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The purpose of this paper is to develop optimal estimation procedures for the stress-strength reliability (SSR) parameter R = P(X > Y) of an inverse Pareto distribution (IPD).

We estimate the SSR parameter R = P(X > Y) of the IPD under the minimum risk and bounded risk point estimation problems, where X and Y are strength and stress variables, respectively. The total loss function considered is a combination of estimation error (squared error) and cost, utilizing which we minimize the associated risk in order to estimate the reliability parameter. As no fixed-sample technique can be used to solve the proposed point estimation problems, we propose some “cost and time efficient” adaptive sampling techniques (two-stage and purely sequential sampling methods) to tackle them.

We state important results based on the proposed sampling methodologies. These include estimations of the expected sample size, standard deviation (SD) and mean square error (MSE) of the terminal estimator of reliability parameters. The theoretical values of reliability parameters and the associated sample size and risk functions are well supported by exhaustive simulation analyses. The applicability of our suggested methodology is further corroborated by a real dataset based on insurance claims.

This study will be useful for scenarios where various logistical concerns are involved in the reliability analysis. The methodologies proposed in this study can reduce the number of sampling operations substantially and save time and cost to a great extent.

This paper is focused at studying the current state of research involving the four dimensions of defect management strategy, i.e. software defect analysis, software quality, software reliability and software development cost/effort.

The methodology developed by Kitchenham (2007) is followed in planning, conducting and reporting of the systematic review. Out of 625 research papers, nearly 100 primary studies related to our research domain are considered. The study attempted to find the various techniques, metrics, data sets and performance validation measures used by researchers.

The study revealed the need for integrating the four dimensions of defect management and studying its effect on software performance. This integrated approach can lead to optimal use of resources in software development process.

There are many dimensions in defect management studies. The authors have considered only vital few based on the practical experiences of software engineers. Most of the research work cited in this review used public data repositories to validate their methodology and there is a need to apply these research methods on real datasets from industry to realize the actual potential of these techniques.

The authors believe that this paper provides a comprehensive insight into the various aspects of state-of-the-art research in software defect management. The authors feel that this is the only research article that delves into the four facets namely software defect analysis, software quality, software reliability and software development cost/effort.

Reliability and maintainability estimation of any system depends on the identification of the best-fitted probability distribution of failure and repair rates. The parameters of the best-fitted probability distribution are also contributing significantly to reliability estimation. In this work, a case study of load haul dump (LHD) machines is illustrated that consider the optimization of failure and repair rate parameters using two well established metaheuristic approaches, namely, genetic algorithm (GA) and particle swarm optimization (PSO). This paper aims to analyze the aforementioned points.

The data on time between failures (TBF) and time to repairs (TTR) are collected for a LHD machine. The descriptive statistical analysis of TBF & TTR data is performed, trend and serial correlation tested and using Anderson–Darling (AD) value best-fitted distributions are identified for repair and failure times of various subsystems. The traditional methods of estimation like maximum likelihood estimation, method of moments, least-square estimation method help only in finding the local solution. Here, for finding the global solution two well-known metaheuristic approaches are applied.

The reliability of the LHD machine after 60 days on the real data set is 28.55%, using GA on 250 generations is 17.64%, and using PSO on 100 generations and 100 iterations is 30.25%. The PSO technique gives the global best value of reliability.

The present work will be very convenient for reliability engineers, researchers and maintenance managers to understand the failure and repair pattern of LHD machines. The same methodology can be applied in other process industries also.

In this case study, initially likelihood function of the best-fitted distribution is optimized by GA and PSO. Reliability and maintainability of LHD machines evaluated by the traditional approach, GA and PSO are compared. These results will be very helpful for maintenance engineers to plan new maintenance strategies for better functioning of LHD machines.

This paper seeks to focus on the study and estimation of reliability characteristics of Maxwell distribution under Type‐II censoring scheme.

Maximum likelihood estimation and Bayes estimation methods have been used for the estimation of reliability characteristics. Monte‐Carlo simulation is used to compare the efficiency of the estimates developed by these estimation methods.

With prior information on the parameter of Maxwell distribution, Bayes estimation provides better estimates of reliability characteristics; otherwise Maximum likelihood estimation is good enough to use for reliability practitioners.

When items are costly, Type‐II censoring scheme can be used to save the cost of the experiment and the discussed methods provide the means to estimate the reliability characteristics of the proposed lifetime model under this scheme.

The study is useful for researchers and practitioners in reliability theory and also for scientists in physics and chemistry, where Maxwell distribution is widely used.

The purpose of this paper is to consider the estimation of multicomponent stress-strength reliability. The system is regarded as alive only if at least s out of k (s<k) strengths exceed the stress. The reliability of such a system is obtained when strength, stress variates are from Erlang-truncated exponential (ETE) distribution with different shape parameters. The reliability is estimated using the maximum likelihood (ML) method of estimation when samples are drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation. Using real data sets the authors illustrate the procedure.

The authors have developed multicomponent stress-strength reliability based on ETE distribution. To estimate reliability, the parameters are estimated by using ML method.

The simulation results indicate that the average bias and average mean square error decreases as sample size increases for both methods of estimation in reliability. The length of the confidence interval also decreases as the sample size increases and simulated actual coverage probability is close to the nominal value in all sets of parameters considered here. Using real data, the authors illustrate the estimation process.

This research work has conducted independently and the results of the author’s research work are very useful for fresh researchers.

The purpose of this article is to derive inference for multicomponent reliability where stress-strength variables follow unit generalized Rayleigh (GR) distributions with common scale parameter.

The authors derive inference for the unknown parametric function using classical and Bayesian approaches. In sequel, (weighted) least square (LS) and maximum product of spacing methods are used to estimate the reliability. Bootstrapping is also considered for this purpose. Bayesian inference is derived under gamma prior distributions. In consequence credible intervals are constructed. For the known common scale, unbiased estimator is obtained and is compared with the corresponding exact Bayes estimate.

Different point and interval estimators of the reliability are examined using Monte Carlo simulations for different sample sizes. In summary, the authors observe that Bayes estimators obtained using gamma prior distributions perform well compared to the other studied estimators. The average length (AL) of highest posterior density (HPD) interval remains shorter than other proposed intervals. Further coverage probabilities of all the intervals are reasonably satisfactory. A data analysis is also presented in support of studied estimation methods. It is noted that proposed methods work good for the considered estimation problem.

In the literature various probability distributions which are often analyzed in life test studies are mostly unbounded in nature, that is, their support of positive probabilities lie in infinite interval. This class of distributions includes generalized exponential, Burr family, gamma, lognormal and Weibull models, among others. In many situations the authors need to analyze data which lie in bounded interval like average height of individual, survival time from a disease, income per-capita etc. Thus use of probability models with support on finite intervals becomes inevitable. The authors have investigated stress-strength reliability based on unit GR distribution. Useful comments are obtained based on the numerical study.

In the present worldwide situation, the survival of a business is a major crucial aspect. The business cannot be succeeded unless it produces the anticipated production levels. Achievement of this can be possible only by maintaining the equipment into an adequate level. Load-Haul-Dumpers (LHDs), as the main workhorse and massive transporting machines, are highly utilized in underground mining operations. Despite the usage of LHDs, these are prone to the uneven and unexpected occurrence of potential failures. These are causes to minimize the production and productivity of capital intensive equipment. To get a good profitability index, it is very necessary to have the required levels of equipment reliability and availability. Estimation of reliabilities and availabilities play a critical role in the performance evaluation of equipment.

By keeping the significance of the present research work in view in this research paper one of the well appropriate techniques such as fault tree analysis (FTA) was utilized to assess the reliability of the LHD system based on the function flow diagram. Best fit distribution of data sets were made by the utilization of Kolmogorov–Smirnov (K-S) test. Parametric estimation of theoretical probability distributions was done by utilizing the maximum likelihood estimation (MLE). Failure rate of each LHD system has computed based on the best fit results from “Isograph Reliability Workbench 13.0”. Reliability configuration of each LHD system has modeled using reliability block diagram (RBD), as well as the FTA.

Independent and identical distribution (IID) assumption of data sets was validated through statistic U-test (Chi Squared test). On the basis of test results, the data sets are in accordance with IID assumption. Therefore renewal process approach has been utilized for further investigation. Allocations of best fit distribution of data sets were made by the utilization ofK-S test. Parametric estimation of theoretical probability distributions was made by utilizing maximum likelihood estimation (MLE) method. Reliability of each individual subsystem has been computed according to the best fit distribution. The deductive method called RBD was utilized to investigate the given system reliability by analyzing with graphical representations of logic system and observed highest percentage of reliability as 69.44% (LH29). FTA has been utilized to investigate the availability percentage of a system and observed highest percentage value as 79.51% (LH29). This technique also helps to identify the most critical parts/cut sets by using Fussell-Vesely (F-V) importance measure.

As the reliability analysis is one of the complex techniques, it requires strategic decision-making knowledge for the selection of methodology to be used. As the present case study was from a public sector company, operating under financial constraints the conclusions/findings may not be universally applicable.

The present study throws light on this equipment that need a tailored maintenance schedules, partly due to the peculiar mining conditions, under which they operate. This analysis provides the information on several aspects such as present working condition of the machines, occurrence of various potential failure modes, influence of failure modes on its performance and reliable life aspects etc. Also, these investigations asses the forecasting of necessary managerial practices or control measures like possible design modifications and replacement actions of components to ensure the required levels of availability and utilization of the equipment. Both qualitative and quantitative analysis of FTA has been performed to determine the minimal/most influencing cut sets of the system and to estimate overall system availability within the work environment. Based on the computed results reasons for performance drop of each machine was identified and suitable recommendations were suggested to improve the performance of capital intensive systems.

The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG distribution with common scale parameter.

The reliability of a multicomponent stress–strength system is obtained by the maximum likelihood (MLE) and Bayesian method of estimation. Bayes estimates of system reliability are obtained by using Lindley’s approximation and Metropolis–Hastings (M–H) algorithm methods when all the parameters are unknown. The highest posterior density credible interval is obtained by using M–H algorithm method. Besides, uniformly minimum variance unbiased estimator and exact Bayes estimates of system reliability have been obtained when the common scale parameter is known and the results are compared for both small and large samples.

Based on the simulation results, the authors observe that Bayes method provides better estimation results as compared to MLE. Proposed asymptotic and HPD intervals show satisfactory coverage probabilities. However, average length of HPD intervals tends to remain shorter than the corresponding asymptotic interval. Overall the authors have observed that better estimates of the reliability may be achieved when the common scale parameter is known.

Most of the lifetime distributions used in reliability analysis, such as exponential, Lindley, gamma, lognormal, Weibull and Chen, only exhibit constant, monotonically increasing, decreasing and bathtub-shaped hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rates are upside-down bathtub and bathtub-shaped, which are found in the unit-Gompertz distribution. Furthermore, when reliability is measured as percentage or ratio, it is important to have models defined on the unit interval in order to have plausible results. Therefore, the authors have studied the multicomponent stress–strength reliability under the unit-Gompertz distribution by comparing the MLEs, Bayes estimators and UMVUEs.

Inferences for multicomponent reliability is derived for a family of inverted exponentiated densities having common scale and different shape parameters.

Different estimates for multicomponent reliability is derived from frequentist viewpoint. Two bootstrap confidence intervals of this parametric function are also constructed.

Form a Monte-Carlo simulation study, the authors find that estimates obtained from maximum product spacing and Right-tail Anderson–Darling procedures provide better point and interval estimates of the reliability. Also the maximum likelihood estimate competes good with these estimates.

In literature several distributions are introduced and studied in lifetime analysis. Among others, exponentiated distributions have found wide applications in such studies. In this regard the authors obtain various frequentist estimates for the multicomponent reliability by considering inverted exponentiated distributions.

The purpose of this paper is to deal with the Bayesian and non-Bayesian estimation methods of multicomponent stress-strength reliability by assuming the Chen distribution.

The reliability of a multicomponent stress-strength system is obtained by the maximum likelihood (MLE) and Bayesian methods and the results are compared by using MCMC technique for both small and large samples.

The simulation study shows that Bayes estimates based on γ prior with absence of prior information performs little better than the MLE with regard to both biases and mean squared errors. The Bayes credible intervals for reliability are also shorter length with competitive coverage percentages than the condence intervals. Further, the coverage probability is quite close to the nominal value in all sets of parameters when both sample sizes n and m increases.

The lifetime distributions used in reliability analysis as exponential, γ, lognormal and Weibull only exhibit monotonically increasing, decreasing or constant hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rate is bathtub-shaped found in the Chen distribution. Therefore, the authors have studied the multicomponent stress-strength reliability under the Chen distribution by comparing the MLE and Bayes estimators.