chart
      1. If R < LCLR
        or R > UCLR
        or there is an inappropriate pattern (see Fig 4.1 p136, Fig 4.3 p149)
        then process is considered out of control.
      2. Determination of LCLR , UCLR
        UCLR = D4 R
        LCLR = D3 R
      3. Example 4.4 - page 145
        From Table 4.1,   D4=2.11,    D3=0
        UCLR = 2.115(.115) = .243
        LCLR = 0.0
                            Do assigned HW - Problem 4-25.
  5. *Acceptance Sampling by Attributes
    1. Definitions (page 173, Ch 4 Supplement)
      1. Input
        AQL - acceptable quality level - desire to accept all lots with fraction defective = AQL.
        a = Prob[ reject lot with fraction defective = AQL ]
        LTPD - lot tolerance percent defective - desire to reject all lots with fraction defective = LTPD
        b = Prob[ accept lot with fraction defective = LTPD ]
      2. Output - Sampling Plan
        n - sample size
        c - maximum number of defectives permitted for acceptance
      3. Operating Characteristic Curve - shows probability of acceptance vs. fraction defective for a given n and c. See page 174.
      4. Typical Replacement Procedure
            If lot accepted, only replace defectives in sample.
            If lot rejected, replace defectives in entire lot.
      5. Average Outgoing Quality Limit - AOQL - with the above replacement procedure, the Average Outgoing Quality has a maximum independent of the fraction defective. This guarantees, on average, the quality leaving the inspection station. See page 176.
               Do assigned HW - Additional Problem        .
                                                          (This page was lasted edited on August 29, 2006.)