A Two Control Limits Double Sampling Control Chart by Optimizing Producer and Customer Risks - Dradjad Irianto; Ani Juliani (Journal of Engineering and Technological Sciences, 2010)
Standard Shewhart process control chart has been widely used, but it is  not  sensitive  in  detecting  small  shift.  A  number  of  alternatives  have  been proposed to improve the  capability  of control chart. The double sampling (DS) control chart is aimed at improving the capability to detect any small shift out-of control  condition  by  observing  the  second  sample  without  interruption.  The capabilities  of DS control chart were measured as the expected sample size (as a measure  of  inspection  cost)  or  the  control  chart  power  (as  a  measure  for customer  risk).  Optimization  of  these  criteria  is  used  to  determine  the  control limits.  In  this  paper,  we  optimize  both  producer  and  customer  risks  under  a certain expected number of sample sizes as the constraint. Comparing the result to  the  previous  procedure  that  only  optimize  customer  risk,  the  proposed optimization  procedure  gives  the  same  first  control  limit  but  smaller  second control limits with higher value of control chart power.