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n South African Journal of Industrial Engineering - The effects of parameter estimation on minimising the in-control average sample size for the double sampling x̄ chart

Volume 24, Issue 3
  • ISSN : 1012-277X
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Abstract

The double sampling (DS) x̄ chart, one of the most widely-used charting methods, is superior for detecting small and moderate shifts in the process mean. In a right skewed run length distribution, the median run length (MRL) provides a more credible representation of the central tendency than the average run length (ARL), as the mean is greater than the median. In this paper, therefore, MRL is used as the performance criterion instead of the traditional ARL. Generally, the performance of the DS x̄ chart is investigated under the assumption of known process parameters. In practice, these parameters are usually estimated from an in-control reference Phase-I dataset. Since the performance of the DS x̄ chart is significantly affected by estimation errors, we study the effects of parameter estimation on the MRL-based DS x̄ chart when the in-control average sample size is minimised. This study reveals that more than 80 samples are required for the MRL-based DS x̄ chart with estimated parameters to perform more favourably than the corresponding chart with known parameters.

Die dubbelmonster x̄-beheerkaart, wat grootskaals gebruik word, is voortreflik vir die opsporing van geringe en middelmatige verskuiwings van prosesmediaan. By 'n regsskuinse verdeling van looplengte lewer de mediaanlooplengte (MLL) 'n beter groottewaarde as die gemiddelde looplengte. Gewoonlik word die vertoning van die bogenoemde x̄-beheerkaart bepaal met geskatte prosesparameters. Die skattings word bepaall op die veronderstelling dat die proses onder beheer is. Aangesien die MLL gebaseerde beheerkaartvertoning betekenisvol beïnvloed word deur skattingsfoute, word dit ondersoek uit minimum gemiddelde monstergrootte. Die uiteindelike resultaat van die navorsing toon dat 80 monsters benodig word vir 'n beter vertoning as die ooreenstemmende beheerkaart vir bekende parameters.

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/content/indeng/24/3/EJC145254
2013-11-01
2016-12-10

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