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At present, a cloud computing is attracting attention as a network service to share the computing resources, i.e., networks, servers, storage, applications, and services. We focus on a cloud computing environment by using open source software such as OpenStack and Eucalyptus because of the unification management of data and low cost. In this paper, we propose a new approach to software dependability assessment based on stochastic differential equation modeling in order to consider the interesting aspect of the numbers of components, cloud applications, and users. Also, we analyze actual data to show numerical examples of software dependability assessment considering such characteristics of cloud computing. Moreover, we discuss the determination of optimum software maintenance times minimizing the total expected software cost.

Demand for highly reliable software is increasing day by day which in turn has increased the pressure on the software firms to provide reliable software in no time. Ensuring high reliability of the software can only be done by prolonged testing which in result consumes more resources which is not feasible in the existing market situation. To overcome this, software firms are providing patches after software release so as to fix the remaining number of bugs and to give better product experience to users. An update/fix is a minor portion of software to repair the bugs. With such patches, organizations enhance the performance of the software. Delivering patches after release demands extra effort and resources which are costly and hence not economical for the firms. Also, early patch release might cause improper fixation of bugs, on the other hand, delayed release may increase the chances of more failure during the operational phase. Therefore, determining optimal patch release time is imperative. To overcome the above issues we have formulated a two-dimensional time and effort-based cost model to regulate the optimum release and patch time of software, so that the total cost is minimized. Proposed model is validated on a real life data set.

In the last decade, we have seen enormous growth in software security related problems. This is due to the presence of bad guys who keep eye on the software vulnerabilities and create the security breach. Because of which software firms face huge loss. The problems of the software firms is two folded. One is to decide the optimal discovery time of the software vulnerability and another one is to determine the optimal patching time of those discovered vulnerability. Optimal discovery time of vulnerability is necessary as not disclosing the vulnerability on time may cause serious loss in the coming future. On the other hand, after discovering the vulnerabilities, it is more important to fix them too. Fixing of vulnerabilities is done by patching. But when to patch the vulnerabilities is also a great concern for the software firms. As delay in patch may cause more breaches in security and disadoption of the software and early patching early may reduce the risk but bad patching may increase the risk of security breach even after remedial patch release. In the current work, we have proposed a bi-criterion framework to minimizing cost and risk together under risk and budgetary constraints to determine the optimal vulnerability discovery and patching time. The proposed model is validated using real life data set.

This paper presents a description and research of the model of the team of experts in the application of the Failure Mode and Effects Analysis (FMEA). The main factors affecting the efficiency of the team of experts are highlighted. The generalized mathematical model of influence of these factors on efficiency of work of team is described. The research of this model on three different sets of initial data characterizing typical situations arising at the enterprise at application of the FMEA method is presented. An assessment was made of the simultaneous change of two types of competencies and motivation of both the participants and the team-wide single parameter. The model is studied on three typical situations with a different set of initial conditions and the corresponding parameters. The use of this technique allows for a preliminary assessment of the change in the effectiveness of the analysis by a team of specialists over time, which allows on the one hand to plan correctly not only the application of the FMEA itself within the overall schedule of work, but also to properly organize the training of the team. In addition, this technique will allow you to visually compare the various teams with each other and choose the most optimal or effective team.

The consecutive linear $(k_1,k_2,\dots ,k_{n-r+1})$-out-of-$r$-from-$n$:F system consists of $n$ linear ordered components and the consecutive circular $(k_1,k_2,\dots ,k_n)$-out-of-$r$-from-$n$:F system consists of $n$ circular ordered components. In this paper, we suggest, for the first time, modeling and exact reliability for these models. The linear system fails if and only if there exists a $k_j$-order statistic of $j$-consecutive $r$$(x_j,x_{j+1},\dots ,x_{j+r-1})$ of components in the failed state, $j=1,2,\dots ,n-r+1$, $k_j\in \{1,2,\dots ,r\}$; and the circular system fails if and only if there exists a $k_j$-order statistic of $j$-consecutive $r$$(x_j,x_{j+1},\dots ,x_{j+r-1})$ of components in the failed state, $j=1,2,\dots ,n$, $k_j\in \{1,2,\dots ,r\}$. In this paper, we designed an innovative algorithm to obtain the exact reliability for an extensive class of consecutive linear and circular systems. In continuation, there are the MATLAB Programs of exact reliability for consecutive linear and circular systems. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.