Quantile-Based Reliability Analysis

Quantile functions are equivalent alternatives to distribution functions in modeling and analysis of statistical data. The present article discusses the role of quantile functions in reliability studies. We present the hazard, mean residual, variance residual, and percentile residual quantile functions, their mutual relationships and expressions for the quantile functions in terms of these functions. Further, some theoretical results relating to the Hankin and Lee (2006 Hankin , R. K. S. , Lee , A. ( 2006 ). A new family of non-negative distributions . Austral. N.Z. J. Statist. 48 : 67 – 78 .[Crossref], [Web of Science ®] , [Google Scholar]) lambda distribution are discussed.     

Supply Networks as a Complex Adaptive System: Toward Simulation‐Based Theory Building on Evolutionary Decision Making

In this article, we examine how the firms embedded in supply networks engage in decision making over time. The supply networks as a complex adaptive system are simulated using cellular automata (CA) through a dynamic evolution of cooperation (i.e., “voice” decision) and defection (i.e., “exit” decision) among supply network agents (i.e., firms). Simple local rules of interaction among firms generate complex patterns of cooperation and defection decisions in the supply network. The incentive schemes underlying decision making are derived through different configurations of the payoff‐matrix based on the game theory argument. The prisoner's dilemma game allows capturing the localized decision‐making process by rational agents, and the CA model allows the self‐organizing outcome to emerge. By observing the evolution of decision making by cooperating and defecting agents, we offer testable propositions regarding relationship development and distributed nature of governance mechanisms for managing supply networks.     

On some aspects of a flexible class of additive Weibull distribution

Here we consider a more flexible class of the additive Weibull distribution of Xie and Lai (Reliab. Eng. Syst. Safety, 1995) and investigate some of its important properties such as expressions for its cumulative distribution function, reliability measures, quantile function, characteristic function, raw moments, incomplete moments, etc. The distribution and moments of order statistics are obtained along with certain structural properties. The maximum-likelihood estimation of the parameters of the distribution is attempted and the usefulness of the model in certain applied areas is illustrated with the help of certain real life data sets.     

Proportional hazards model with quantile functions

Proportional Hazards Model (PHM) introduced by Cox (1972) is extensively studied in literature. In this paper, we study reliability properties of the PHM using quantile functions. Some special properties of the quantile function, which are not shared by distribution function are explored to study various properties of the PHM. We discuss ageing properties and stochastic orders for the PHM. The quantile-based dynamic cumulative Kullback-Leibler divergence of PHM is studied. Characterizations of some important quantile densities using PHM are also proved.     

Powerline Frequency Electric and Magnetic Fields: A Pilot Study of Risk Perception

The perception of the potential risk arising from human exposure to 50/60 Hz electric and magnetic fields was studied with a quasi-random sample of 116 well-educated, opinion leaders using the risk perception framework previously developed by Slovic, Fischhoff, and Lichtenstein. These individuals rated exposure to fields from transmission lines and electric blankets on a variety of scales that have been found useful in characterizing people's risk attitudes and perceptions. These judgments allowed us to conjecture about the likely desire for regulation of these potential hazards and the likely response to a publicized problem (e.g., an accident or ominous research finding) involving these two sources of exposure. Various forms of detailed information about 50/60 Hz fields were supplied to respondents. The provision of information produced modest, but statistically significant, changes in perceptions in the direction of greater concern about the risks. In response to questions of public policy, participants desired modest regulatory control of field exposure from transmission lines and little or no control of field exposure from appliances like electric blankets.     

Small Group Studies of Regulatory Decision-Making for Power-Frequency Electric and Magnetic Fields

Three groups of lay opinion leaders were used in a group role-playing decision exercise designed to explore problems in public risk management decision-making. The application domain was possible risks from the 60 Hz electric and magnetic fields associated with high-voltage power transmission lines. While there were differences in the make-up and dynamics of the three groups, the structure and substantive content of the tasks undertaken dominated intergroup variation in terms of the factors that were most important to group members' decisions. The groups displayed sophistication in their identification of decision attributes and in many of the arguments they advanced, but experienced difficulties in structuring and making trade-offs and decisions. The groups were not good at normalizing or otherwise manipulating quantitative information, and used it largely in the form it was received. Upper-bound risk estimates were treated operationally in most group discussions as expected values. Several kinds of strong framing effects were observed in the use of cost and risk information. Specific quantitative results obtained must be treated with care but may provide a starting place for further work on the acceptable level of transmission line risk.     

On some reliability aspects of Pearson family of distributions

We characterize the Pearson family of distributions by finding a relationship between the failure rate and the higher order moments of residual life. We also present a characterization theorem of IFR(DFR) class of distributions in the Pearson family.     

Kernel Density Estimation on a Linear Network

This paper develops a statistically principled approach to kernel density estimation on a network of lines, such as a road network. Existing heuristic techniques are reviewed, and their weaknesses are identified. The correct analogue of the Gaussian kernel is the ‘heat kernel’, the occupation density of Brownian motion on the network. The corresponding kernel estimator satisfies the classical time‐dependent heat equation on the network. This ‘diffusion estimator’ has good statistical properties that follow from the heat equation. It is mathematically similar to an existing heuristic technique, in that both can be expressed as sums over paths in the network. However, the diffusion estimate is an infinite sum, which cannot be evaluated using existing algorithms. Instead, the diffusion estimate can be computed rapidly by numerically solving the time‐dependent heat equation on the network. This also enables bandwidth selection using cross‐validation. The diffusion estimate with automatically selected bandwidth is demonstrated on road accident data.     

Multivariate discrete reversed hazard rates

In the present paper, we define and study four versions of multivariate discrete reversed hazard rates, namely scalar reversed hazard rate, vector reversed hazard rate, alternative reversed hazard rate, and conditional reversed hazard rate. Various properties of these functions are studied. Interrelationships between these reversed hazard rates are explored. We also present characterization of discrete distributions using these reversed hazard rates.     

On characterizing mixtures of some life distributions

Received: October 15, 1998; revised version: January 10, 2000