Because the normal process capability indices (PCIs) C p , C pu , C pl , and C pk represent the times that the process standard deviation is within the specification limits; then, based on and by using the direct relations among the parameters of the Weibull, Gumbel (minimum extreme value type I) and lognormal distributions, the Weibull and lognormal PCIs are derived in this paper. On the other hand, because the proposed PCIs P p , P pu , P pl , and P pk were derived as a function of the mean and standard deviation of the analyzed process, they have the same practical meaning with those of the normal distribution. Results show that the proposed PCIs could be used as the standard C p , C pu , C pl , and C pk if a short-term variance is analyzed. An application to a set of simulated data is presented.

No abstract

Although the recently proposed Weibull process capability indices (PCIs) actually measure the times that the standard deviation (σx) is within the tolerance specifications, because they not accurately estimate neither the log‐mean (μx) nor the σx values, then the actual PCIs are biased. This actually because μx and σx are both estimated without considering the effect that the sample size (n) has over their values. Hence, μx is subestimated and σx is overestimated. As a response to this issue, in this paper, μx and σx are estimated in function of n. In particular, the PCIs' efficiency is based on the following facts: (1) the derived n value is unique and it completely determines η, (2) the μx value completely determines the η value, and (3) the σx value completely determines the β value. Thus, now, since μx and σx are in function of n and they completely determine β and η, then the proposed PCIs are unbiased, and they completely represent the analyzed process also. Finally, a step by step numerical application is given.

En el análisis de confiabilidad, las distribuciones Weibull y lognormal son ambas analizadas utilizando el logaritmo de los datos observados. Debido a que mientras el logaritmo de datos Weibull presenta sesgo, el logaritmo de datos lognormales es simétrico, entonces en este artículo basados en 1) los coeficientes de variación (CV), 2) en la desviación estándar del logaritmo de los datos, 3) en la posición del percentil de la media del logaritmo de los datos y 4) en dispersión acumulada del logaritmo antes y después de la media, un método para discriminar entre ambas distribuciones es presentado. La eficiencia del método propuesto está basado en el hecho de que el radio entre los coeficientes de regresión (pendientes) b1ln/b1w de la distribución lognormal (b1ln) y de la distribución Weibull (b1w), eficientemente representa el comportamiento del sesgo. De esta manera, dado que el radio de los coeficientes de correlación de la distribución lognormal (Rln) y de la distribución Weibull (Rw), (para un tamaño de muestra fijo), solo depende del radio b1ln/b1w, entonces el coeficiente de correlación múltiple R2 es utilizado como un índice para discriminar entre ambas distribuciones. Una aplicación y el impacto que una mala selección tiene sobre R(t) son también dadas.

The method to determine the minimum strength that a product must present to improve the product's reliability from its actual R(t) to a desired R(t2) index are given. The method can be performed in both the normal and accelerated scenarios. It can be done by using either complete failure time data or based only on the applied stress range. The addressed minimum strength that corresponds to the R(t2) index is then used in the stress/strength reliability function to determine the corresponding reliability R(t/S,s) index. From the comparison between the R(t2) and R(t/S,s) indices, we found they are similar only for high reliability indices (say R(t) > 0.90). For lower indices their difference is significant, implying more research must be undertaken. In the application a zero accelerated test plan (ZATP) is performed to experimentally demonstrate the improved product presents the desired R(t2) index. Finally, because by applying the proposed method we always can reproduce the product's average, then the formulation to determine the capability Cp and ability Cpk indices of the R(t2) index is also given.