Optimal designs of the double sampling X¯ chart with estimated parameters

Michael B.C. Khoo, W.L. Teoh, Philippe Castagliola and M.H. Lee

International Journal of Production Economics, 2013, vol. 144, issue 1, 345-357

Abstract: The double sampling (DS) X¯ chart detects small and moderate mean shifts quickly. Furthermore, this chart can reduce the sample size. The DS X¯ 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 X¯ 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 X¯ 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.

Keywords: Double sampling (DS) X¯ chart; Average run length; Average sample size; Standard deviation of the run length; Average extra quadratic loss; Optimization design (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:proeco:v:144:y:2013:i:1:p:345-357

DOI: 10.1016/j.ijpe.2013.02.022

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