Journal of Reliability and Statistical Studies

Prediction of the Mean Time to Failures of a Complex System Using the Monte Carlo Simulation Method

Hedi A. Guesmi — Tue, 05 Nov 2024 00:00:00 +0100

This paper presents a Monte Carlo-based algorithm for predicting the Mean Time to Failure (MTTF) of complex structures, specifically a “Bridge-type network” with five elements exhibiting various failure distributions. The proposed algorithm involves generating element lifetimes through the inverse of their failure distribution functions, providing a robust approach to evaluating MTTF for systems beyond traditional series or parallel configurations.

The approach was implemented in MATLAB, and the software underwent extensive testing across different scenarios, including both exponential and Weibull distributions. The results demonstrated the method’s accuracy and its capability to handle diverse failure distributions with minimal error. This tool offers reliability engineers a versatile solution for predicting and improving the reliability of complex systems.

In summary, the proposed method and software significantly advance the reliability assessment of intricate structures and offer a solid foundation for further research and practical applications in the field of reliability engineering.

A New Exponential Gompertz Distribution: Theory and Applications

Ibtesam Ali Alsaggaf — Mon, 18 Nov 2024 00:00:00 +0100

With the rise of numerous phenomena that require interpretation and investigation, developing novel distributions has become an important need. This research introduced a new probability distribution called New Exponential Gompertz distribution based on the new exponential-X family to enhance flexibility and improve performance. The most significant benefit of this novel distribution is that its hazard function could be increasing, decreasing and bathtub which reflects the flexibility of the distribution to fit various applications. Furthermore, its density can adopt a variety of symmetric and asymmetric possible shapes. Some of the theoretical characteristics such as quantile, order statistic and moment are provided. The parameter estimates are derived using five different estimation methods including maximum likelihood, ordinary least square, weighted least square, Cramér-von mises and maximum product of spacing methods. Simulation studies are conducted to assess the effectiveness of the five estimation methods. The maximum likelihood estimate shows the most reliable estimate for estimating parameters since it provides the smallest mean square error While the maximum product of spacing method is less efficient. The performance of the proposed distribution is assessed through real-world applications in medical, engineering and physics with competitive distributions. The results indicate that the new distribution efficiently represents various types of data compared to other distributions.

Reliability Optimization Using Progressive Batching L-BFGS

Mohammad Etesam, Gholam Reza Mohtashami Borzadaran — Thu, 12 Dec 2024 00:00:00 +0100

Reliability optimization can be applied to find parameters that increase reliability and decrease costs, in the presence of uncertainty. Nowadays, with the increasing complexity of systems, it is important to find suitable optimization methods. In this regard, we can refer to gradient-based optimization methods. The power of stochastic gradient-based approaches in optimization under uncertainty resides in efficiency in using sampling information. These methods allow applying a small sample size in updating problem parameters. Using a small sample size also has its disadvantages, and it leads to oscillation around the minimum point when approaching the minimum. One of the ways to solve this problem is to use progressive batching. Here, to increase stability Progressive Batching L-BFGS (PB-LBFGS) and Progressive Batching L-BFGS with momentum (PB-mLBFGS) are used for reliability optimization, and with an example, the effectiveness of these approaches is compared with some other optimization methods.

Reliability Estimation of Parallel Systems with Diverse Failure Modes: Semi-Markov Model Approach

Priya Baloda, Amit Kumar, Vikas Garg — Thu, 19 Dec 2024 00:00:00 +0100

This paper introduces a novel system consisting of two dissimilar units operating in parallel, each with distinct failure modes. This flexibility in units characteristics minimizes the risk of simultaneous failures due to common causes. The system’s mathematical model is developed using a semi-Markov approach, and a numerical method based on the regenerative point technique is applied to estimate various reliability measures, such as the mean time to system failure (MTSF) and system availability. Failure rates are modeled as exponentially distributed, while repair rates are allowed to follow arbitrary distributions. Additionally, the proposed model undergoes graphical analysis to evaluate system performance under varying parameters.

Reliability–Redundancy Allocation of Pharmaceutical Plant Using Cuckoo Search and Hybrid of GWO-CS

Mangey Ram, Nupur Goyal, Shivani Choudhary, Seema Saini — Thu, 19 Dec 2024 00:00:00 +0100

The Reliability-Redundancy Allocation Problem (RRAP) is a non-linear mixed-integer programming problem. It is essential to the design of any system and the enhancement of reliability. In this article, two metaheuristic techniques: Cuckoo-Search (CS) and a Hybrid of Grey-Wolf Optimization (GWO) and CS (HGWOCS) are proposed to address the reliability optimization of pharmaceutical plant. This plant illustrates RRAP to optimize reliability under designed constraints such as weight, cost, and volume. The GWO exploration ability and the CS exploitation ability are merged in this hybrid technique. These approaches are compared in terms of optimal solution and accuracy with each other results and previous literature. The statistical outcomes and convergence rate show the expected approach’s excellent performance. The final conclusion revealed that the proposed optimization algorithm can accurately enhance the reliability of the pharmaceutical plant.

Cost-Effectiveness Analysis of a System of Distinguishable Subsystems with Repair Preference and Weather Conditions

Lalit Kumar, D. Pawar, Kailash Kumar — Thu, 19 Dec 2024 00:00:00 +0100

Cost-effectiveness analysis of a reliability model of two distinguishable electricity resources is done in this paper. Subsystem-A is taken as the primary, whereas subsystem-B is taken as the secondary source of electricity. Subsystem-A has three modes – operation, repair, and activation, and subsystem-B has four modes – operation, inspection, minor repair, and major repair. Availability of a full-time technician is considered to perform all repair and activation activities. The technician initiates the repair of subsystem-A immediately whenever required, whereas inspection is carried out for subsystem-B to identify the type of repair required. Normal and abnormal weather conditions are considered to study the impact of weather conditions on repair and activation activities. Only subsystem-A needs activation after repair, and no repair/activation is carried out in abnormal weather, while weather conditions do not affect inspection or repair activities of subsystem-B. Failure and repair rates of both the subsystems are exponentially distributed, whereas a general distribution is taken for the operation rate of subsystem-A. Various reliability components like Mean Time to System Failure (MTSF), steady-state availability, busy period of the server, and profit of the system model are evaluated using the semi-Markov process. Random values are taken to show the impact of increasing failure rate of subsystem-A and rate of change of weather condition from normal to abnormal on MTSF and the cost-benefit of the system model. Graphs are drawn for MTSF and profit of the system model, which clearly indicates that MTSF and profit of the system model are higher for a lesser rate of change in weather conditions.

Unveiling the Evolution: Multi-Patch Multi-Release Software Reliability Growth Model with Testing Effort

Veenu Singh, Vijay Kumar, V. B. Singh, Arun Prakash Agrawal — Thu, 09 Jan 2025 00:00:00 +0100

Reliance on software has increased expectations for software organizations to deliver high-quality software to meet the increasing demand from end-users. Continuous testing is imperative to ensure software quality, yet prolonged testing can lead to increased market opportunity costs. Consequently, organizations often opt to release software early and subsequently conduct testing during the operational phase, addressing existing bugs through patch deployment. These patches, small programs aimed at fixing, improving, or updating software, serve to rectify security vulnerabilities or bugs efficiently. For minor changes, patch releases prove more practical and cost-effective than launching entirely new software versions. The adoption of multi-release software endows developers with a competitive advantage, catering to the diverse needs of end-users. This paper introduces a testing effort-based software reliability growth model, evaluating the impact of multi-patching on multi-release software. The model operates under the assumption of continuous fault removal post-release, using different distribution functions to construct three framework variations. Parameter estimation employs the Statistical Package for Social Sciences, with a real dataset serving as a basis for a numerical example illustrating the model’s practical application. Additionally, a comparative analysis of model performance, based on different distribution functions, is conducted through multi-criteria decision-makingtechniques.

Enhancing Accuracy in Population Mean Estimation with Advanced Memory Type Exponential Estimators

Poonam Singh, Prayas Sharma, Pooja Maurya — Thu, 09 Jan 2025 00:00:00 +0100

For a number of reasons, mean estimate is an essential sampling activity as it offers crucial information and forms the basis of statistical inference and judgement. In this study, we estimate the population mean using the Exponentially Weighted Moving Average (EWMA) statistic and provide generalized family of exponential estimators. The theoretical aspects of the suggested estimator are evaluated via rigorous mathematical derivations of the bias and mean square error (MSE), which are then compared to other exponential estimators that are already in use. Furthermore, a thorough simulation research is carried out to thoroughly assess the effectiveness and empirical performance of the suggested strategy. The results highlight how the estimator’s effectiveness is significantly increased when both recent and historical data are used in tandem.