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2 On the Optimization of the Cost Rate of Coherent Reliability Structures under Replacement Policy
Published in Amit Kumar, Mangey Ram, Operations Research, 2022
In order to implement the step-by-step procedure mentioned in Section 2.2, we next assume that the components of the underlying reliability structure follow the exponentiated Gamma distribution with parameter θ > 0. Generally speaking, Gupta et al. (1998) established a parametric approach for modeling failure time data under the assumption that a baseline continuous distribution function is available. Their exponentiated models include, among others, the so-called exponentiated Weibull distribution and the exponentiated Pareto distribution. We next assume that the components' lifetimes of the bridge structure follow the exponentiated Gamma distribution with parameter θ > 0. Under the exponentiated Gamma model, the probability density function and the cumulative distribution function of components' lifetimes X1,X2,...,Xn are given as (see, e.g. Gupta et al. (1998)) f(t)=θte−t1−e−t−te−tθ−1,t≥0andF(t)=1−e−t−te−tθ,t≥0
The additive Perks distribution and its applications in reliability analysis
Published in Quality Technology & Quantitative Management, 2022
Luis Carlos Méndez-González, Luis Alberto Rodríguez-Picón, Ivan Juan Carlos Pérez Olguín, Vicente García, David Luviano-Cruz
Similarly, some authors propose a mixture of two distributions from which a failure rate can be obtained in the form of a bathtub. Lai et al. (2016) introduced a new form of parameterization, which involves the representation of the hazard function as a generalized beta function ratio, with which it is possible to obtain bathtub curve representations. Lee et al. (2007) proposed the Beta-Weibull (BWD) distribution of four parameters, where the properties of the Beta and Weibull Distribution are combined for modeling a non-monotonic failure rate in reliability analysis. Nadarajah et al. (2013) studied the Exponentiated Weibull Distribution (EWD), which is a generalization of the two-parameter WD to accommodate non-monotone hazard rates. Mahdavi and Kundu (2017) introduced the Alpha Power Transformation (APT); this transformation proposes to add a new parameter to the family of exponential distributions. The proposed new parameter incorporates skewness, which allows the distributions to have better flexibility to represent non-monotonic behaviors. A practical case of the application of the APT with the WD where the reliability of electronic devices (ELD) is determined is reported by Méndez-González et al. (2022)
A New Flexible Exponentiated-X Family of Distributions: Characterizations and Applications to Lifetime Data
Published in IETE Journal of Research, 2022
Muhammad Arif, Dost Muhammad Khan, Muhammad Aamir, Mahmoud El-Morshedy, Zubair Ahmad, Zardad Khan
This article contributes to the probability theory by providing a prominent and flexible family of distributions named a new flexible exponentiated-X family of distribution. For illustration of the newly recommended family, a distinctive sub-case of the new family is presented in the form of a new flexible exponentiated Weibull distribution. The plots of density and the hazard functions for NFEW model are provided using different combinations of the parameter values. The numerical values of the model parameters along with their corresponding standard errors are derived using the ML technique. Furthermore, a simulation study is performed to support these numerical estimates. Two lifetime data sets are incorporated to check the flexibility and goodness-of-fit of the NFEW model. From the given numerical facts and the fitted plots for NFEW and other competing models, it is clearly indicated that the NFEW model is a good alternative to the Weibull distribution for modeling lifetime data. The NFEW distribution provides the lowest values for all the analytical measures, where AIC = 28.031, BIC = 34.460, CAIC = 28.438, HQIC = 30.560, K.S = 0.098, C.M = 0.080, and A.D = 0.463 for the glass fibers data; AIC = 249.05, BIC = 256.04, HQIC = 251.84, BIC = 256.04, K.S = 0.095, C.M = 0.098, and A.D = 0.583 for the fatigue fracture data. Therefore, the proposed NFEW distribution is recommended for modeling and applications to real-lifetime data.