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The purpose of this paper is to analyze conditional failure rates, and prioritize water pipelines for replacement based on their expected failure rate where pipes are grouped based on age and pipe type. Thus, predictions can be made on the expected number of breaks in future years.

The time to failure of a pipe can be characterized by the stochastic properties of the population as a whole, from which the likelihood of component failure is derived. When the corresponding failure rate is plotted against time, a bathtub‐shaped curve results. The bathtub curve assists in determining maintenance schedules depending on the age of the pipe. Failure rates help determine whether the rates are more than an acceptable best practice threshold to signal replacement.

Ductile iron pipes had the highest failure rates, followed by asbestos cement pipes; PVC and concrete cylinder pipes had the lowest failure rates, but because concrete cylinder pipes are very time‐consuming to repair and very expensive to install, only PVC pipes are recommended on the basis of this study. Cast iron pipes fit the bathtub shape; ductile iron and asbestos concrete were somewhat bathtub shaped, though the early phase period was not apparent; the bathtub curve for concrete cylinder was fully inverted; while PVC pipes showed zero probability of failure during the middle period. The shapes of bathtub curves drawn on conditional failure rates were similar to those for the failure rates. The bathtub curves indicate that the general failure performance of pipe materials is somewhat contrary to general principles in manufacturing.

Analysis of failure serves a practical purpose for water utilities to allocate funds for pipe maintenance and prepare a schedule for pipe replacement, so as to provide the best quality services and safe drinking water to users of the utility.

The proper prioritization of water supply pipes for repair and replacement is of great social importance to the public at large, which expends considerable funds to maintain their drinking water supply.

The study of bathtub curves has not been seen before in the analysis of water supply pipes. A unique discovery is that the traditional shape of the bathtub curve is not always applicable for water supply pipes.

This study aims to obtained the failure probability distributions of subsystems for industrial robot and filtrate its fault data considering the complicated influencing factors of failure rate for industrial robot and numerous epistemic uncertainties.

A fault data screening method and failure rate prediction framework are proposed to investigate industrial robot. First, the failure rate model of the industrial robot with different subsystems is established and then the surrogate model is used to fit bathtub curve of the original industrial robot to obtain the early fault time point. Furthermore, the distribution parameters of the original industrial robot are solved by maximum-likelihood function. Second, the influencing factors of the new industrial robot are quantified, and the epistemic uncertainties are refined using interval analytic hierarchy process method to obtain the correction coefficient of the failure rate.

The failure rate and mean time between failure (MTBF) of predicted new industrial robot are obtained, and the MTBF of predicted new industrial robot is improved compared with that of the original industrial robot.

Failure data of industrial robots is the basis of this prediction method, but it cannot be used for new or similar products, which is the limitation of this method. At the same time, based on the series characteristics of the industrial robot, it is not suitable for parallel or series-parallel systems.

This investigation has important guiding significance to maintenance strategy and spare parts quantity of industrial robot. In addition, this study is of great help to engineers and of great significance to increase the service life and reliability of industrial robots.

This investigation can improve MTBF and extend the service life of industrial robots; furthermore, this method can be applied to predict other mechanical products.

This method can complete the process of fitting, screening and refitting the fault data of the industrial robot, which provides a theoretic basis for reliability growth of the predicted new industrial robot. This investigation has significance to maintenance strategy and spare parts quantity of the industrial robot. Moreover, this method can also be applied to the prediction of other mechanical products.

The purpose of this paper is to compare four life data models, namely the exponential and the Weibull models, and their corresponding generalized versions, q-exponential and q-Weibull models, by means of one practical application.

Application of the models to a practical example (a welding station), with estimation of parameters by the use of the least squares method, and the Akaike Information Criterion (AIC).

The data of the example considered in this paper is divided into three regimes, decreasing, constant and increasing failure rate, and the q-Weibull model describes the bathtub curve displayed by the data with a single set of parameters.

The simplicity and flexibility of the q-Weibull model may be very useful for practitioners of reliability analysis, and its benefits surpasses the inconvenience of the additional parameter, as AIC shows.

The q-Weibull model is compared in detail with other three models, through the analysis of one example that clearly exhibits a bathtub curve, and it is shown that it can describe the whole time range with a single set of parameters.

To investigate the optimal burn‐in time from the perspective of minimizing the expected total cost (i.e. manufacturing plus warranty costs) per unit of product sold under a failure‐free renewing warranty policy. The conditions indicating when burn‐in becomes beneficial were also derived.

An age‐dependent general repairable product sold under a failure‐free renewing warranty agreement was considered. In the case of such a general repairable model, there are two ways in which the product can fail: type I failure (minor) can be rectified through minimal repairs; while in type II failure (catastrophic), the product must be replaced. Then optimal burn‐in time is then examined in order to achieve a trade‐off between reducing the warranty cost and increasing the manufacturing cost.

The optimal burn‐in time depends on the failure/repair characteristics, length of warranty, cost parameters and the probability of failure type II (catastrophic). A burn‐in program is beneficial if the initial failure rate is high or product failures during the warranty period are costly. Moreover, the optimal burn‐in time is always less than the infant mortality period.

The product considered in this paper is an age‐dependent general repairable product: on which no such study has yet been conducted. This is also the first study to apply a failure‐free renewing warranty to a general repairable item. It can be seen that the present model is a generalization of the model considered by Chien and Sheu.

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.

The purpose of this paper is to introduce a new probability density function having both unbounded and bounded support with a wider applicability. While the distribution with bounded support on [0, 1] has applications in insurance and inventory management with ability to fit risk management data on proportions better than existing bounded distributions, the same with unbounded support is used as a lifetime model and is considered as an attractive alternative to some existing models in the reliability literature.

The new density function, called modified exponential-geometric distribution is derived from the exponential-geometric distribution introduced by Adamidis and Loukas (1998). The support of the density function is shown to be both unbounded and bounded depending on the values of one of the shape parameters. Various properties of the density function are studied in detail and the parameters are estimated through maximum likelihood method of estimation. A number of applications related to reliability, insurance and inventory management are exhibited along with some useful data analysis.

A single probability distribution with both unbounded and bounded support, which does not seem to exist in the reliability literature, is introduced in this paper. The proposed density function exhibits varying shapes including U-shape, and the failure rate also shows increasing, decreasing and bathtub shapes. The Monte Carlo simulation shows that the estimates of the parameters are quite stable with low standard errors. The distribution with unbounded support is shown to have competitive features for lifetime modeling through analysis of two data sets. The distribution with bounded support on [0, 1] is shown to have application in insurance and inventory management and is found to t data on proportions related to risk management better than some existing bounded distributions.

The authors introduce an innovative probability distribution which contributes significantly in insurance and inventory management besides its remarkable statistical and reliability properties.

The problem is to devise a life‐test acceptance procedure of an electrical item that has a Weibull failure distribution with an increasing hazard rate. The test‐bed facility has some constraints on the number of test samples and testing time.

The life‐test plan is obtained using censoring of experiments and the properties of order statistics. In this article, the author has derived expressions for order statistics and their moments for some commonly used hazard‐rate functions; for example, constant, linearly increasing, exponentially increasing, power function, etc. and the same is used in planning the life‐test acceptance procedure.

Results and findings are discussed in full. It is postulated that further research in this direction will definitely bring some fruitful results that have immense importance in the field of reliability analysis and life‐testing experiments.

The same methodology can be adopted for devising life‐test acceptance procedure using censoring of experiments.

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.

The purpose of this study is to extend a sensitivity-based reliability technique for the processors deployed in industrial drive (ID).

The processor provides flexible operation, re-configurability, and adaptable compatibility in industrial motor drive system. A sensitivity-based model allows a robust tool for validating the system design. Sensitivity is the probability of a partial failure rate for a distributed variable; sensitivity and failure rates are also complementary. Conversely, traditional power electronic components reliability estimating standards have overlooked it, and it is essential to update them to account for the sensitivity parameter. A new sensitivity-based reliability prediction methodology for a typical 32-bit microprocessor operating at 30ºC deployed in ID is presented to fill this gap. The proposed techniques are compared with the estimated processor reliability values obtained from various reliability standards using the validated advanced logistics development tool. The main contribution of this work is to provide a sensitivity extended reliability method over the conventional method directing toward improving reliability, availability, and maintainability in the design of ID.

The analysis shows that the sensitivity of the processor’s circuit increases due to increases in complexity of the system by reducing the overall mean time between failure upon comparing among conventional reliability standards.

The significance of this paper lies in the overall, sensitivity-based reliability technique for processors in comparison to the traditional reliability complexity in IDs.

The purpose of this paper is to study a geometric process (GP) maintenance model and policy for a repairable system.

Lam first introduced the GP and its application to maintenance model. Assume that a replacement policy N is applied by which the system will be replaced by a new, identical one following the Nth failure.

For a deteriorating system, an optimal replacement policy is determined analytically, and the monotonicity properties of the optimal replacement policy are then studied.

For an improving system, the paper shows that the optimal replacement policy is the ∞ policy, i.e., the policy without replacement.