Vidhyashree Nagaraju

Maximum-Likelihood Estimation of Parameters of NHPP Software Reliability Models Using Expectation Conditional Maximization Algorithm

Since its introduction in 1977, the expectation maximization (EM) algorithm has been one of the most important and widely used estimation method in estimating parameters of distributions in the presence of incomplete information. In this paper, a variant of the EM algorithm, the expectation conditional maximization (ECM) algorithm, is introduced for the first time and it provides a promising alternative in estimating the parameters of nonhomogeneous poisson (NHPP) software reliability growth models (SRGM). This algorithm circumvents the difficult M-step of the EM algorithm by replacing it by a series of conditional maximization steps. The utility of the ECM approach is demonstrated in the estimation of parameters of several well-known models for both time domain and time interval software failure data. Numerical examples with real-data indicate that the ECM algorithm performs well in estimating parameters of NHPP SRGM with complex mean value functions and can produce a faster rate of convergence.

Impact of Correlated Component Failure on Preventive Maintenance Policies

A primary goal of maintenance is to minimize the consequences of component and system failures. Two subcategories of maintenance actions include: preventive maintenance (PM) at predetermined time intervals prior to failure and emergency repair (ER) upon failure, where the cost and downtime of ER is significantly greater than PM. Most maintenance models developed over the past several decades assume component failures are statistically independent. This assumption simplifies calculations, but is dangerous for safety critical systems that must be maintained because correlated failures can lower the mean time to failure and increase the probability of ER. This paper presents a simple method with an explicit correlation parameter to characterize the impact of correlated component failures on the optimal PM interval of a system with arbitrary structure. This method is applied to five maintenance policies, including: periodic group repair based on operation time, minimal repair with complete renewal, minimal repair with partial renewal, age replacement to minimize cost, and age replacement to maximize availability. Examples illustrate our approach identifies optimal maintenance strategies for these policies such as reward or cost per unit time, cost per renewal period, and stationary availability despite correlated failures.

An adaptive EM algorithm for NHPP software reliability models

Non-homogeneous Poisson process (NHPP) software reliability growth models (SRGM) enable several quantitative metrics that can be used to guide important decisions during the software engineering life cycle such as testing resource allocation and release planning. However, many of these SRGM possess complex mathematical forms that make them difficult to apply in practice because traditional statistical procedures such as maximum likelihood estimation must solve a system of non-linear equations to identify the numerical parameters that best characterize a set of failure data. Recently, researchers have made significant progress in overcoming this difficulty by developing an expectation-maximization (EM) algorithm that exhibits better convergence properties and can therefore find the maximum likelihood estimates of complex SRGM with greater ease. This EM algorithm, however, assumes that some model parameters are constant and thus the approach is not capable of identifying the set of numerical parameters that maximize the likelihood function. This paper presents an adaptive EM algorithm to identify the maximum likelihood estimates of all parameters of multiple NHPP SRGM with complex mathematical forms. We illustrate our enhanced algorithm through a series of examples. The results show that the algorithm can efficiently identify the set of numerical parameters that globally maximizes the likelihood function. Thus, the adaptive algorithm can significantly simplify the application of complex SRGM.

An adaptive em algorithm for the maximum likelihood estimation of non-homogeneous poisson process software reliability growth models

Non-homogeneous Poisson process (NHPP) software reliability growth models (SRGMa) enable quantitative metrics to guide decisions during the software engineering life cycle, including test resource allocation and release planning. However, many SRGM possess complex mathematical forms that make them difficult to apply. Specifically, traditional procedures solve a system of nonlinear equations to identify the numerical parameters that best characterize failure data. Recently, researchers have developed expectation-maximization (EM) algorithms for NHPP SRGM that exhibit better convergence properties and can therefore find maximum likelihood estimates with greater ease. This paper presents an adaptive EM (AEM) algorithm, which combines an earlier EM algorithm for NHPP SRGM with unconstrained search of the model parameter space. Our performance analysis shows that the AEM outperforms state-of-the-art EM algorithms for NHPP SRGM with very strong statistical significance, which is as much as hundreds of times faster on some data sets. Thus, the approach can fit SRGM very quickly. We also incorporate this high performance adaptive EM algorithm into a heuristic nested model selection procedure to objectively select a model of least complexity that best characterizes the failure data. Results indicate this heuristic approach often identifies the model possessing the best model selection criteria.

Reliability improvement to minimize average procurement unit cost of a rotorcraft fleet

Tradespace Exploration (TSE) is a Department of Defense (DOD) Engineered Resilient Systems (ERS) thrust, with overarching goals to develop processes and products capable of performing in a wide range of adverse conditions commonly encountered by military systems. TSE technologies are modernizing system engineering, facilitating stakeholder engagement through distributed collaborative environments for design and analysis of alternatives. However, the majority of TSE research emphasizes tradeoffs between functional requirements, especially those related to performance, not nonfunctional requirements such as reliability, availability, and maintainability, which impact operation and support costs (O&S). This paper presents a model to explicitly consider the impact of reliability improvement on availability and cost with special attention to fleet size and average procurement unit cost (APUC). Examples illustrate how reliability improvement could significantly increase availability as well as reduce lifecycle and average procurement unit cost.

Impact of correlated component failure on age replacement maintenance policies

A primary goal of maintenance is to minimize the consequences of component and system failures. Two subcategories of maintenance actions include: Preventive Maintenance (PM) at predetermined time intervals prior to failure and Emergency Repair (ER) upon failure, where the cost and downtime of emergency repair is significantly greater than preventive maintenance. Most maintenance models developed over the past several decades assume component failures are statistically independent. This assumption simplifies calculations, but is dangerous for safety critical systems that must be maintained because correlated failures can lower the mean time to failure, increasing the probability that emergency repair will be required. This paper presents a simple method with an explicit correlation parameter to characterize the impact of correlated component failures on the optimal preventive maintenance interval of a system with arbitrary structure. This method is applied to two maintenance policies, including: age replacement to minimize cost and age replacement to maximize availability. Examples illustrate that our approach identifies optimal maintenance strategies for these policies such as cost per unit time and stationary availability despite correlated failures.

A survey of fault and attack tree modeling and analysis for cyber risk management

Cyber security is of great concern to the Department of Homeland Security (DHS) and other organizations within government, as cyberspace is the gateway to services and infrastructure, making them vulnerable to a wide range of software-based attacks that could result in physical and cyber threats and hazards. It is extremely difficult to secure these cyber-physical systems (CPS) due to the complexity of their interfaces, which often leaves them exposed to elevated levels of risk to severe disruptions, including information security violations that could threaten national and economic security. Therefore, many researchers have dedicated substantial effort to model and analyze cyber-physical systems through red teaming in order to identify various potential strategies an attacker may take to hack into the system so that they can develop effective countermeasures. Reliability and risk modeling approaches discussed in the literature include fault trees (FT), event trees (ET), binary decision diagrams (BDD), Petri nets (PN), Markov modeling (MM), and attack trees (AT) to systematically characterize the risks latent in cyber-physical systems. This paper provides a survey of the two most popular modeling approaches including fault and attack trees, discussing their benefits and potential limitations. This survey should be beneficial to security professionals who wish to apply techniques from reliability and risk modeling to ensure the cyber security of their systems as well as researchers seeking to identify new modeling opportunities.