New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

Multiscale Characterization of Acrylic Bone Cement Modified with Functionalized Mesoporous Silica Nanoparticles

Acrylic bone cement is widely used to anchor orthopedic implants to bone and mechanical failure of the cement mantle surrounding an implant can contribute to aseptic loosening. In an effort to enhance the mechanical properties of bone cement, a variety of nanoparticles and fibers can be incorporated into the cement matrix. Mesoporous silica nanoparticles (MSNs) are a class of particles that display high potential for use as reinforcement within bone cement. Therefore, the purpose of this study was to quantify the impact of modifying an acrylic cement with various low-loadings of mesoporous silica. Three types of MSNs (one plain variety and two modified with functional groups) at two loading ratios (0.1 and 0.2 wt/wt) were incorporated into a commercially available bone cement. The mechanical properties were characterized using four-point bending, microindentation and nanoindentation (static, stress relaxation, and creep) while material properties were assessed through dynamic mechanical analysis, differential scanning calorimetry, thermogravimetric analysis, FTIR spectroscopy, and scanning electron microscopy. Four-point flexural testing and nanoindentation revealed minimal impact on the properties of the cements, except for several changes in the nano-level static mechanical properties. Conversely, microindentation testing demonstrated that the addition of MSNs significantly increased the microhardness. The stress relaxation and creep properties of the cements measured with nanoindentation displayed no effect resulting from the addition of MSNs. The measured material properties were consistent among all cements. Analysis of scanning electron micrographs images revealed that surface functionalization enhanced particle dispersion within the cement matrix and resulted in fewer particle agglomerates. These results suggest that the loading ratios of mesoporous silica used in this study were not an effective reinforcement material. Future work should be conducted to determine the impact of higher MSN loading ratios and alternative functional groups. (C) 2014 Elsevier Ltd. All rights reserved.