scholarly journals Copula based Measures of Repairable Parallel System with Fault Coverage

2020 ◽  
Vol 6 (1) ◽  
pp. 322-344
Author(s):  
Vaishali Tyagi ◽  
Ritu Arora ◽  
Mangey Ram ◽  
Ioannis S. Triantafyllou
Keyword(s):  
Process Time ◽  
Time To Failure ◽  
Supplementary Variable ◽  
Coverage Factor ◽  
Reliability Measures ◽  
Failed State ◽  
Finite State ◽  
Laplace Transformations ◽  
Human Failure ◽  
Mean Time

The main objective of this study is to analyse the reliability behaviour of parallel systems with three types of failure, namely unit failure, human failure and major failure. For this purpose, we apply three different statistical techniques, namely copula, coverage and copula-coverage. More precisely, this study presents a stochastic model for analysing the behaviour of a multi-state system consisting of two non-identical units by incorporating the concept of coverage factor and two types of repair facilities between failed state to a normal state. The system could be characterized as being in a failed state due to unit failures, human failure and major failures, such as catastrophic and environmental failure. All failure rates are constant and it is assumed that these are exponentially distributed whereas, repair rates follow the Gumbel-Hougaard copula distribution. The entire system is modelled as a finite-state Markov process. Time-dependent reliability measures like availability, reliability and mean time to failure (MTTF) are obtained by supplementary variable techniques and Laplace transformations. The present study provides a comparative analysis for reliability measures among the aforementioned techniques, while a discussion referring to which technique makes the system more reliable is also developed. Furthermore, numerical simulations are presented to validate the analytical results.

Reliability Measures Analysis of an Industrial System under Standby Modes and Catastrophic Failure

2016 ◽  
Vol 7 (3) ◽  
pp. 36-56 ◽  
Author(s):  
Mangey Ram ◽  
Monika Manglik
Keyword(s):  
Catastrophic Failure ◽  
System Failure ◽  
Time To Failure ◽  
Industrial System ◽  
Supplementary Variable ◽  
Repair Cost ◽  
Reliability Measures ◽  
System Availability ◽  
Parallel Configuration ◽  
Mean Time

The objective of this research paper is, to present the reliability measures of a model by representing an industrial system having three subsystems. Two of the subsystems have standby unit while the third one has n units in parallel configuration. The entire system can fail due to a failure in subsystems or due to the catastrophic failure. The system failure and the repair rates are assumed to be constant. Markov and supplementary variable methodologies have been used to achieve the mathematical analysis of this model. Generalized expressions of state probabilities, system availability, reliability, mean time to failure, mean time to repair, cost analysis and sensitivity analysis are developed. Graphs for the resulting expressions have been shown.

A Bayesian Estimation of Reliability Measures of Stepwise Exponential Distribution System

1991 ◽  
Author(s):  
M. H. Hu
Keyword(s):  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Distribution System ◽  
Failure Process ◽  
Reliability Function ◽  
Distribution Model ◽  
Time To Failure ◽  
Reliability Measures ◽  
In Series ◽  
Mean Time

Abstract This paper presents an analysis method for reliability measures of a system with step changes in failure and repair rates. Both failure and repair time have exponential function of time. Such a system is called a stepwise exponential distribution system. This kind of failure process can take place in various equipments. This paper deals with the system having components in series arrangement. Bayesian statistics is used in defining prior and posterior probability density functions of failure and repair rates. These functions provide information for the estimation of reliability measures: 1) failure and repair rates, 2) mean time to failure, 3) mean time to repair, 4) reliability function and 5) availability. A sample problem is given to illustrate the methodology. The Bayesian estimation of the stepwise exponential distribution model is useful in the planning of equipment predictive maintenance.

Welding Process under Fault Coverage Approach for Reliability and MTTF

2017 ◽  
pp. 222-245
Author(s):  
Nupur Goyal ◽  
Mangey Ram ◽  
Pranshu Kumar
Keyword(s):  
Transition State ◽  
Welding Process ◽  
Fault Coverage ◽  
State Probability ◽  
Time To Failure ◽  
Supplementary Variable ◽  
Markov Modelling ◽  
Practical Utility ◽  
Suitable Combination ◽  
Mean Time

This chapter deals with the problems occur in the welding under the consideration of many causes of defects such as cracking, distortion, porosity, inclusion and undercutting. Welding is very useful for every industry. It is used as a fabrication and sculptural that joins the two parts of materials, generally metals or thermoplastic, through a restricted amalgamation from a suitable combination of temperature, pressure and metallurgical conditions. In this chapter, authors study that the welding process is how much reliable when many causes of defects taken account into this process and try to find out the reliability and mean time to failure of welding process with the help of Markov modelling and supplementary variable technique. They derived the generalised expression for the probability of each possible transition state, probability of upstate and downstate of welding, and also studied the sensitivity in reliability and MTTF of welding. Fault coverage technique has been developed to enhance the reliability of the welding process for practical utility in the industry.

Sensitivity analysis of a three-unit series system under k-out-of-n redundancy

2017 ◽  
Vol 34 (6) ◽  
pp. 770-784 ◽  
Author(s):  
Nupur Goyal ◽  
Mangey Ram ◽  
Shubham Amoli ◽  
Alok Suyal
Keyword(s):  
Sensitivity Analysis ◽  
Performance Measure ◽  
General Distribution ◽  
Time To Failure ◽  
Reliability Measures ◽  
Mean Time To Failure ◽  
Content Type ◽  
Failure Cost ◽  
In Series ◽  
Mean Time

Purpose The purpose of this paper is to investigate the reliability measures, namely, availability, reliability, mean time to failure and expected profit. The authors also analyse the sensitivity of these reliability measures. Design/methodology/approach Depending upon the real industrial relevance, a generalized system which is easily repairable, extremely reliable and of high quality is expected by the rapid growth of the digital economy. Considering reliability, as one of the performance measure, the authors have designed a complex system which consists of three subsystems, namely, A, B and C in series configuration. The subsystem A consists of n numbers of units which are arranged in parallel configuration, subsystem B consists of two sub-subsystems X and Y align parallel to one another, where X is a type of 1-out-of-n:F. Failure and repair rates are assumed to be follow the general distribution. Findings The system is deeply studied by the usage of the supplementary variable technique, Laplace transformation and Markov’s law. Various conclusive results such as availability and reliability of the system, mean time to failure, cost and sensitivity analysis have been discussed further. Originality/value Through the systematic view of reliability measures of the proposed system, performance of the system can be enhanced under high profit.

scholarly journals Stochastic Biometric System Modelling with Rework Strategy

2016 ◽  
Vol 1 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Mangey Ram ◽  
Monika Manglik
Keyword(s):  
Liquid Crystal Display ◽  
System Modelling ◽  
Time To Failure ◽  
Supplementary Variable ◽  
Biometric System ◽  
Variable Technique ◽  
Efficient System ◽  
Whole Process ◽  
Long Time ◽  
Mean Time

In this paper, the authors proposed the reliability mathematical modeling of a biometric system that computerizes the whole process of taking attendance and keeping its records in an academic institute. Manually taking attendance and sustaining it for a long time is very difficult as well as wastes a lot of time. For this cause, an efficient system has to be designed. This system takes attendance electronically with the help of a fingerprint scanner, and all the records are saved on a computer server. In order to mark the attendance, student or employee has to place his/her finger on the fingerprint sensor. On proof of identity student’s or employee’s record is well-run in the database, and he/she is reported through liquid-crystal display screens. Here, the authors evaluated reliability measures of the system such as availability, reliability, mean time to failure (MTTF), cost analysis and sensitivity analysis with the help of Laplace transformation, supplementary variable technique, and Markov technique.

Reliability and Availability analysis of a cloud computing transition system under multiple failures

2020 ◽  
Vol 37 (6/7) ◽  
pp. 823-835
Author(s):  
Monika Manglik ◽  
Nitesh Rawat ◽  
Mangey Ram
Keyword(s):  
Mathematical Model ◽  
Cloud Computing ◽  
Design Methodology ◽  
Transition System ◽  
Time To Failure ◽  
Reliability Measures ◽  
Variable Technique ◽  
Content Type ◽  
Availability Analysis ◽  
Mean Time

PurposeTo analyze the performance of multistate cloud computing transition system through the various reliability measures is the purpose of this paper.Design/methodology/approachIn this article, a mathematical model for a multistate cloud computing transition system with various types of failures has been analyzed by using the Markov process, supplementary variable technique and Laplace transformation.FindingsVarious reliability measures such that reliability, availability, mean time to failure (MTTF), mean time to repair and cost analysis have also been analyzed. This article presents some geographic illustrations for the practical utility of the model.Originality/valueThe authors developed a mathematical model to analyze the reliability of the cloud computing transition system by considering the possible failures.

A Bayesian Estimation of Reliability Measures of Stepwise Exponential Distribution System

1993 ◽  
Vol 115 (1) ◽  
pp. 61-68
Author(s):  
M. H. Hu
Keyword(s):  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Distribution System ◽  
Failure Process ◽  
Reliability Function ◽  
Distribution Model ◽  
Time To Failure ◽  
Reliability Measures ◽  
Posterior Probability Density ◽  
Mean Time

This paper presents an analysis method for reliability measures of a system with step changes in failure and repair rates. Both failure and repair time have exponential functions of time. Such a system is called a stepwise exponential distribution system. This kind of failure process can take place in various kinds of equipment. This paper deals with the system having components in a series arrangement. Bayesian statistics are used in defining prior and posterior probability density functions of failure and repair rates. These functions provide information for the estimation of several reliability measures: (1) failure and repair rates, (2) mean time to failure, (3) mean time to repair, (4) reliability function and (5) availability. A sample problem is given to illustrate the methodology. Bayesian estimation of the stepwise exponential distribution model is useful in the planning predictive maintenance of equipment.

scholarly journals Reliability Measures of Two Dissimilar Units Parallel System Using Gumbel-Hougaard Family Copula

2019 ◽  
Vol 4 (1) ◽  
pp. 116-130 ◽  
Author(s):  
Garima Chopra ◽  
Mangey Ram
Keyword(s):  
Laplace Transformation ◽  
Present System ◽  
Time To Failure ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Common Cause Failure ◽  
Complete Failure ◽  
Parallel Network ◽  
System Breakdown ◽  
Mean Time

The goal of the present study is to investigate the availability and the reliability of the system, which has two dissimilar units in the parallel network under copula. Other key parameters, such as mean time to failure (MTTF) and expected profit are also evaluated. Simultaneous malfunctioning of units, common cause failure and human fault are the causes of system breakdown. The present mathematical model is examined under the assumption that each failure rate is constant and is exponentially distributed. The system undergoes repair in the completely failed state as well as in degraded state. In the case of complete failure, the system is repaired by two repair facilities and that are tackled by utilizing Gumbel-Hougaard family copula. The present system has been studied by applying the concepts of probability theory, supplementary variable technique and Laplace transformation.

scholarly journals Surveillance System in Smart Cities: A Dependability Evaluation Based on Stochastic Models

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 876
Author(s):  
Igor Gonçalves ◽  
Laécio Rodrigues ◽  
Francisco Airton Silva ◽  
Tuan Anh Nguyen ◽  
Dugki Min ◽  
...  
Keyword(s):  
Surveillance System ◽  
Smart Cities ◽  
Heterogeneous Data ◽  
Time To Failure ◽  
Video Streams ◽  
Dependability Evaluation ◽  
The Mean ◽  
Mean Time ◽  
The Internet Of Things

Surveillance monitoring systems are highly necessary, aiming to prevent many social problems in smart cities. The internet of things (IoT) nowadays offers a variety of technologies to capture and process massive and heterogeneous data. Due to the fact that (i) advanced analyses of video streams are performed on powerful recording devices; while (ii) surveillance monitoring services require high availability levels in the way that the service must remain connected, for example, to a connection network that offers higher speed than conventional connections; and that (iii) the trust-worthy dependability of a surveillance system depends on various factors, it is not easy to identify which components/devices in a system architecture have the most impact on the dependability for a specific surveillance system in smart cities. In this paper, we developed stochastic Petri net models for a surveillance monitoring system with regard to varying several parameters to obtain the highest dependability. Two main metrics of interest in the dependability of a surveillance system including reliability and availability were analyzed in a comprehensive manner. The analysis results show that the variation in the number of long-term evolution (LTE)-based stations contributes to a number of nines (#9s) increase in availability. The obtained results show that the variation of the mean time to failure (MTTF) of surveillance cameras exposes a high impact on the reliability of the system. The findings of this work have the potential of assisting system architects in planning more optimized systems in this field based on the proposed models.

On classes of life distributions based on the mean time to failure function

2021 ◽  
Vol 58 (2) ◽  
pp. 289-313
Author(s):  
Ruhul Ali Khan ◽  
Dhrubasish Bhattacharyya ◽  
Murari Mitra
Keyword(s):  
Damage Model ◽  
Replacement Policy ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Moment Convergence ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
The Mean ◽  
Age Replacement ◽  
Mean Time

AbstractThe performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

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