MULTIVARIATE SURVIVAL DISTRIBUTIONS OF AGE AND RESIDUAL LIFETIME PROCESSES IN NONHOMOGENEOUS POISSON PROCESS

Let {V(t),t≤0} be the nonhomogeneous Poisson process with cumulative intensituy parameter A(t). |δ,t≥0 the, age process, and y, t≥0} the residual lifetime process. In the present-paper the expressions of n-dimensional survival distribution functions of the processes {δ and γ, and their Lebesgue decompositions are derived.

RESEARCH ON RELIABILITY GROWTH FOR SYNCHRONOUSLY DEVELOPED MULTI-SYSTEMS

An advanced reliability growth model, i. e. exponential model, was presented to estimate the model parameters for multi-systems, which was synchronously tested, synchronously censored, and synchronously improved. In the presented method, the data during the reliability growth process were taken into consideration sufficiently, including the failure numbers, safety numbers and failure time at each censored time. If the multi-systems were synchronously improved for many times, and the reliability growth of each system fitted AMSAA （Army Material Systems Analysis Activity） model, the failure time of each system could be considered rationally as an exponential distribution between two adjoining censored times. The nonparametric method was employed to obtain the reliability at each censored time of the synchronous multisystems. The point estimations of the model parameters, a and b, were given by the least square method. The confidence interval for the parameter b was given as well. An engineering illustration was used to compare the result of the presented method with those of the available models. The result shows that the presented exponential growth model fits AMSAA-BISE （ Army Material Systems Analysis Activity-Beijing Institute of Structure and Environment） model rather well, and two models are suitable to estimate the reliability growth for the synchronously developed multi-systems.

Analysis of Data from a Series of Events by a Geometric Process Model

Geometric process was first introduced by Lam.A stochastic process {X_i,i=1,2,...} iscalled a geometric process (GP) if,for some a>0,{a^(i-1)X_i,i=1,2,...} forms a renewal process.In thispaper,the GP is used to analyze the data from a series of events.A nonparametric method is introduced forthe estimation of the three parameters in the GP.The limiting distributions of the three estimators are studied.Through the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous Poisson models.It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.

SOLUTION TO BSDE WITH NONHOMOGENEOUS JUMPS UNDER LOCALLY LIPSCHITZIAN CONDITION

In this paper, we investigate the existence and uniqueness of the solution to a quasilinear backward stochastic differential equation with Poisson jumps. By introducing a series of approximate equations, we can show that BSDE has a unique adapted solution.

A THREE-PARAMETER FAULT-DETECTION SOFTWARE RELIABILITY MODEL WITH THE UNCERTAINTY OF OPERATING ENVIRONMENTS

As requirements for system quality have increased, the need for high system reliability is also increasing. Soflnvare systems are extremely important, in terms of enhanced reliability and stability, for providing high quality services to customers. However, because of the complexity of software systems, soft-ware development can be time-consuming and expensive. Many statistical models have been developed in the past years to estimate soflnvare reliability. In this paper, we propose a new three-parameter fault-detection software reliability model with the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness-of-fit of the proposed model and several existing non-homogeneous Poisson process （NHPP） models based on three sets of failure data collected from software applications. The results show that the proposed model fits significantly better than other existing NHPP models based on three criteria such as mean squared error （MSE）, predictive ratio risk （PRR）, and predictive power （PP）.

Reliability Modeling and Maintenance Policy Optimization for Deteriorating System Under Random Shock

Performance degradation and random shock are commonly regarded as two dependent competing risks for system failures. One method based on effective service age is proposed to jointly model the cumulative effect of random shock and system degradation, and the reliability model of degradation system under Nonhomogeneous Poisson processes(NHPP) shocks is derived. Under the assumption that preventive maintenance(PM) is imperfective and the corrective maintenance(CM) is minimal repair, one maintenance policy which combines PM and CM is presented. Moreover, the two decision variables, PM interval and the number of PMs before replacement,are determined by a multi-objective maintenance optimization method which simultaneously maximizes the system availability and minimizes the system long-run expect cost rate. Finally, the performance of the proposed maintenance optimization policy is demonstrated via a numerical example.