Manuel R. Piña-Monarrez

Non-normal Capability Indices for the Weibull and Lognormal Distributions

Because the normal process capability indices (PCIs) Cp, Cpu, Cpl, and Cpk 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 Pp, Ppu, Ppl, and Ppk 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 Cp, Cpu, Cpl, and Cpk if a short-term variance is analyzed. An application to a set of simulated data is presented. Copyright

Weibull and lognormal Taguchi analysis using multiple linear regression

Abstract The paper provides to reliability practitioners with a method (1) to estimate the robust Weibull family when the Taguchi method (TM) is applied, (2) to estimate the normal operational Weibull family in an accelerated life testing (ALT) analysis to give confidence to the extrapolation and (3) to perform the ANOVA analysis to both the robust and the normal operational Weibull family. On the other hand, because the Weibull distribution neither has the normal additive property nor has a direct relationship with the normal parameters (µ, σ), in this paper, the issues of estimating a Weibull family by using a design of experiment (DOE) are first addressed by using an L9 (34) orthogonal array (OA) in both the TM and in the Weibull proportional hazard model approach (WPHM). Then, by using the Weibull/Gumbel and the lognormal/normal relationships and multiple linear regression, the direct relationships between the Weibull and the lifetime parameters are derived and used to formulate the proposed method. Moreover, since the derived direct relationships always hold, the method is generalized to the lognormal and ALT analysis. Finally, the method’s efficiency is shown through its application to the used OA and to a set of ALT data.

Multiobjective optimization of torch brazing process by a hybrid of fuzzy logic and multiobjective artificial bee colony algorithm

This paper describes an application of a hybrid of fuzzy logic (FL) and multiobjective artificial bee colony algorithm (MOABC) for optimizing the torch brazing process of aluminum in the fabrication of condensers in the automotive manufacturing industry of Juarez, Mexico. This work aims to show how artificial intelligence is being applied in the manufacturing sector of Mexico for optimizing processes leading to cost reduction. The approach consists of using FL as surrogate model of the brazing process; after, MOABC is applied to find the nondominated solutions for leak rate which is a quality test of the condenser and production time. Results show the use of artificial intelligence is an excellent tool for optimizing manufacturing processes leading to improve productivity, mainly in the selected region, where this type of methodologies are fairly new in applicability.

Conditional Weibull Control Charts Using Multiple Linear Regression

Because in Weibull analysis, the key variable to be monitored is the lower reliability index (R(t)), and because the R(t) index is completely determined by both the lower scale parameter (η) and the lower shape parameter (β), then based on the direct relationships between η and β with the log-mean (μx) and the log-standard deviation (σx) of the analyzed lifetime data, a pair of control charts to monitor a Weibull process is proposed. Moreover, because the fact that in Weibull analysis, right censored data is common, and because it gives uncertainty to the estimated Weibull parameters, then in the proposed charts, μx and σx are estimated of the conditional expected times of the related Weibull family. After that both, μx and σx are used to monitor the Weibull process. In particular, μx was set as the lower control limit to monitor η, and σx was set as the upper control limit to monitor β. Numerical applications are used to show how the charts work. Copyright

Reliability Analysis for Laptop Computer Under Electrical Harmonics

Because of electrical variations presented in the power line, the estimated reliability of electronic devices, such as a laptop computer, differs from the real reliability. The found sources of electrical variations in the power lines were the electrical harmonics in the order of frequencies of 3, 5, 7, 11, and 13. As a consequence of these harmonics, the voltage in the power line has a time varying behavior. And because the power law model used to estimate the reliability does not consider this varying behavior, the estimated reliability differs from the real one. Thus, in this paper, a model that incorporates the electrical harmonics in the power law model is presented. The model was developed according to the Cumulative Damage Model and the time varying voltage into the power law model was modeled by using the compact form of the Fourier series. A comparative study between constant and time varying voltage is presented to analyze the effect of the electrical harmonics in the laptop computer. The conclusions of the study showed that the laptop computer reduces its lifetime by 2000 h on average and the failure rate increases when the electrical harmonics are present in the power lines. Copyright

Unbiased Weibull capabilities indices using multiple linear regression

Manufacturing and Industrial Engineering Department of the Engineering and Technological Institute, Universidad Autónoma de Ciudad Juárez, Cd. Juárez Chih, Mexico Doctoral Student of the Technological Doctoral Program at the Engineering and Technological Institute, Universidad Autónoma de Ciudad Juárez, Cd. Juárez, Chih, Mexico Validation Laboratory Department, Ted de México S.A de C.V., Cd. Juárez, Chih, Mexico