ALT Analysis Research Papers - Academia.edu (original) (raw)

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In Weibull accelerated life test analysis (ALT) with two or more variables (X2, X3, ... Xk), we estimated, in joint form, the parameters of the life stress model r{X(t)} and one shape parameter β. These were then used to extrapolate the... more

In Weibull accelerated life test analysis (ALT) with two or more variables (X2, X3, ... Xk), we estimated, in joint form, the parameters of the life stress model r{X(t)} and one shape parameter β. These were then used to extrapolate the conclusions to the operational level. However, these conclusions are biased because in the experiment design (DOE) used, each combination of the variables presents its own Weibull family (βi, ηi). Thus the estimated β is not representative. On the other hand, since (βi, ηi) is determined by the variance of the logarithm of the lifetime data σt2 , the response variance σy2 and the correlation coefficient R2, which increases when variables are added to the analysis, β is always overestimated. In this paper, the problem is statistically addressed and based on the Weibull families (βi, ηi) a vector Yη is estimated and used to determine the parameters of r{X(t)}. Finally, based on the variance σy2 of each level, the variance of the operational level σop2 is estimated and used to determine the operational shape parameter βop. The efficiency of the proposed method is shown by numerical applications and by comparing its results with those of the maximum likelihood method (ML).

• • by and +3
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  • Experimental Design, Multiple Linear Regression, ALT Analysis, Weibull Analysis

espanolEn el analisis de pruebas de vida acelerada Weibull con dos o mas variables aceleradas (X2,X3,...Xk) , estimamos en forma conjunta los parametros del modelo de relacion vida esfuerzo r{X(t)} y un parametro de forma s. Despues estos... more

espanolEn el analisis de pruebas de vida acelerada Weibull con dos o mas variables aceleradas (X2,X3,...Xk) , estimamos en forma conjunta los parametros del modelo de relacion vida esfuerzo r{X(t)} y un parametro de forma s. Despues estos parametros son utilizados para extrapolar las conclusiones al nivel operacional. Como sea, estas conclusiones estan sesgadas debido a que dentro del diseno de experimentos (DOE) utilizado, cada combinacion de las variables presenta su propia familia Weibull (si,ni) . De esa forma la estimada s no es representativa. Por otro lado, dado que s esta determinada por la varianza del logaritmo de los tiempos de vida o²t , por la varianza de la respuesta o²y y por el coeficiente de correlacion , el cual crece cuando se agregan variables al analisis, s es siempre sobre estimada. En este articulo, el problema es estadisticamente identificado y basado sobre las familias Weibull (si,ni) un vector Yn es estimado y utilizado para determinar los parametros de r{X...

• • by Piña Monarrez
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  • Engineering, Experimental Design, Multiple Linear Regression, ALT Analysis
• • by Carlos Avila
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  • Experimental Design, Multiple Linear Regression, ALT Analysis, Weibull Analysis