Optimal designs of the double sampling X̄ chart with estimated parameters

Michael Boon Chong Khoo, Wei Lin Teoh, Philippe Castagliola, Ming Ha Lee

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


The double sampling (DS) X̄ chart detects small and moderate mean shifts quickly. Furthermore, this chart can reduce the sample size. The DS X̄ chart is usually investigated assuming that the process parameters are known. Nevertheless, the process parameters are usually unknown and are estimated from an in-control Phase-I dataset. This paper (i) evaluates the performances of the DS X̄ chart when process parameters are estimated by means of a new proposed theoretical method, (ii) shows that performances with estimated parameters are different from that with known parameters, and (iii) proposes three optimal design procedures: the first design minimizes the out-of-control average run length, the second design minimizes the in-control average sample size and the third design minimizes the average extra quadratic loss, by considering the number of Phase-I samples in these three designs. Additionally, for ease of implementation, this paper provides the new optimal parameters specially computed for the DS X̄ chart with estimated parameters, based on the number of Phase-I samples used in practice. These findings will lead to a more economically feasible process monitoring situation, especially when the process parameters are unknown.

Original languageEnglish
Pages (from-to)345-357
Number of pages13
JournalInternational Journal of Production Economics
Issue number1
Publication statusPublished - Jul 2013


  • Average extra quadratic loss
  • Average run length
  • Average sample size
  • Double sampling (DS) X ̄ chart
  • Optimization design
  • Standard deviation of the run length

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • General Business,Management and Accounting
  • Management Science and Operations Research
  • Economics and Econometrics


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