A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature

Statistical estimation of the model parameters of component lifetime distribution based on system lifetime data with known system structure is discussed here. We propose the use of stochastic expectation-maximization (SEM) algorithm for obtaining the maximum likelihood estimates of model parameters based on complete and censored system lifetimes. Different ways of implementing the SEM algorithm are also studied. We have shown that the proposed methods are feasible and are easy to implement for various families of component lifetime distributions. The proposed methodologies are then illustrated with two popular lifetime models—the Weibull and Birnbaum-Saunders distributions. Monte Carlo simulation is then used to compare the performance of the proposed methods with the corresponding estimation by direct maximization. Finally, two illustrative examples are presented along with some concluding remarks.     

Sonochemical reactions with mesoporous alumina

Herein, we report the sonochemical reactions with MSU-X mesoporous alumina (m-Al₂O₃) in aqueous solutions. Sonication (f = 20 kHz, I = 30 W cm^?2, W_aq = 0.67 W mL^?1, T = 36–38 °C, Ar) causes significant acceleration of m-Al₂O₃ dissolution in the pH range of 4–11. Moreover, power ultrasound has a dramatic effect on the textural properties and phase composition of m-Al₂O₃. Short-time sonication at pH = 4 leads to the formation of nanorods and nanofibers of boehmite, AlO(OH). Prolonged ultrasonic treatment causes high aspect morphology transformation to aggregated nanosheets in weakly acid solutions or plated nanocrystals in alkaline solutions. Sonochemical products in alkaline medium are composed principally from boehmite and small amounts of bayerite, Al(OH)₃. Silent hydrolysis of m-Al₂O₃ yields boehmite at pH = 4 and bayerite at pH = 11. The effect of ultrasound on the textural properties of mesoporous alumina as well as on the transformation of nanosized bayerite to boehmite can be consistently attributed to the transient strong heating of the liquid shell surrounding the cavitation bubble which caused the chemical processes similar to those occurred during hydrothermal treatment.