As a system complexity increases and technology innovation progresses rapidly, it tends to lease a system rather than own one. This paper deals with a decision-making model to determine the preventive maintenance strategy for leased equipment. Various maintenance options are presented and formulated via the non-homogeneous Poisson process. During the lease period, the preventive maintenance strategy that minimizes the total cost among the presented maintenance options is selected. A numerical example is provided to illustrate the proposed model.

The rapid growth of engineering technology and the emergence of systemized and large-scale engineering systems have resulted in complexity and uncertainty throughout the lifecycle activities of engineering systems. This complex and large-scale engineering system consists of numerous components, but system failure can be caused by failure of any one of a number of components. There is a real difficulty in managing such a complex and large-scale system as a part. In order to efficiently manage the system and have high reliability, it is necessary to structure a system with a complex structure as a sub-system. Also, in the case of a system in which cause of failures exist at the same time, it is required to identify the correlation of the components lifetime and utilize it for the design policy or maintenance activities of the system. Competitive risk theory has been used as a theory based on this concept. In this study, we apply the competitive risk theory to the models with combined structure of series and parallel which is the basic structure of most complex engineering systems. We construct a competing risks model and propose a mathematical model of net lifetime and crude lifetime for each cause of failure, assuming that the components consisting a parallel system are mutually dependent. In addition, based on the constructed model, the correlation of cause of failure is mathematically analyzed and the hazard function is derived by dividing into net lifetime and crude lifetime.

This study is to develop a mathematical analysis model to grasp the behaviors of cartels. Cartels are formed tacitly and cause tremendous damage to consumers in modern society which is composed of advanced industry structure. The government authorities have instituted the leniency programs to respond cartels. However, cartels will continue unless there are legal sanctions against cartels based on an accurate analysis of leniency programs. The proposed cartel equilibrium analysis model is a mathematical behavior model which is based on the existing methods and the prison’s dilemma of game theory. Therefore, the model has a form of pay off matrix of two players. We use a iterated polymatrix approximation (IPA) method to deduct a Nash equilibrium point. The model is validated by an empirical analysis as well.

In this paper, a mathematical model is developed for finding a degree of influence of risks affecting the project. At risk identification step, all risks are structured in forms of block diagrams after risks of project activities are identified. At risk analysis step, reliability functions are derived based on block diagrams of risks. Reliability function represents the probability of the project success. Based on the derived reliability functions, risks importance is defined as a criterion for expressing a degree of influence of each risk affecting the success of the project, which is. Risks importance includes the structural importance of risk, the probability of risk, and the impact of risk. It could be applied to determine the priorities of risks which should be controlled, and the use of such priorities could guarantee successful project activities. Finally, examples of the proposed mathematical models will be given.

This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to pro

This paper is intended to compare the hazard rate estimations from Bayesian approach and maximum likelihood estimate(MLE) method. Hazard rate frequently involves unknown parameters and it is common that those parameters are estimated from observed data by

This paper is intended to compare between the Bayesian estimate of a failure rate and the failure rate of a mixed distribution. For the sake of simplification, an exponential distribution and a gamma distribution are adopted as a sampling distribution and its natural conjugate prior distribution. The result shows that both the failure rates are being updated using data and they differ in whether they are functions of unobserved future data or not.

Used as a mixing distribution for an unknown Poisson parameter, the gamma distribution leads to the negative binomial distribution. The hyperparameters of the gamma distribution have their own meanings according to what the Poisson parameter represents. Different sources in the randomness of the Poisson parameter give different interpretations of the negative binomial distribution.

This paper presents an approach to derive likelihood models for use in engineering design problems. One main point is made. It is that incorporating engineering knowledge into a likelihood model is possible. The work is foundational in nature, but is developed with an explicit example taken from fatigue failure problem of a structural component, the Paris crack-propagation criterion, and a modified truncated Gaussian distribution.