Inference for a simple step-stress model with competing risks for failure from the exponential distribution under time constraint

In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under time constraint when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. Since it is found that the MLEs do not exist when there is no failure by any particular risk factor within the specified time frame, the exact sampling distributions of the MLEs are derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions, the parametric bootstrap method, and the Bayesian posterior distribution, we discuss the construction of confidence intervals and credible intervals for the parameters. Their performance is assessed through Monte Carlo simulations and finally, we illustrate the methods of inference discussed here with an example.     

MIEX对水中溴离子的去除效能及其影响因素

利用烧杯试验研究了一种新型磁性离子交换树脂(MIEX)对水中溴离子的去除效能,并考察了水中常见阴离子及有机物对其去除效果的影响.试验结果表明,MIEX可以有效去除纯水中的溴离子,投加量为10 mL/L和20 mL/L时其对溴离子去除率均在90％以上,且达到交换平衡时间分别为5 min和3 min.水中常见的其它带负电物质会在一定程度上影响溴离子的去除效果,在常见的含量条件下10 mL/L的MIEX对溴离子的去除率一般在50％以上.阴离子含量以及MIEX的选择性是影响其对溴离子去除效果的主要因素.有机物的存在使MIEX对溴离子的去除率明显下降,去除率在70％左右.MIEX对有机物、阴离子的去除过程存在差异:10 mL/L的MIEX去除阴离子的反应平衡时间在5 min左右,而去除有机物的平衡时间则较长,其对2种表征有机物含量的指标(UV254、DOC)的去除稳定时间均在20 min以上.     

PPY掺杂离子对电催化脱氯Pd/PPY/Ni电极的影响

为制备高效稳定的用于电催化去除氯代有机物的电极,采用扫描电子显微镜和电催化脱氯实验考察不同聚吡咯掺杂离子对Pd/PPY/Ni复合电极的形貌和电催化加氢脱氯性能的影响.将制备的电极在强吸附性阴离子存在情况下,考察其电催化性能的变化.结果表明,掺杂离子对复合电极的形貌和电催化性能有显著的影响,对甲苯磺酸掺杂的聚吡咯对应的Pd/PPY(PTS)/Ni电极有最高的电催化加氢脱氯效率(高达91.1％),高氯酸钠掺杂的聚吡咯对应的电极电催化性能最差.电催化体系中强吸附离子(ClO4-,Cl-)的存在对电极性能有微弱影响,表明电极具有良好的稳定性,可高效去除水中的氯酚类氯代有机物.     

On the pitting corrosion currents of zinc by chloride anions

The changes in the pitting corrosion current density with time on zinc electrode concerning the concentration of both the passivating borate and the aggressive chloride anions were followed using a simple electrolytic cell. The pitting corrosion currents started to flow after an induction period, τ. This period is found to be a function of the concentration of Cl⁻ anion, according to the relation logτ=β−γlogC_Cl⁻. The pitting corrosion currents finally reached a steady-state value, which depended on the concentration of both B₄O₇²⁻ and Cl⁻ anions. At a constant B₄O₇²⁻ anion concentration, the pitting corrosion current varied with the concentration of Cl⁻ anion according to the relation logi_pit=a₁+b₁logC_Cl⁻. It also varies at constant Cl⁻ anion concentration and various B₄O₇²⁻ anion concentration according to the relation logi_pit=a₂−b₂logC_B4O7²⁻. The susceptibility of the passivating zinc to pitting corrosion was found to be increasing as the temperature and pH of the solution increases. Results are discussed on the basis of adsorption of the aggressive anion on the passivating film, followed by penetration through the film and incorporation in it. This undermines the oxide film and causes pitting corrosion.     

Effect of delayed link failure on probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links

Weak link (WL)/strong link (SL) systems constitute important parts of the overall operational design of high-consequence systems, with the SL system designed to permit operation of the system only under intended conditions and the WL system designed to prevent the unintended operation of the system under accident conditions. Degradation of the system under accident conditions into a state in which the WLs have not deactivated the system and the SLs have failed in the sense that they are in a configuration that could permit operation of the system is referred to as loss of assured safety. The probability of such degradation conditional on a specific set of accident conditions is referred to as probability of loss of assured safety (PLOAS). Previous work has developed computational procedures for the calculation of PLOAS under fire conditions for a system involving multiple WLs and SLs and with the assumption that a link fails instantly when it reaches its failure temperature. Extensions of these procedures are obtained for systems in which there is a temperature-dependent delay between the time at which a link reaches its failure temperature and the time at which that link actually fails.     

Concerted mechanisms of acid-base catalysis in coordination sphere of metal complexes

Kinetics and mechanisms of the following reactions in organic solvents have been studied: (i) formation of Schiff bases from aniline and derivatives of salicylic aldehyde coordinated to Cu(II) and Zn(II); (ii) substitution of one -diketonate ligand coordinated to Fe(III) by another -diketonate ligand; (iii) formation of coordinated hemiacetals from -diketonate ligands and alcohols in coordination sphere of Fe(III); and (iv) formation of urethanes in coordination sphere of Fe(III) (acac)₂ OR where acac and OR are acetylacetonate and alkoxide anions. Such compounds as aniline, alcohols and phenylacetylene serve as catalysts of these reactions. Their catalytic action is explained by concerted processes of hydrogen atom transfer in cyclic intermediate structures.Presented in part at the Royal Society-U.S.S.R. Academy Workshop on Catalysis, Oxford, April 1989.     

Software reliability estimation: A realization of competing risk

A software reliability model presented here assumes a time-dependent failure rate and that debugging can remove as well as add faults with a nonzero probability. Based on these assumptions, the expected number of faults and mean standard error of the estimated faults remaining in the system are derived. The model treats the capability of correcting errors as a random process under which most of the existing software reliability models become special cases of this proposed one. It, therefore, serves to realize a competing risk problem and to unify much of the current software reliability theory. The model deals with the nonindependence of error correction and should be extremely valuable for a large-scale software project.     

Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links

Relationships to determine the probability that a weak link (WL)/strong link (SL) safety system will fail to function as intended in a fire environment are investigated. In the systems under study, failure of the WL system before failure of the SL system is intended to render the overall system inoperational and thus prevent the possible occurrence of accidents with potentially serious consequences. Formal developments of the probability that the WL system fails to deactivate the overall system before failure of the SL system (i.e. the probability of loss of assured safety, PLOAS) are presented for several WL/SL configurations: (i) one WL, one SL; (ii) multiple WLs, multiple SLs with failure of any SL before any WL constituting failure of the safety system; (iii) multiple WLs, multiple SLs with failure of all SLs before any WL constituting failure of the safety system; and (iv) multiple WLs, multiple SLs and multiple sublinks in each SL with failure of any sublink constituting failure of the associated SL and failure of all SLs before failure of any WL constituting failure of the safety system. The indicated probabilities derive from time-dependent temperatures in the WL/SL system and variability (i.e. aleatory uncertainty) in the temperatures at which the individual components of this system fail and are formally defined as multidimensional integrals. Numerical procedures based on quadrature (i.e. trapezoidal rule, Simpson's rule) and also on Monte Carlo techniques (i.e. simple random sampling, importance sampling) are described and illustrated for the evaluation of these integrals.     

Template Effect on Structure and Morphology of Ni(OH)2 Powders Prepared by Hydro-chemical Method

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Surface vs. interior failure behaviors in a structural steel under gigacycle fatigue: Failure analysis and life prediction

The failure behaviors of a structural Cr–Ni–W steel under gigacycle fatigue were investigated, and a life prediction method based on the crack growth was proposed. The discovery of two failure phenomena, including the coexistence of surface and interior cracks and the coexistence of multiple fish-eyes, verifies the possibility of competing failure. The developed interior crack growth model reveals the failure progress at a slow rate below 10⁻¹⁰ m/cycle within the fish-eye induced by the inclusion or the inhomogeneous matrix area. The validity of the life prediction method is proved by the good agreement between the predicted and the experimental lives.