Load Sharing Models

Consider a system of components whose lifetimes are governed by a probability distribution. Load sharing refers to a model of stochastic interdependency between components that operate within a system. If components are set up in a parallel system (see Parallel, Series, and Series–Parallel Systems) for example, the system survives as long as at least one component is operating. In a typical load-sharing system, once a component fails, the remaining components suffer an increase in failure rate due to the extra “load” they must encumber due to the failed component

Statistical Reliability with Applications

This chapter reviews fundamental ideas in reliability theory and inference. The first part of the chapter accounts for lifetime distributions that are used in engineering reliability analyis, including general properties of reliability distributions that pertain to lifetime for manufactured products. Certain distributions are formulated on the basis of simple physical properties, and other are more or less empirical. The first part of the chapter ends with a description of graphical and analytical methods to find appropriate lifetime distributions for a set of failure data. The second part of the chapter describes statistical methods for analyzing reliability data, including maximum likelihood estimation and likelihood ratio testing. Degradation data are more prevalent in experiments in which failure is rare and test time is limited. Special regression techniques for degradation data can be used to draw inference on the underlying lifetime distribution, even if failures are rarely observed. The last part of the chapter discusses reliability for systems. Along with the components that comprise the system, reliability analysis must take account of the system configuration and (stochastic) component dependencies. System reliability is illustrated with an analysis of logistics systems (e.g., moving goods in a system of product sources and retail outlets). Robust reliability design can be used to construct a supply chain that runs with maximum efficiency or minimum cost

Detection and Estimation of a Mixture in Power Law Processes for a Repairable System

The power law process has proved to be a useful tool in characterizing the failure process of repairable systems. This paper presents a procedure for detecting and estimating a mixture of reliable and unreliable (defective) systems. The test of a mixture, based on a simple likelihood ratio, is illustrated with truncated failure data for copy machines. Bootstrap methods are used to gauge the estimation uncertainty, and optimal decisions for system replacement are determined based on the observed likelihood

Reliability Modeling in Spatially Distributed Logistics System

This article proposes methods for modeling service reliability in a supply chain. The logistics system in a supply chain typically consists of thousands of retail stores along with multiple distribution centers (DC). Products are transported between DC & stores through multiple routes. The service reliability depends on DC location layouts, distances from DC to stores, time requirements for product replenishing at stores, DC\u27s capability for supporting store demands, and the connectivity of transportation routes. Contingent events such as labor disputes, bad weather, road conditions, traffic situations, and even terrorist threats can have great impacts on a system\u27s reliability. Given the large number of store locations & multiple combinations of routing schemes, this article applies an approximation technique for developing first-cut reliability analysis models. The approximation relies on multi-level spatial models to characterize patterns of store locations & demands. These models support several types of reliability evaluation of the logistics system under different probability scenarios & contingency situations. Examples with data taken from a large-scale logistics system of an automobile company illustrate the importance of studying supply-chain system reliability

Extending the Skill Test for Disease Diagnosis

For diagnostic tests, we present an extension to the skill plot introduced by Briggs and Zaretski (Biometrics 2008; 64:250–261). The method is motivated by diagnostic measures for osteopetrosis in a study summarized by Hans et al. (The Lancet 1996; 348:511–514). Diagnostic test accuracy is typically defined using the area (or partial area) under the receiver operator characteristic (ROC) curve. If partial area is used, the resulting statistic can be highly subjective because the focus region of the ROC curve corresponds to a set of low false‐positive rates that are chosen by the experimenter. This paper introduces a more objective diagnostic test for which the focus region depends on a skill score, which in turn depends on the loss functions associated with misdiagnosis. More specifically, the skill‐based diagnostic test serves as a more objective version of the nonparametric test introduced by Dodd and Pepe (Biometrics 2003; 59:614–623)

Adjusted Empirical Likelihood Models with Estimating Equations for Accelerated Life Tests

This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology

Analysis of Environmental Data with Censored Observations

The potential threats to humans and to terrestrial and aquatic ecosystems from environmental contamination could depend on the sum of the concentrations of different chemicals. However, direct summation of environmental data is not generally feasible because it is common for some chemical concentrations to be recorded as being below the analytical reporting limit. This creates special problems in the analysis of the data. A new model selection procedure, named forward censored regression, is introduced for selecting an appropriate model for environmental data with censored observations. The procedure is demonstrated using concentrations of atrazine (2-chloro- 4-ethylamino-6-isopropylamino-s-triazine), deethylatrazine (DEA, 2-amino-4-chloro-6-isopropylamino-s-triazine), and deisopropylatrazine (DIA, 2-amino-4-chloro-6-ethylamino-striazine) in groundwater in the midwestern United States by using the data derived from a previous study conducted by the U.S. Geological Survey. More than 80% of the observations for each compound for this study were left censored at 0.05 μg/L. The values for censored observations of atrazine, DEA, and DIA are imputed with the selected models. The summation of atrazine residue (atrazine + DEA + DIA) can then be calculated using the combination of observed and imputed values to generate a pseudo-complete data set. The all-subsets regression procedure is applied to the pseudo-complete data to select the final model for atrazine residue. The methodology presented can be used to analyze similar cases of environmental contamination involving censored data

A 9 bp cis-element in the promoters of class I small heat shock protein genes on chromosome 3 in rice mediates L-azetidine-2-carboxylic acid and heat shock responses

In rice, the class I small heat shock protein (sHSP-CI) genes were found to be selectively induced by L-azetidine-2-carboxylic acid (AZC) on chromosome 3 but not chromosome 1. Here it is shown that a novel cis-responsive element contributed to the differential regulation. By serial deletion and computational analysis, a 9 bp putative AZC-responsive element (AZRE), GTCCTGGAC, located between nucleotides –186 and –178 relative to the transcription initiation site of Oshsp17.3 was revealed. Deletion of this putative AZRE from the promoter abolished its ability to be induced by AZC. Moreover, electrophoretic mobility shift assay (EMSA) revealed that the AZRE interacted specifically with nuclear proteins from AZC-treated rice seedlings. Two AZRE–protein complexes were detected by EMSA, one of which could be competed out by a canonical heat shock element (HSE). Deletion of the AZRE also affected the HS response. Furthermore, transient co-expression of the heat shock factor OsHsfA4b with the AZRE in the promoter of Oshsp17.3 was effective. The requirement for the putative AZRE for AZC and HS responses in transgenic Arabidopsis was also shown. Thus, AZRE represents an alternative form of heat HSE, and its interaction with canonical HSEs through heat shock factors may be required to respond to HS and AZC