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n South African Journal of Industrial Engineering - Exact run length distribution of the double sampling X chart with estimated process parameters

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Abstract

Since the run length distribution is generally highly skewed, a significant concern about focusing too much on the average run length (ARL) criterion is that we may miss some crucial information about a control chartâ??s performance. Thus it is important to investigate the entire run length distribution of a control chart for an in-depth understanding before implementing the chart in process monitoring. In this paper, the percentiles of the run length distribution for the double sampling (DS) X chart with estimated process parameters are computed. Knowledge of the percentiles of the run length distribution provides a more comprehensive understanding of the expected behaviour of the run length. This additional information includes the early false alarm, the skewness of the run length distribution, and the median run length (MRL). A comparison of the run length distribution between the optimal ARL-based and MRL-based DS X chart with estimated process parameters is presented in this paper. Examples of applications are given to aid practitioners to select the best design scheme of the DS X chart with estimated process parameters, based on their specific purpose.

Aangesien die lopielengte verdeling in die algemeen baie skeef is, bestaan daar kommer oor die gebruik van die gemiddelde lopielengte (ARL) kriteria, omdat kritiese informasie op die beheerkaart gemis mag word. Dit is dus belangrik om die totale lopielengte verdeling van 'n beheerkaart te ondersoek, voordat die kaart geïmplementeer word. In hierdie artikel word die persentiele van die lopielengte verdeling van die dubbelmonster (DS) X kaart met geskatte prosesparameters bereken. Kennis van die persentiele van die lopielengte verdeling gee 'n meer omvattende verstaan van die verwagte lopielengte vertoning. Dié addisionele informasie sluit die vroeë vals alarm, die skeefheid van die verdeling en die mediaan van die lopielengte (MRL) in. 'n Vergelyking van die lopielengte verdeling tussen optimale ARL-gebaseerde en MRL-gebaseerde DS X kaart met geskatte proses parameters word voorgehou. Voorbeelde word ook voorgehou om beoefenaars te help om die beste weergawe van die DS X kaart met geskatte proses parameters vir hul toepassing te kies.

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/content/indeng/27/1/EJC189201
2016-05-01
2016-12-04
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