Journal of Applied Mathematics and Decision Sciences, 2005
مدل AR صحيح مقدار با تغييرات هندسی
Direct and vicarious experience of volcanic hazards: Implications for risk perception and adjustment adoption
Australian Journal …, 2000
Informit is an online service offering a wide range of database and full content publication prod... more Informit is an online service offering a wide range of database and full content publication products that deliver the vast majority of Australasian scholarly research to the education, research and business sectors. Informit is the brand that encompasses RMIT Publishing's online products ...
On Conditional Correlation Coefficients of a Wold Markov Process of Gamma Intervals
A concise definition expressed in terms of the mortality (hazard) rate as well as the survival fu... more A concise definition expressed in terms of the mortality (hazard) rate as well as the survival function is proposed for modeling human mortality decelerating to a plateau. Several mortality leveling-off aging distributions are considered and the question concerning the identification of the 'onset of deceleration' is discussed.
In this paper we study an approximation of system reliability using one-step conditioning. It is ... more In this paper we study an approximation of system reliability using one-step conditioning. It is shown that, without greatly increasing the computational complexity, the conditional method may be used instead of the usual minimal cut and minimal path bounds to obtain more accurate approximations and bounds. We also study the conditions under which the approximations are bounds on the reliability. Some further extensions are also presented.
Journal of Applied Mathematics and Decision Sciences
The sample correlation coefficientRis almost universally used to estimate the population correlat... more The sample correlation coefficientRis almost universally used to estimate the population correlation coefficientρ. If the pair(X,Y)has a bivariate normal distribution, this would not cause any trouble. However, if the marginals are nonnormal, particularly if they have high skewness and kurtosis, the estimated value from a sample may be quite different from the population correlation coefficientρ.The bivariate lognormal is chosen as our case study for this robustness study. Two approaches are used: (i) by simulation and (ii) numerical computations.Our simulation analysis indicates that for the bivariate lognormal, the bias in estimatingρcan be very large ifρ≠0, and it can be substantially reduced only after a large number (three to four million) of observations. This phenomenon, though unexpected at first, was found to be consistent to our findings by our numerical analysis.
Journal of Applied Mathematics and Decision Sciences
We describe a simple discrete time renewal process of an event where a success is preceded by a f... more We describe a simple discrete time renewal process of an event where a success is preceded by a failure. Its properties, especially the distributions of the counting and the interval processes, are investigated. We also propose an application to statistical process control based on the waiting time between two adjacent events. It is shown that the average number inspected under the new control scheme is larger than with the so called CCC control chart.
We address several theoretic issues involved in the design of geometric control charts. Primary a... more We address several theoretic issues involved in the design of geometric control charts. Primary among these is the question of setting probability limits, based on notions of "unbiasedness" and "conditional power". A nearly ARL-unbiased design is defined by setting the in-control ARL as near as possible, given the discrete nature of the geometric distribution, to the peak of the ARL curve. An optimal design criterion, based on minimizing the sum of out-of-control ARLs for upward and downward shift is also suggested. These are shown to produce improved conditional power compared with the usual design.
We consider various methods of constructing discrete lifetime models by discretizations of contin... more We consider various methods of constructing discrete lifetime models by discretizations of continuous lifetime models, in particular, through discretizations of their hazard rates. It is well known that there are at least two possible definitions of discrete hazard rates. While this rich source of supply is indeed a good thing, it could also become an impediment when selecting the best model for a given discrete data set. An example is given for each proposed construction method. Included also is a study on discrete distributions that have bathtub shaped hazard rates.
Journal of Applied Mathematics and Decision Sciences
This paper addresses the problem of estimating the ratio of the means of independent normal varia... more This paper addresses the problem of estimating the ratio of the means of independent normal variables in agricultural research. The first part of the research examines the distributional properties of the ratio of independent normal variables, both theoretically and using simulation. The second part of the research evaluates the relative merits of two common estimators of the ratio of the means of independent normal variables in agricultural research, an arithmetic average and a weighted average, via simulation experiments using normal distributions. The results are then tested using research data from rice breeding multi-environment trials in Jilin Province, China, in 1994. These data are used to demonstrate the diagnostic approach developed for assessing the “safe” use of the arithmetic and the weighted average methods for estimating the ratio of the means of independent normal variables.
The basic Weibull distribution is considered the most fundamental and basic lifetime distribution... more The basic Weibull distribution is considered the most fundamental and basic lifetime distribution. Various extensions of the Weibull distribution have been proposed since the 1970s and are useful in the modeling of complex lifetime data that are beyond the capability of the basic Weibull. This article reviews the properties of the basic Weibull distribution and lists the various extensions. It describes the use of Weibull probability plots as a tool for model selection and discusses the parameter estimation and model validation. It concludes with some topics for future research.
Journal of Applied Mathematics and Decision Sciences
A generalized Weibull model that allows instantaneous or early failures is modified so that the m... more A generalized Weibull model that allows instantaneous or early failures is modified so that the model can be expressed as a mixture of the uniform distribution and the Weibull distribution. Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained. Some selected plots of these functions are also presented. An R script was written to fit the model parameters. An application of the modified model is illustrated.
Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function
Reliability Engineering & System Safety
ELSEVIER 09518320(95)001492 Reliability Engineering and System Safety 52 (1995) 8793 1996 Elsevie... more ELSEVIER 09518320(95)001492 Reliability Engineering and System Safety 52 (1995) 8793 1996 Elsevier Science Limited Printed in Northern Ireland. All rights reserved 09518320 95 15.00 Reliability analysis using an additive Weibull model with bathtubshaped failure rate ...
Bathtub Shaped Failure Rate Life Distributions
Stochastic Ageing and Dependence for Reliability, 2000
Dependence and Ageing Properties of Bivariate Lomax Distribution
Series on Quality, Reliability and Engineering Statistics, 2001
A Note on Central Limit Theorem for the Wold's Markov Process of Gamma Intervals
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