Effect of the Amount of Phase I Data on the Phase II Performance of S2 and S Control Charts

• Autores: Eugenio K. Epprecht, Lorena D. Loureiro, S. Chakraborti
• Localización: Journal of quality technology: A quarterly journal of methods applications and related topics, ISSN 0022-4065, Nº. 2, 47, 2015, págs. 139-155
• Idioma: inglés
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• Resumen

  • Studies on the effect of parameter estimation on control-chart performance have mostly focused on the marginal (unconditional) run length (RL) distribution and some associated characteristics. However, once process parameters are estimated from an in-control (IC) reference sample, the RL follows its conditional distribution given the parameter estimates. With this in mind, the authors' focus in this article is the conditional RL distribution of the S and S² charts. First, the article concentrates on the IC conditional RL distribution, which is geometric with parameter (probability of success) α-TRUE, the unknown attained false-alarm probability, given the estimate of the process standard deviation. The authors obtain and examine the distribution of α-TRUE as a function of the number and the size of the reference samples. The authors then consider a one-sided prediction interval for α-TRUE and, for several sample sizes, obtain the minimum number of reference sample observations that guarantees, with a specified probability, that α-TRUE will not exceed the nominal value of the false-alarm probability, α-NOM, by more than a pre-specified percentage. Next, the authors argue that (and demonstrate why), in the particular case of S and S² charts, there is no practical need of a similar analysis of the effects of parameter estimation on their out-of-control performance, and draw some conclusions in terms of guidance for the user.