An Economic Design of the Chart with Variable Sample Size Scheme

  • Park, Chang-Soon (Department of Applied Statistics, Chung-Ang University) ;
  • Ji, Seon-Su (Department of Office Automation, National Wonju Jr. College)
  • Published : 1994.12.01


An economic design of the $\bar{X}-R$ chart using variable sample size (VSS) scheme is proposed in this paper. In this design the sample size at each sampling time changes according to the values of the previous two sample statistics, sample mean and range. The VSS scheme uses large sample if the sample statistics appear near inside the control limits and smaller sample otherwise. The set of process parameters, such as the sampling interval, control limits and the sample sizes, are chosen to minimize the expected cost per hour. The efficiency of the VSS scheme is compared to the fixed sample size one for cases where there is multiple of assignable causes. Percent reductions of the expected cost in the VSS design are calculated for some given sets of cost parameters. It is shown that the VSS scheme improves the confidence of the procedure and performs statistically better in terms of the number of false alarms and the average time to signal, respectively.


  1. Journal of the American Statistical Association v.51 The Economic Design of X-Charts Used to Maintain Current Control of a Process Duncan,A.J.
  2. Journal of Americian Statistical Association v.66 The Economic Design of X-Charts When There Is a Multiplicity of Assignable Causes Duncan,A.J.
  3. ACM Transactions on Mathematical Software v.4 Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming Lasdon,L.S.;Waren,A.D.;Jain,A.;Ratner,M.
  4. Technometrics v.28 The Economic Design of Control Charts : A Unified Approach Lorenzen,T.J.;Vance,L.C.
  5. Journal of Quality Technology v.12 Economic Control Chart Design and the Incontrol Time Distribution : A Sensitivity Study McWilliams,T.P.
  6. Journal of Quality Technology v.12 The Economic Design of Control Charts : A Review and Literature Survey Montgomery,D.C.
  7. Communications in Statistics : Simulation and Computation v.23 no.2 Economic Design of a Variable Sample Size X chart Park,C.;Reynolds,M.R.Jr.
  8. Biometrika v.32 The Probability Integral of the Range in Samples of n Observation from a Normal Population Pearson,E.C.;Hartley,H.O.
  9. Presented at the Winter Conference of the American Statistical Association Variable Sample Size X Control Charts Sawalapurkar,U.;Reynolds,M.R.Jr.;Arnord,J.C.
  10. Technometrics v.31 Economic Statistical Control Chart Designs With an Application to X and R Charts Saniga,E.M.