Asymptotic distribution of the downtime of a monotone system

To compute the distribution of the downtime in a time interval [0,t] for a highly available monotone system, a Compound Poisson process (CP(t)) approximation is often used. In this paper we give sufficient conditions for when the distribution ofCP(t) is an asymptotic limit. We also study the convergence to the normal distribution.     

Use of butyl phosphate in steel analyses : Determination of aluminum

The analysis of steel is simplified in a large measure by the removal of iron prior to the determination of a number of constituents. This report deals with the extraction of iron as the thiocyanate complex with n-butyl phosphate. The condition for optimal iron extraction were investigated. It was found that at a thiocyanate to iron ratio of 6 : 1, removal of iron by the ester is 97.5 % using one extraction. This technique was successfully applied to the determination of aluminum in steel.     

A Redetermination of the crystal structure of 2-aminophenol

The crystal structure of 2-aminophenol has been redetermined from automatic diffractometer data in order to locate the hydroxyl and amino hydrogens and confirm the nature of the intermolecular hydrogen bonding. Crystals are orthorhombic, space groupPbca, witha =19.751(6),b = 7.250(3), andc = 7.852(5) Å, and eight molecules per cell. The structure was solved by Multan and refined to a conventionalR value of 0.030. The molecular geometry compares well with previously reported structures of related species. The molecules are hydrogen bonded from OH to N to form chains parallel to theb axis, with these chains linked together to form sheets by NH to O hydrogen bonds essentially parallel toc. The NH - O hydrogen bonds are 0.33 Å longer than the OH - N ones, and an explanation for this is provided which incorporates newly computed values for atomic electronegativities. Pairs of molecules are mutually hydrogen bonded across inversion centers. There are large cavities between the sheets which could conceivably result in easy intercalation of small foreign molecules, much as in the clathrates formed by urea and -quinol.     

Adsorption of fish oil and poly(vinylbutyral) onto aluminum oxide particles studied by light scattering

The effects of added poly(vinylbutyral) (PVB) and oxidized Menhaden fish oil (O-FO) on dilute suspensions of Al₂O₃ in the azeotropic solvent mixture 73/27 Wt.-% trichloroethylene/ethanol were studied by static (SLS) and dynamic light-scattering (DLS). The DLS correlation function consisted of four terms from: 1) interdiffusion of the two solvents, 2) diffusion of Al₂O₃, 3) diffusion of added O-FO and/or PVB, and 4) an induced velocity of particles through the scattering volume due to laser pressure. The amplitude and relaxation time of all terms could be determined. Addition of PVB to the Al₂O₃ suspension resulted in an increase in particle size corresponding to the adsorption of a monolayer of coils. Addition of O-FO to the Al₂O₃ suspension did not produce a significant increase in particle size, indicating either no adsorption or a compact conformation of O-FO molecules on the Al₂O₃ surface.     

A minimal repair replacement model with two types of failure and a safety constraint

Consider a system subject to two types of failures. If the failure is of type 1, the system is minimally repaired, and a cost C₁ is incurred. If the failure is of type 2, the system is minimally repaired with probability p and replaced with probability 1−p  . The associated costs are _C2,_m$C_{2\text{,}m}$ and _C2,_r$C_{2\text{,}r}$, respectively. Failures of type 2 are safety critical and to control the risk, management has specified a requirement that the probability of at least one such failure occurring in the interval [0, A] should not exceed a fixed probability limit ω. The problem is to determine an optimal planned replacement time T, minimizing the expected discounted costs under the safety constraint. A cost C_r is incurred whenever a planned replacement is performed. Conditions are established for when the safety constraint affects the optimal replacement time and causes increased costs.