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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.

The study based on the estimation of the stress–strength reliability parameter plays a vital role in showing system efficiency. In this paper, considering independent strength and stress random variables distributed as inverted exponentiated Rayleigh model, the author have developed estimation procedures for the stress–strength reliability parameter R = P(X>Y) under Type II hybrid censored samples.

The maximum likelihood and Bayesian estimates of R based on Type II hybrid censored samples are evaluated. Because there is no closed form for the Bayes estimate, the author use the Metropolis–Hastings algorithm to obtain approximate Bayes estimate of the reliability parameter. Furthermore, the author construct the asymptotic confidence interval, bootstrap confidence interval and highest posterior density (HPD) credible interval for R. The Monte Carlo simulation study has been conducted to compare the performance of various proposed point and interval estimators. Finally, the validity of the stress–strength reliability model is demonstrated via a practical case.

The performance of various point and interval estimators is compared via the simulation study. Among all proposed estimators, Bayes estimators using MHG algorithm show minimum MSE for all considered censoring schemes. Furthermore, the real data analysis indicates that the splashing diameter decreases with the increase of MPa under different hybrid censored samples.

The frequentist and Bayesian methods are developed to estimate the associated parameters of the reliability model under the hybrid censored inverted exponentiated Rayleigh distribution. The application of the proposed stress–strength reliability model will help the reliability engineers and also other scientists to estimate the system reliability.

The aim of this research paper is to generalize the previous works on the design of accelerated life tests (ALTs) for periodic inspection and Type I censoring and to promote the use of an exponentiated Weibull (EW) distribution in accelerated life testing.

Statistically optimal ALT plans are suggested for items whose lifetime follows the EW distribution under periodic inspection and Type I censoring. It is assumed that the mean lifetime (scale parameter) is a log‐linear function of stress and that the shape parameters are independent of stress. Given shape parameters, design stress and high test stress, the test plan is optimized with respect to the low test stress and the proportion of test units are also allocated to this test stress. The asymptotic variance (AsVar) of the maximum likelihood estimator of log mean life at the design stress is used as an optimality criterion with equally spaced inspection times. A FORTRAN program was written to calculate the optimal plans. Procedures for planning of an ALT, including selection of sample size, have also been discussed. An illustration of the optimal ALT plans has been done through a numerical example.

Computational findings for various values of the shape parameters indicate that the AsVar of log mean life at the design stress is insensitive to the number of inspection times and to misspecifications of imputed failure probabilities at design and high test stresses. Computational findings also show that optimal designs of ALT previously obtained for exponential, Rayleigh, and Weibull distributions become special cases of the EW distribution. Thus, the EW distribution is a useful and widely applicable reliability model for optimal ALT plans.

The present investigation features the EW distribution of lifetimes of test items and it generalizes the previous works on accelerated life testing. Furthermore, the propose test plans can be applied to estimate the lifetime of highly reliable product or material, if a researcher designs a test under the assumption of this model.

The purpose of this paper is to present designs for an accelerated life test (ALT).

Bayesian methods and simulation Monte Carlo Markov Chain (MCMC) methods were used.

In the paper a Bayesian method based on MCMC for ALT under EW distribution (for life time) and Arrhenius models (relating the stress variable and parameters) was proposed. The paper can conclude that it is a reasonable alternative to the classical statistical methods since the implementation of the proposed method is simple, not requiring advanced computational understanding and inferences on the parameters can be made easily. By the predictive density of a future observation, a procedure was developed to plan ALT and also to verify if the conformance fraction of the manufactured process reaches some desired level of quality. This procedure is useful for statistical process control in many industrial applications.

The results may be applied in a semiconductor manufacturer.

The Exponentiated‐Weibull‐Arrhenius model has never before been used to plan an ALT.

In this paper, new procedures for a fuzzy Markov reward model are introduced to find the reliability measures.

It is supposed that the introduced system consisted of n identical units connected in parallel and each unit has m different types of failures. Also, each unit of the system is allowed to have d levels of degradation from a working state to complete failure. Non-homogeneous Markov reward model is used to construct the system of differential equations of the model. Procedures are proposed to obtain reliability measures of the model under considering that the failure and repair rates of the systems unit are fuzzy. An application is constructed to analyze a system of 2-unit, and results are shown graphically.

Non-homogeneous Markov reward model is used to construct the system of differential equations of the model.

All papers in literature assumed Markov reward model with deterministic parameters. In this paper, a generalization of classical Markov reward model is introduced.

The study aims to design the limited number of random working cycle as a warranty term and propose two types of warranties, which can help manufacturers to ensure the product reliability during the warranty period. By extending the proposed warranty to the consumer's post-warranty maintenance model, besides the authors investigate two kinds of random maintenance policies to sustain the post-warranty reliability, i.e. random replacement first and random replacement last. By integrating depreciation expense depending on working time, the cost rate is constructed for each random maintenance policy and some special cases are provided by discussing parameters in cost rates. Finally, sensitivities on both the proposed warranty and random maintenance policies are analyzed in numerical experiments.

The working cycle of products can be monitored by advanced sensors and measuring technologies. By monitoring the working cycle, manufacturers can design warranty policies to ensure product reliability performance and consumers can model the post-warranty maintenance to sustain the post-warranty reliability. In this article, the authors design a limited number of random working cycles as a warranty term and propose two types of warranties, which can help manufacturers to ensure the product reliability performance during the warranty period. By extending a proposed warranty to the consumer's post-warranty maintenance model, the authors investigate two kinds of random replacement policies to sustain the post-warranty reliability, i.e. random replacement first and random replacement last. By integrating a depreciation expense depending on working time, the cost rate is constructed for each random replacement and some special cases are provided by discussing parameters in the cost rate. Finally, sensitivities to both the proposed warranties and random replacements are analyzed in numerical experiments.

It is shown that the manufacturer can control the warranty cost by limiting number of random working cycle. For the consumer, when the number of random working cycle is designed as a greater warranty limit, the cost rate can be reduced while the post-warranty period can't be lengthened.

The contribution of this article can be highlighted in two key aspects: (1) the authors investigate early warranties to ensure reliability performance of the product which executes successively projects at random working cycles; (2) by integrating random working cycles into the post-warranty period, the authors is the first to investigate random maintenance policy to sustain the post-warranty reliability from the consumer's perspective, which seldom appears in the existing literature.

In this paper, the authors design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this paper we design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this study, the authors design accelerated life test under Type-I censoring when the lifetime of test items follows PID and also provides its application in the field of warranty policy. The following conclusion is made on the basis of this study. (1) An inverse relationship is shown between the shape parameter with the expected total cost and expected cycle time, while the shape parameter directly relates to the expected cost rate (see Table 5). (2) A direct relationship is shown between the scale parameter with the expected total cost and expected time cycle, while the inverse relationship is shown with the expected cost rate (see Table 5). (3) An inverse relationship is shown between the replacement age and the expected cost rate, while there are direct relationships between expected total cost and expected time cycle (see Table 5).

This paper is neither published or neither accepted anywhere.

The purpose of this research is to incorporate the exponentiated Weibull testing‐effort functions into software reliability modeling and to estimate the optimal software release time.

This paper suggests a software reliability growth model based on the non‐homogeneous Poisson process (NHPP) which incorporates the exponentiated Weibull (EW) testing‐efforts.

Experimental results on actual data from three software projects are compared with other existing models which reveal that the proposed software reliability growth model with EW testing‐effort is wider and effective SRGM.

This paper presents a SRGM using a constant error detection rate per unit testing‐effort.

Software reliability growth model is one of the fundamental techniques to assess software reliability quantitatively. The results obtained in this paper will be useful during the software testing process.

The present scheme has a flexible structure and may cover many of the earlier results on software reliability growth modeling. In general, this paper also provides a framework in which many software reliability growth models can be described.

Lifetime data are used in many different applied sciences, like biomedicine, engineering, insurance and finance and others. The purpose of this paper is to develop a new acceptance sampling plans for Rama distribution when the mean lifetime test is truncated at a pre-determined time. The minimum sample sizes required to assert the specified life mean is obtained for a given customer’s risk. The operating characteristic function values of the sampling plans and producer’s risk are calculated.

The results are illustrated using numerical examples and a real data set is considered to illustrate the performance of the suggested acceptance sampling plans and how it can be used for the industry applications.

This paper shows a new acceptance sampling plans based on Rama distribution in the particular case when the mean life time test is truncated.

The results calculated in this paper demonstrate the differences between OC values for different distributions taken into account. In particular, OC values of Rama distribution are found to be less than the proposed distribution counterparts.