Stochastic comparison of parallel systems with Pareto components

Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686-687] from support to general supports, (a), 0. As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering. © 2021 The Author(s). Published by Cambridge University Press

The optimal allocation of active redundancies to k-out-of-n systems with respect to hazard rate ordering

This paper deals with the allocation of active redundancies to a k-out-of-n system with independent and identically distributed (i.i.d.) components in the sense of the hazard rate order. It is shown that the system's hazard rate may be decreased by balancing the allocation of active redundancies. This generalizes the main result of Singh and Singh (1997) and improves the corresponding one of Hu and Wang (2009) as well. As an application, we build the reversed hazard rate order on order statistics from sample having proportional hazard rates, which strengthens the usual stochastic order in Theorem 2.1 of Pledger and Proschan (1971) to the reversed hazard order in the situation that all components are of (rational) proportional hazard rates. (C) 2012 Elsevier B.V. All rights reserved.National Natural Science Foundation of Chin

Normal families of solutions for modified equilibrium equations and their applications

Abstract Using boundary behaviors of solutions for certain Laplace equation proved by Yan and Ychussie (Adv. Difference Equ. 2015:226, 2015) and applying a new method to dispose of the impulsive term with finite mass subject presented by Shi and Liao (J. Inequal. Appl. 2015:363, 2015) from another point of view, we prove that there exists a supra-open in ( X , τ ) $(X,\tau)$ for each V ∈ σ $V \in\sigma$ in which the modified equilibrium equation has normal families of solutions. Moreover, we establish a new expression of a harmonic multifunction for the above equation. As applications, we not only prove the existence of normal families of solutions for modified equilibrium equations but also obtain several characterizations and fundamental properties of these new classes of superharmonic multifunctions

MONOTONICITY PROPERTIES OF RESIDUAL LIFETIMES OF PARALLEL SYSTEMS AND INACTIVITY TIMES OF SERIES SYSTEMS WITH HETEROGENEOUS COMPONENTS

Here, we discuss the stochastic comparison of residual lifetimes of parallel systems and inactivity times of series systems by means of the reversed hazard rate order when the components of the systems are independent but not necessarily identically distributed. We also establish some monotonicity properties of such residual lifetimes of parallel systems and inactivity times of series systems. These results extend some of the recent results in this direction due to Zhao, Li, and Balakrishnan [21], Kochar and Xu [12], and Saledi and Asadi [16]

On hazard rate ordering of parallel systems with two independent components

Natural Science Foundation of China [10771090]This note builds a sufficient condition for the hazard rate ordering between lifetimes of parallel systems with two independent components having proportional hazard rates. Some comparisons on lifetimes of such systems with general components are also obtained. (C) 2010 Elsevier B.V. All rights reserved

Hydraulic Fracture Propagation and Permeability Evolution in the Composite Thin Coal Seam

Hydraulic fracturing can improve the permeability of composite thin coal seam. Recently, characterizing hydraulic fracture (HF) propagation inside the coal seam and evaluating the permeability enhancement with HF extension remain challenging and crucial. In this work, based on the geological characteristics of the coal seam in a coal mine of the southwest China, the RFPA2D-Flow software is employed to simulate the HF propagation and its permeability-increasing effect in the composite thin coal seam, and a couple of outcomes were obtained. (1) Continuous propagation of the hydraulic microcrack-band is the prominent characteristic of HF propagation. With the increment of the injection-water pressure, HF generation in the composite thin coal seam can be divided into three stages: stress accumulation, stable fracture propagation, and unstable fracture propagation. (2) The hydraulic microcrack-band propagates continuously driven by the fluid-injection pressure. The microcrack-band not only cracks the coal seam but also fractures the gangue sandwiched between the coal seams. (3) The permeability in the composite thin coal seam increases significantly with the propagation of hydraulic microcrack-band. The permeability increases by 1~2 magnitudes after hydraulic fracturing. This study provides references to the field applications of hydraulic fracturing in the composite thin coal seam, such as optimizing hydraulic fracturing parameters, improving gas drainage, and safe-efficient mining

Development of two enzyme-linked immunosorbent assay formats for thifluzamide residues’ analysis based on distinct polyclonal antibodies

Haptens 2-Methyl-4-(trifluoromethyl)thiazole-5-carboxylic acid and 2,6-Dibromo-4-(trifluoromethoxy)aniline, the two moieties of thifluzamide, were conjugated with carrier proteins for the synthesis of artificial antigens. Two distinct anti-thifluzamide polyclonal antibodies (PAb-1 and PAb-2) were produced from the immunized female Balb/c mice. The indirect competitive enzyme-linked immunosorbent assay (ic-ELISA) in two formats based on the PAbs was developed for thifluzamide analysis. The concentration of 50% inhibition (IC50) of ELISA-1 was 1.39 mg L−1 and its limit of detection (LOD) was 0.082 mg L−1. Meanwhile, ELISA-2 had a similar IC50 of 1.96 mg L−1 and a LOD of 0.074 mg L−1 as ELISA-1. Both the raised PAbs exhibited high specificity to thifluzamide. The recoveries for spiked samples including water and wheat ranged from 72.0% to 128.4%, and the accuracy of ELISA was confirmed by high-performance liquid chromatography. In summary, the ic-ELISA might be a promising tool for simple, sensitive and rapid detection of thifluzamide residues in real samples