Evaluating Six Sigma failure rate for inverse Gaussian cycle times

Six Sigma is a quality philosophy and methodology that aims to achieve operational excellence and delighted customers. The cost of poor quality depends on the sigma quality level and its corresponding failure rate. Six Sigma provides a well-defined target of 3.4 defects per million. This failure rate is commonly evaluated under the assumption that the process is normally distributed and its specifications are two-sided. However, these assumptions may lead to implementation of quality-improvement strategies that are based on inaccurate evaluations of quality costs and profits. This paper defines the relationship between failure rate and sigma quality level for inverse Gaussian processes. The inverse Gaussian distribution has considerable applications in describing cycle times, product life, employee service times, and so on. We show that for these processes attaining Six Sigma target failure rate requires higher quality efforts than for normal processes. A generic model is presented to characterise cycle times in manufacturing systems. In this model, the asymptotic production is described by a drifted Brownian motion, and the cycle time is evaluated by using the first passage time theory of a Wiener process to a boundary. The proposed method estimates the right efforts required to reach Six Sigma goals.     

On computational homogenization of microscale crack propagation

The effective response of microstructures undergoing crack propagation is studied by homogenizing the response of statistical volume elements (SVEs). Because conventional boundary conditions (Dirichlet, Neumann and strong periodic) all are inaccurate when cracks intersect the SVE boundary, we herein use first order homogenization to compare the performance of these boundary conditions during the initial stage of crack propagation in the microstructure, prior to macroscopic localization. Using weakly periodic boundary conditions that lead to a mixed formulation with displacements and boundary tractions as unknowns, we can adapt the traction approximation to the problem at hand to obtain better convergence with increasing SVE size. In particular, we show that a piecewise constant traction approximation, which has previously been shown to be efficient for stationary cracks, is more efficient than the conventional boundary conditions in terms of convergence also when crack propagation occurs on the microscale. The performance of the method is demonstrated by examples involving grain boundary crack propagation modelled by conventional cohesive interface elements as well as crack propagation modelled by means of the extended finite element method in combination with the concept of material forces. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.     

Bootstrapping Analysis of Lifetime Data with Subsampling

Because of cost and time limitations, reliability experiments frequently contain subsampling, which is a restriction on randomization. A two‐stage approach can analyze right censored Weibull distributed reliability data with subsampling. However, in implementing such a method, we found that it did not address the problems of how to perform confidence intervals of low percentiles and reduce the bias of estimates. In this paper, we present a two‐stage bootstrapping approach and an unbiasing factor approach to solve the aforementioned problems. An example is provided to illustrate the proposed method. In addition, the proposed method is compared with existing methods through simulation. The resulting simulations show that the proposed method performs well in low percentiles. Copyright © 2015 John Wiley & Sons, Ltd.     

Smart Utilization of Carbon Dots in Semiconductor Photocatalysis

Efficient capture of solar energy will be critical to meeting the energy needs of the future. Semiconductor photocatalysis is expected to make an important contribution in this regard, delivering both energy carriers (especially H₂) and valuable chemical feedstocks under direct sunlight. Over the past few years, carbon dots (CDs) have emerged as a promising new class of metal‐free photocatalyst, displaying semiconductor‐like photoelectric properties and showing excellent performance in a wide variety of photoelectrochemical and photocatalytic applications owing to their ease of synthesis, unique structure, adjustable composition, ease of surface functionalization, outstanding electron‐transfer efficiency and tunable light‐harvesting range (from deep UV to the near‐infrared). Here, recent advances in the rational design of CDs‐based photocatalysts are highlighted and their applications in photocatalytic environmental remediation, water splitting into hydrogen, CO₂ reduction, and organic synthesis are discussed.