Software for warranty optimization Abstract The research article is associated with warranty optimization. Warranty is one of the most important factors for each organization because it accounts for a large profit in the organizations. In the past research articles, the models developed are only for specific problems of warranty optimization. In this research, a generic model is developed that can be applied to any system for calculating the optimal alternatives, optimal types of warranty policy and optimal warranty durations for various components within a system. The constraints considered in the past by the researches are either related to customer’s criteria or related to manufacturer’s criteria. For the first time, this research article is able to provide solution for warranty optimization considering both the criteria as major constraints together. In this research article, an optimized model of warranty is developed. The model is made in the form of software (OptiW) for easy implementation for the users. This software can be applied to any system having various components like Weibull distribution or exponential distribution. This software can determine the type of warranty policies, type of alternatives used and optimum warranty duration period for various components within a system. In this model, life cycle cost is a non-linear objective function of minimization type subjected to two constraints. The constrains are mean time between failure (MTBF) taking into account the customer’s perspective and spare parts cost taking into account the manufacturers’ perspective. First, the numbers of failures for various warranty plans are simulated using inverse function of the cdf of Weibull distribution. The results of the simulation were required in the optimization model. Genetic algorithm is used to solve non-linear optimization model in the MATLAB. Graphical user interface is developed using guide tool in MATLAB. The software exe file is developed using deploy tool to make this software applicable to any window. Using this software OptiW, an engine problem having 29 components as a case study is solved. The results obtained from the OptiW have reduced life cycle cost as compared to existing model of warranty. The optimum warranty duration for 29 components was larger as compared to various existing warranty models. For the future scope, this research paper can be useful for other extended warranty models or for further research.

Probabilistic dynamic analysis of composite plates due to low velocity impact Abstract The low velocity impact (LVI) analysis of fiber-reinforced plastic (FRP) plates is a significant study to evaluate the reliability of lightweight structures. This study has wide applications in offshore and naval industries. Safety and reliability assessment as per the international standards is one of the basic objectives of the study. LVI on FRP plates are studied taking the material parameters and loading as random variables. FRP plates are subjected to failure under impact by in-plane loading. To evaluate the safe load carrying capacity and the reliability under impact, dynamic analysis of composite plate subjected to LVI is carried out. Reliability analysis is performed to calculate the stochastic behavior of FRP plates. During impact, the in-plane damage modes such as matrix cracking, fiber failure, and shear cracking are modeled using a failure criterion. The out of plane delamination is modeled using cohesive surfaces. The variability related with the system properties due to the inherent scatter in the geometric and material properties and input loads are modeled in a stochastic fashion. The stochastic finite element analysis (SFEA) is performed to determine the stochastic response of system using Gaussian process response surface method (GPRSM). The safety level qualification is achieved in terms of reliability level targeted.

Graphic illustration for mechanical reliability design (1): concepts and practices Abstract In this paper, the concepts and practices of mechanical reliability design are described through a variety of graphics and text. Using simple, straightforward language, and clear illustrations, the mysterious framework of mechanical reliability is intuitively presented and scientifically interpreted. Starting from the story of reliability, this paper comprises a brief history on the development, basic concepts, and implications and extensions of mechanical reliability, among other topics, and acquaints readers with the potential and practicality of mechanical reliability engineering. The block diagrams on the course of mechanical reliability development and the systems of mechanical reliability are drawn to clearly explain the relationship between the performance requirements for mechanical products and mechanical reliability for the first time. This paper is intended to popularise the concepts of mechanical reliability engineering and thereby provides rigorous and powerful basic resources in mechanical reliability engineering for the design, manufacturing, application, and assessment of mechanical products.

Empirical Bayes estimator of parameter, reliability and hazard rate for Kumaraswamy distribution Abstract This paper proposes empirical Bayes estimators of parameter, reliability and hazard function for Kumaraswamy distribution under the linear exponential loss function for progressively type II censored samples with binomial removal and type II censored samples. The proposed estimators have been compared with the corresponding Bayes estimators for their simulated risks. The applicability of the proposed estimators have been illustrated through ulcer patient data.

Discrete additive Perks–Weibull distribution: properties and applications Abstract In this study, we introduce a discrete version of continuous additive Perks–Weibull distribution proposed by Singh (Commun Math Stat 4(4):473–493, 2016), and named as discrete additive Perks–Weibull distribution. This proposed distribution has bathtub-shaped as well as increasing hazard rate, and due to this characteristic it lies in the class of few discrete models exhibit bathtub-shaped hazard rate. We have discussed some important distributional properties including moment generating function, probability generating function, moments, cumulative distribution function, quantile function, order statistics, infinite divisibility and some reliability properties such as survival function, hazard rate function and stress–strength reliability. In classical scenario, the parameters of the proposed distribution are estimated by using method of maximum likelihood, whereas in Bayesian approach, we assume joint prior as Dirichlet Type-II distribution for the estimation of parameters involved in the model. A simulation study is performed to compare the performance of different estimation methods. Finally, the model applications are demonstrated by using three real datasets.

A new systematic ranked set-sampling scheme for symmetric distributions Abstract In this paper, a new sampling scheme called systematic ranked set sampling for estimating the population mean is introduced. The performance of the proposed estimator is discussed along with its properties, and it is also shown that the new sampling scheme generates an unbiased estimator. The variance and percentage relative efficiency of the proposed estimator are computed using different symmetric distributions. It is observed from both simulation study and real data set that the new sampling scheme is more efficient than usual ranked set sampling and simple random-sampling schemes.

Profit analysis of a warm standby non-identical unit system with single server performing in normal/abnormal environment Abstract A system/unit is called working in normal environment if it is operating within prescribed conditions set by the manufacturer, otherwise the system is called working in abnormal environment. For example; a hydraulic machine having capacity uplifting the weight of 500 tons exceeds its capacity is termed as working in abnormal environment conditions. In this paper, profit analysis of a warm standby non-identical unit system with single server subject normal/abnormal environment conditions has been discussed. There is a single server who is allowed to do job in normal weather condition only and while performing its job it adopts FCFS (first come first serve) policy. The system model consists of two non-identical units—one is operative and the other kept as warm standby. The main unit may fail directly from normal mode, while failure of warm standby unit takes place owing to remaining unused for a longer period of time. The time taken for repair activity by the server follows negative exponential distribution. The expressions of various reliability measures are analyzed in steady state using semi-Markov process and regenerative point technique. Also, take the arbitrary values for the parameters (i.e., λ, μ, ϕ and θ) to delineate the behavior of some important performance measures to check the efficacy of the system model under such situations shown in the graphs.

A new class of regression cum ratio estimators of population mean in ranked set sampling Abstract This study proposes a new class of regression cum ratio estimators, using transformation of the auxiliary variables. The expressions for the biases and mean squared errors of the new class of estimators are derived in the study. Both the theoretical and numerical comparison of the proposed estimators and their respective competitive estimators are made. To check the performance of estimators, a simulation study was performed. The performance of the new class of estimators was assessed and proven better in comparison to their competitive estimators.

Assessing the process capability index $$S_\mathrm{{pmk}}$$ S pmk using improved estimators Abstract Process capability indices (PCIs) are widely used to determine whether the production process is working according to given specifications or not. It plays an important role in monitoring and analyzing process quality and productivity. Since PCI is based on sample observations, it is a point estimate of the true PCI. It is well known that confidence interval (CI) provides much more information about the population characteristic of interest than a point estimate. In this paper, new estimator for PCI \(S_\mathrm{{pmk}}\) has been proposed using improved estimators of population mean and variance. The proposed and classical index is compared with respect to mean squared error (MSE). Numerical results are provided to illustrate the proposed index and to judge the merits of the proposed estimators. Further, asymptotic confidence interval (ACI) and three non-parametric BCIs, namely, standard bootstrap (s-boot), percentile bootstrap (p-boot) and bias-corrected percentile bootstrap (BCp-boot) of the proposed modified PCI \(S_\mathrm{{pmk}}\) are studied through simulation when the underlying distribution follows Lindley distribution. Method of maximum likelihood is used to estimate the parameter of the model. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the ACI and BCIs for the modified PCI \(S_\mathrm{{pmk}}\) . Finally, four real data sets are analyzed for illustrative purposes.

Bayesian estimation of stress–strength reliability for Lomax distribution under type-II hybrid censored data using asymmetric loss function Abstract In this article, the classical and Bayesian estimation procedures for stress–strength reliability parameter \(R = P[Y < X]\) for Lomax distribution have been discussed where the sample information is type-II hybrid censored. In classical estimation setup, the maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. The Bayes estimator is computed with gamma priors for both parameters using asymmetric loss function. The Monte Carlo simulation study has been performed to compare the obtained estimators for the different combination of censoring parameters. Lastly, the medical data set has been used to demonstrate the applicability of the proposed study as well as the model.