This special issue of IJPE on Reliability Research in India focuses on the current reliability research being conducted in Indian industries, research organizations, and academic institutes. All papers submitted for the special issue were reviewed by the experts in the field. Based on the referee comments and theme of the special issue, 10 best papers out of 20 submitted, have been selected and are supposed to reflect the current reliability research trend in India. In addition, this special issue includes a brief overview article, which highlights the important reliability contributions and the milestones achieved in the advancement of reliability engineering education and practice in India.

The first paper, Risk-Informed Method for Safety Re-Assessment of Irradiation Facilities, by Varde, Joshi, Mishra, Bandi, Srivastava and Kohlik, presents a new risk-informed methodology for re-assessment studies of irradiation facilities used in nuclear industry. This paper discusses the salient features of the methodology through a case study performed on a 30-year-old irradiation facility, ISOMED, operating in BARC - Mumbai.

The second paper, jointly from BARC and IIT Mumbai, A New Uncertainty Importance Measure in Fuzzy Reliability Analysis, Durga Rao, Kushwaha, Verma and Srividya, proposes a fuzzy framework to rank the components based on their uncertainty contribution to the over all uncertainty of system reliability. The proposed method is validated with comparative studies on a reliability problem and found that proposed fuzzy uncertainty importance measure is matching with probabilistic uncertainty importance measures.

The third paper from IIT-Roorkee, A Multi-objective Genetic Algorithm for Reliability Optimization Problem, by Amar Kishor, Shiv Prasad Yadav and Surendra Kumar, considers a multi-objective optimization problem under fuzzy environment where the component reliability allocations are performed for maximizing the system reliability while minimizing the cost of the system. The method used in this paper is described using a simplified version of a life-support system in a space capsule.

The fourth paper from DRDO, Vehicular Fleet Reliability Estimation: A Case Study, by Hari Prasad, Singh and Bhat, presents a case study on a large fleet of vehicles. The paper discusses a technique of mission reliability prediction and the weak links identification in the system using field data.? The method is demonstrated using Weibull probability plot.

The fifth paper, Additive Weibull Model for Reliability Analysis, by Usgaonkar and Mariappan, demonstrates that additive Weibull model can be used for describing the bathtub shaped failure rate functions that arise in many practical reliability applications.? The paper discusses the parameter estimation methods based on the graphical estimation techniques. The applicability of proposed model is demonstrated through various case studies.

The sixth paper from Reliability Engineering Centre of IIT Kharagpur, Global Reliability Evaluation using g-Minimal Cutsets, by Rajesh Mishra and Chaturvedi, presents an algorithm for global reliability evaluation of undirected networks using g-minimal Cutsets. Through several examples, it is demonstrated that the proposed g-minimal Cutsets based algorithm produces much smaller number of terms for the global reliability expression as compared to spanning trees based algorithms.

The seventh paper from Centre for Reliability, Chennai, A Parametric Empirical Bayesian Software Reliability Model, by Duraiswamy and Govindasamy, proposes an easy to adopt software reliability model considering the generalized exponential distribution for the time between failures. The model parameters are obtained using Bayesian approach and least squares method. The usefulness of the model has been demonstrated using three sets of actual software failure data.

The eighth paper from Delhi University, A New Insight into Software Reliability Growth Modeling, by Kapur, Anu Aggarwal, Sameer Anand, shows that different unified approaches proposed recently in capturing different software reliability growth curves are, in fact, equivalent. Further, it is shown that the unified approach based on hazard rate function is more general and can handle both Imperfect Debugging and Fault generation scenarios.

The ninth paper, Pareto Distribution – A Software Reliability Growth Model, by Kantam and Subba Rao, proposes a new software reliability growth model based on Non-Homogeneous Poisson Process (NHPP) using Pareto type mean value function. Using a well known test data obtained from Naval Tactical Data System (NTDS), it is shown that the proposed model is efficient compared to the existing models.

Lastly, the tenth paper, Markov Model and Simulation Analysis of 110 kV Transmission Lines: A Case Study, by? Michael, Amonkar, Mariappan, and Kamat, present an accurate and practical availability analysis of an existing electrical transmission system used in Goa Electricity Department. Using the integrated use of Markov chains and simulation methodology, the authors recommends an optimal cost-effective resource planning strategy for the Goa Electrical Department.

I would like to thank all the authors for the patience and cooperation exhibited and also I am grateful to referees who gave their valuable time to review the papers promptly. I am grateful to Professor Krishna B. Misra, Editor-in-Chief of IJPE, for inviting me to organize this important special issue. I hope we have been able to present the glimpses of current reliability research being carried out in India. Of course this issue may not represent the entire canvass of on-going research in the country but can be called as a representative effort in that direction. I do hope - this special issue will be received enthusiastically by academia, researchers and engineers involved in reliability engineering.

Amari, Suprasad V., is a Senior Reliability Engineer at Relex Software Corporation. He pursued his M.S. and Ph.D. in Reliability Engineering at the Reliability Engineering Centre of Indian Institute of Technology, Kharagpur, India. He has published over 50 research papers in reputed international journals and conferences. He is on the editorial boards of the International Journal of Performability Engineering and International Journal of Reliability, Quality and Safety Engineering and also on a management committee of RAMS. He is a member of the US Technical Advisory Group (TAG) to the IEC Technical Committee on Dependability Standards (TC 56), advisory board member of several international conferences, and a reviewer for several journals on reliability and safety. He received 2009 Stan Oftshun Award from SRE for the best RAMS paper. He is a senior member of ASQ, IEEE, and IIE; and a member of ACM and SRE. He is also an ASQ-certified Reliability Engineer.

Since the early stages of reliability engineering several important research contributions have been made in India to this field. This article briefly discusses the important reliability contributions made in India and the milestones in advancement of reliability engineering in India.? The article also describes the Indian academic programs related to reliability engineering.

A new approach has been developed in support of re-assessment studies for irradiation facilities. Though this work deals with modeling and assessment of irradiation facility, the methodology described in this paper can be easily adopted with minor changes for any engineering system. This paper discusses the salient features of the methodology through a case study performed on a 30-year-old irradiation facility. The basic approach is risk-informed in nature. Here, the insights from the Probabilistic Safety Assessment along with Operation and Maintenance experience was utilized to support decisions related to regulatory re-licensing for life extension of the plant.
Received on March 25, 2008, revised on November 11, 2008
References: 05

Uncertainty is inevitable in any reliability analysis of complex engineering systems due to uncertainties present in models, parameters of the model, phenomena and assumptions. Uncertainties at the component level are propagated to quantify uncertainty at the system level reliability. It is very important to identify all the uncertainties and treat them effectively to make reliability studies more useful for decision making. Conventional probabilistic approaches adopt probability distributions to characterize uncertainty where as fuzzy reliability models adopt membership functions to characterize uncertainty. Both the approaches are widely used in uncertainty propagation for reliability studies. However, identification of critical parameters based on their uncertainty contribution at the system level is very important for effective management of uncertainty. A method is proposed here in the fuzzy framework to rank the components based on their uncertainty contribution to the over all uncertainty of system reliability. It is compared with probabilistic methods using a practical reliability problem in the literature.
Received on December 12, 2007, revised on November 19, 2008
References: 16

This paper considers the allocation of maximum reliability to a complex system, while minimizing the cost of the system, a type of multi-objective optimization problem (MOOP). Multi-objective Evolutionary Algorithms (MOEAs) have been shown in the last few years as powerful techniques to solve MOOP .This paper successfully applies a Nondominated sorting genetic algorithm (NSGA-II) technique to obtain the Pareto optimal solution of a complex system reliability optimization problem under fuzzy environment in which the statements might be vague or imprecise. Decision-maker (DM) could choose, in a "posteriori" decision environment, the most convenient optimal solution according to his/her level of satisfaction. The efficiency of NSGA-II in solving this problem is demonstrated by comparing its results with those of simulated annealing (SA) and nonequilibrium simulated annealing (NESA).
Received on November 1, 2007, revised on October 24, 2008
References: 14

Mission reliability is the probability of successful completion for a stated mission by a group of people holding a set of a given population of equipment deployed in the prevailing operating environment. Thus, while reliability is considered for a single piece of equipment, mission reliability on the other hand is for a group of equipment having mixed vintage which could be deployed as a combined force for a mission. Public transport companies, goods transport organizations, police, paramilitary and military units maintain a large fleet of vehicles to carry out their stated missions. Estimation and prediction of mission reliability is of paramount importance for any operational success. For this purpose, reliability prediction of equipment is estimated from field failure data obtained from their history records. This paper discusses the technique of mission reliability prediction using the Weibull probability plots of identified failure distribution. The identified failure distribution is validated using Chi-Square test. It is followed by identifying the weak links in the system using Pareto Analysis.
Received on May 26, 2008, revised on November 1, 2008
References: 13

Statistical distributions of time to failure for many mechanical systems reveal bathtub-shaped failure rate in practice. Bathtub shaped failure rate is very much useful in reliability engineering for the determination of burn-in and plays key role in provisions of warranty. The traditional Weibull distribution can cover the profile piecewise only and there are very few practical models to model bathtub-shaped failure rate. The Additive Weibull model discussed in this paper is based on adding two Weibull survival functions. Some simplifications of the model are presented and the parameter estimation methods based on the graphical estimation technique are discussed. Various case studies discussed in this paper illustrate the applicability of the model. Results and discussions on cases gave some interesting utilities, which are also presented in this paper.
Received on March 17, 2007, revised on November 03, 2008
References: 08

Among various measures of network reliability, an important reliability measure is the probability that all nodes of the network are connected by up-state links showing a measure that indicates the extent to which the network can be used. Spanning trees and sum-of-disjoint product approach is one of the ways of evaluating this reliability measure. The purpose of this paper is to provide a new dimension to the computation of global reliability in undirected networks by defining and using g-minimal cut sets with SDP based multi-variable inversion (MVI) technique without any requirement of complex mathematics or graph-theory concepts. These cut sets turns out to be much less than the number of spanning tress. The paper presents an algorithm to enumerate such g-minimal cut sets with an illustrative example. Besides, it provides results for several other networks to show the efficacy of the proposed approach.
Received on April 02, 2008, revised on October 30, 2008
References: 19

In this paper, a new parametric empirical Bayesian software reliability model is presented. Times between failures follow generalised exponential distribution with stochastically decreasing order on the failure rate functions of successive failure time intervals with the software tester's intention to improve the software quality by the correction of each failure. With the Bayesian approach, the predictive distribution has been arrived at by combining generalised exponential time between failures and gamma prior distribution for the parameter namely failure rate. The expected time between failure measure, reliability function etc. have been obtained. The posterior distribution of the failure rate measure has been deduced and the mean failure rate is also obtained. For the parameter estimation, least square estimation method has been adopted. The proposed model has been applied to three sets of actual software failure data. It has been observed that the predicted failure times as per the proposed model are closer to the actual failure times. Sum of square errors criteria has been used for comparing the actual time between failure times and predicted time between failures.
Received on April 19, 2008, revised on November 10, 2008
References: 15

Several software reliability growth models have been presented in the literature in the last three decades. They have been developed for uniform and non-uniform operational profile. Some of them are flexible whereas others are not. Model selection becomes an uphill task. Of late, some authors have tried to develop a unifying approach so as to capture different growth curves, thus easing the model selection process. Some of these approaches use (a) Random lag function (b) Infinite server queuing theory (c) Hazard rate function. The purpose of this paper is to show that all these approaches are equivalent and further show that hazard rate approach is more general and can handle both Imperfect Debugging and Fault generation. This paper thus provides a new insight into the model development and it is shown that how a wide variety of existing software reliability can be unified.
Received on October 24, 2008, revised on December 09, 2008
References: 13

A counting process representing the number of failures experienced in a given period of time by a system is proposed as a stochastic model for studying the reliability of the developed software. A Non Homogeneous Poisson Process (NHPP) with its mean value function specified by a Pareto model is considered. Its parameters are estimated to assess the reliability of a software system. The results are illustrated for a live software failure data.
Received on December 27, 2007 and revised on December 20, 2008
References: 11

As technologically advanced distribution system operates economically with high rate of availability of the system, it is essential to integrate the analysis of systems reliability and availability into the process of planning and designing the structure of a transmission system. This paper discusses the availability modeling and analysis in distribution lines. From the data analysis, it was found that Markov model becomes right choice to carry out the investigation. The study involves live case of Goa Electricity Department. The Markovian state transition matrix involved in stochastic modeling has been solved by developing algorithm which is in turn coded in MATLAB 7.0. A Simulation model was developed and analyzed in GPSS World. The model was applied to a live case. Appropriate results and discussion carried out with sensitivity analysis are presented in the paper.
Received on June 22, 2008, revised on December 23, 2008
References: 12

Due to severely constrained resources, sensor nodes are subject to frequent failures. Therefore, wireless sensor networks (WSN) are typically designed with a large number of redundancies to achieve fault tolerance and to maintain the desired network lifetime and coverage. This work proposes an equation to determine the optimal number of redundant sensor nodes required in each layer of a WSN with the layered structure. Matlab simulations are used to verify the proposed equation.
Received on May 16, 2008, revised on December 30, 2008
References: 01