A study on stochastic modelling of the repairable system

All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible.When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

The HectoMAP Cluster Survey: Spectroscopically Identified Clusters and their Brightest Cluster Galaxies (BCGs)

We apply a friends-of-friends (FoF) algorithm to identify galaxy clusters and we use the catalog to explore the evolutionary synergy between brightest cluster galaxies (BCGs) and their host clusters. We base the cluster catalog on the dense HectoMAP redshift survey (2000 redshifts deg−2). The HectoMAP FoF catalog includes 346 clusters with 10 or more spectroscopic members within the range 0.05 < z < 0.55 and with a median z = 0.29. We list these clusters and their members. We also include central velocity dispersions (σ *,BCG) for the FoF cluster BCGs, a distinctive feature of the HectoMAP FoF catalog. HectoMAP clusters with higher galaxy number density (80 systems) are all genuine clusters with a strong concentration and a prominent BCG in Subaru/Hyper Suprime-Cam images. The phase-space diagrams show the expected elongation along the line of sight. Lower-density systems include some low reliability systems. We establish a connection between BCGs and their host clusters by demonstrating that σ *,BCG /σ cl decreases as a function of cluster velocity dispersion (σ cl), in contrast, numerical simulations predict a constant σ *,BCG/σ cl. Sets of clusters at two different redshifts show that BCG evolution in massive systems is slow over the redshift range z < 0.4. The data strongly suggest that minor mergers may play an important role in BCG evolution in clusters with σ cl ≳ 300 km s−1. For lower mass systems (σ cl < 300 km s−1), major mergers may play a significant role. The coordinated evolution of BCGs and their host clusters provides an interesting test of simulations in high-density regions of the universe.

Random Walk Analysis in a Reliability System under Constant Degradation and Random Shocks

In this paper, we study a reliability system subject to occasional random shocks hitting an underlying device in accordance with a general marked point process with position dependent marking. In addition, the system ages according to a linear path that eventually fails even without any external shocks that accelerate the total failure. The approach for obtaining the distribution of the failure time falls into the area of random walk analysis. The results obtained are in closed form. A special case of a marked Poisson process with exponentially distributed marks is discussed that supports our claim of analytical tractability. The example is further confirmed by simulation. We also provide a classification of the literature pertaining to various reliability systems with degradation and shocks.

A STUDY OF VARIOUS SOFTWARE RELIABILITY SYSTEMS BY USING ANN

One of the quantifiable credits of software quality is reliability.Programmable/ Software Reliability Growth Model (SRGM) can be used for continuous quality during difficult times. In all conditions where test work fluctuates over time, the customary time-sensitive SRGM may not be clear enough. In order to close this gap, testing work was used instead of time in SRGM. It may be unwise to put forward a restricted test pressure limit in advance because the test work will be endless within the incomprehensible test time. Later in this article, we propose a permanent test stress service related to the old inhomogeneous Poisson process model (NHPP). We use an artificial neural network (ANN) to configure the proposed model, which contains frustration data from the software. Here, it is reasonable to obtain a huge load of game plans for the comparison model, which represents past disappointment data in a comparable way. We use artificial intelligence methods to select game plans with reasonable load for the model to describe the past and future data well. We use a reasonable software disappointment data set to decompose the presentation of the proposed model from the current model. Use the artificial neural network method to design the general Direct Software Reliability Growth Model (SRGM) through test work.: The true quality software is shown by current research mainly focuses on the best method of general guessing modeling.

Allocating hot standbys to randomly weighted k-out-of-n: G systems

In industrial engineering applications, randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems can model many reliability systems whose components may contribute unequally and randomly to the systems’ performance. This paper investigates optimal allocations of hot standbys for [Formula: see text]-out-of-[Formula: see text]: G systems with random weights. First, optimal allocation policies are presented by maximizing the total capacity according to the usual stochastic ordering and the expectation ordering when the system is constituted by independent and heterogeneous components accompanied with independent random weights. Second, we investigate hot standbys allocation for randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems with right [left] tail weakly stochastic arrangement increasing random weights in the sense of the usual stochastic ordering [increasing concave ordering]. Simulation studies are provided to illustrate our theoretical findings as well. These established results can provide useful guidance for system designers on how to introduce hot standbys in randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems in order to enhance their total capacities.

Optimizations of discrete garbage collections in computer reliability systems

In computer science community, garbage collection is a dynamic storage management technology to ensure the reliability of computer systems. In this paper, we consider two discrete garbage collection policies to meet the goal of time consumption for a generational garbage collector. That is, garbage collections occur at a nonhomogeneous Poisson process, (a) tenuring collection is triggered at the Nth minor collection preventively or at a threshold amount [Formula: see text] of surviving objects correctively, whichever takes place first, and (b), tenuring collection is triggered at the first collection when the amount of surviving objects has exceeded a threshold level [Formula: see text] and major collection is triggered at discrete times kT for a given T. Using the damage process and renewal theory, the expected cost rates are obtained, and their optimal policies for tenuring and major collections are discussed analytically and computed numerically.