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Ch 6 Supplement - Statistical Process Control (SPC)

1. Introduction
   1. Classes of Quality Control Techniques (p222)
      1. Statistical Process Control - techniques used to ensure that processes are meeting standards DURING production.
      2. Acceptance Sampling - techniques used to make accept-or-reject decision on a batch of products AFTER production.
   2. Variations (p222)
      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.
    
2. Statistical Process Control Applied to Services
   1. Historically, SPC has been used to control quality in manufacturing.
   2. Presently, SPC is being used to control quality in services.  See Tables 6.5 and 6.6, p210.
   3. Examples of 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.
                   (Note: the above examples do not appear explicitly in Heizer, but are generalizations of Table 6.5.)
3. Statistical Process Control (for Variables) (p222)
   1. Definitions
      1. µ - process mean
      2. s - process std deviation
      3. X  - sample mean
      4. R - sample range (largest - smallest)
      5. 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 S6.7, p234 for examples of inappropriate patterns.
            
4. *Control Charts for Variables (Items preceded with an * are most appropriate for class participation.  Use Section II.C above for ideas as to where to apply control charts.)
   1. Control Chart for Process Mean (p225)
      1. If   X   <  LCL_X      Lower Control Limit
         or  X   >  UCL_X      Upper Control Limit
         or there is an inappropriate pattern (see p234)
         then process is considered out of control.
      2. Determination of LCL_X , UCL_X
         UCL_X = mean( X  ) + A₂ R 
         LCL_X = mean( X  ) - A₂ R
      3. Example S2 Cola Bottles - p 227
         n=5    mean( X ) = 12.00         R = 0.25
         From Table S6.1 (p227) A₂ = 0.577
         UCL_X = mean( X ) + A₂ R  = 12.00 + .577(.25) = 12.144
         LCL_X = mean( X ) - A₂ R  = 12.00 - .577(.25) = 11.856
   2. Control Chart for Process Range
      1. If   R < LCL_R
         or  R > UCL_R
         or there is an inappropriate pattern (see page 234)
         then process is considered out of control.
      2. Determination of LCL_R , UCL_R
         UCL_R = D₄  R
         LCL_R = D₃  R
      3. Example S2 (continued)
         From Table S6.1,  D₄=2.115,  D₃=0
         UCL_R = 2.115(.25) = .529
         LCL_R = 0.0
                             Do assigned HW
         
5. *Acceptance Sampling   (p237)
   1. Typical example: Acceptance Sampling for Attributes
      1. Single Sampling Plan
         n - sample size
         c - maximum number of defectives permitted for acceptance
      2. Replacement procedure
         If lot accepted, only replace defectives in sample.
         If lot rejected, replace defectives in entire lot.
      3. Average Outgoing Quality Limit - AOQL - (p 239) 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.
                     (This page was last edited on January 15, 2010 .)