Exponentiated additive Weibull distribution

Ahmad, Abd EL-Baset A.; Ghazal, M. G. M.

doi:10.1016/j.ress.2019.106663

Cited by 53 publications

(25 citation statements)

References 30 publications

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“…830‑00060; Sonics & Materials Inc.); thermal profiles developed during macerations were registered using a mercury thermometer. An empirical equation (Eqn (1)), with the Weibull form, 17 was proposed to model temperature changes during ultrasound processes. This model considers two terms given by a constant that indicates the initial temperature of the system and a second term that reflects the exponential increases in this variable:

T = T_{i} + T_{R} ((), 1 - e^{- k_{R} t^{n}})

where T is the temperature at time t , T i is the initial temperature, T R is the change in temperature when the time approaches infinity, k R represents the kinetic coefficient of temperature increase, and n represents the shape factor that could be associated with the order of changes registered in temperature 17 …”

Section: Methodsmentioning

confidence: 99%

Development of an aqueous ultrasound‐assisted extraction process of bioactive compounds from beet leaves: a proposal for reducing losses and increasing biomass utilization

et al. 2020

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BACKGROUND Red beet plants are cultivated worldwide for the consumption of their roots, generating large amounts of unexploited by‐products. In particular, beet leaves (BLs) represent about 50% of the whole plant and are usually discarded as waste. This constitutes not only an economic issue, since multiple resources invested in the production will be wasted, but also an environmental problem because of the pollution associated with their disposal. However, BLs comprise an important source of functional compounds (polyphenols and betalains) that could be recovered from the raw material, representing a sustainable solution for the underutilization of this by‐product. This study proposes the recovery of polyphenols and betalains using an aqueous ultrasound‐assisted extraction (UAE) process at different powers (35, 50, and 100 W) that was characterized and optimized. RESULTS UAE significantly enhanced the recovery of bioactive compounds and shortened the time required for extraction in comparison with traditional macerations (35 < 50 < 100 W). During UAE, the temperature of the systems increased as a function of the power applied, favouring the recovery of these phytochemicals. Additionally, a Box–Behnken design and response surface methodology were employed to optimize UAE conditions (90 W ultrasound power, 1:20 solid:liquid ratio, 16 min extraction time), under which the yields were 14.9 mg g−1 (polyphenols), 949.1 μg g−1 (betaxanthins), and 562.2 μg g−1 (betacyanins), consistent with the values predicted by the models. CONCLUSION This study enabled the development of a green‐solvent UAE process that constitutes an effective post‐harvest by‐products strategy to minimize losses and increase biomass utilization through the recovery of bioactive compounds from BLs, promoting sustainability in the agri‐food chain. © 2020 Society of Chemical Industry

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T = T_{i} + T_{R} ((), 1 - e^{- k_{R} t^{n}})

Section: Methodsmentioning

confidence: 99%

Development of an aqueous ultrasound‐assisted extraction process of bioactive compounds from beet leaves: a proposal for reducing losses and increasing biomass utilization

et al. 2020

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“…where ε is the strain of the composite specimen in section AB; D p is the damage variable of the AB segment. At this stage, the micro element strength of backfill-red sandstone combination specimen obeys Weibull distribution [35,36], the probability density function is…”

Section: Constitutive Model In Quasi-elastic Synergy Deformation Stag...mentioning

confidence: 99%

Experimental and Analytical Investigation into the Synergistic Mechanism and Failure Characteristics of the Backfill-Red Sandstone Combination

et al. 2022

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The stability of underground goaf in filling mining is dominated by the interaction mechanism of the backfill-surrounding rock combination. In order to investigate the interaction mechanism and failure characteristics of the backfill-surrounding rock combination, backfill-red sandstone combinations with three different cement–sand ratios were prepared for uniaxial compression tests. The deformation and failure characteristics of the specimens were analyzed. It was found that at the cement–sand ratio of 1:4, the backfill and red sandstone interacted with and restricted each other, and the through cracks appeared in the whole specimens, which indicated that the backfill and red sandstone can jointly resist external loads and play a role in common bearing. However, with the decrease of the cement–sand ratio, the stress mainly acts on the backfill, and the deformation observed in the backfill is large while there is no obvious rupture in the rock. Based on the failure characteristics and the stress–strain curves of the specimens, the damage constitutive relationship that can describe the failure process and deformation characteristics is proposed. Correlated with the experiment results, the damage constitutive equation is established in three stages including compaction pre-synergy stage, quasi-elastic synergy deformation stage and rupture deformation stage. The failure characteristics observed in each stage are analyzed. The research results are of great significance to accurately understanding the interaction between backfill and surrounding rock, which can be used to design and select the mixture ratio of the filling materials.

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“…This data set is studied by Meeker and Escobar [22] and gives the times of failure and running times for a sample of 30 devices from a field-tracking study of a larger system. The data set is: 2, 10, 13,23,23,28,30,65,80,88,106,143,147,173,181,212,245,247,261,266,275,293, 300, 300, 300, 300, 300, 300, 300, 300. The TTT-transform plot in Figure 6(a) shows that the data set exhibits a bathtub-shaped hazard rate.…”

Section: Data Set 2: Meeker and Escobar Data (Complete Data)mentioning

confidence: 99%

“…According to Nelson [6], the distributions which provide more flexible distributions usually require at least five parameters. Among the five parameters modified Weibull distributions we mention, the beta modified Weibull distribution [7], the McDonald Weibull distribution [8], the beta generalized Weibull distribution [9], the beta Sarhan-Zaindin modified Weibull distribution [10], the additive modified Weibull distribution [11], the new generalized odd log-logistic flexible Weibull distribution [12] and the exponentiated additive Weibull distribution [13]. All theses distributions have monotone, bathtub-shaped and unimodal hazard rate functions.…”

Section: Introductionmentioning

confidence: 99%

The Beta Reduced Modified Weibull Distribution with Applications to Reliability Data

Benkhelifa

2021

JRSS

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[1] C.D. Lai, M. Xie and D.N.P. Murthy. A modified Weibull distribution. EEE Transactions on Reliability, 52(1):33-37, 2003. [2] M. Bebbington, C.D. Lai, and R. Zitikis. A flexible Weibull extension. Reliability Engineering and System Safety, 92:719-726, 2007. [3] A.M. Sarhan and J. Apaloo. Exponentiated modified weibull extension distribution. Reliability Engineering and System Safety, 112:137-144, 2013. [4] F. Famoye, C. Lee and O. Olumolade. The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4(2):121-136, 2005. [5] L. Benkhelifa. The Weibull Birnbaum-Saunders distribution and its applications. Statistics, Optimization and Information Computing, 9(1):61-81, 2021. [6] W. Nelson. Accelerated life testing: statistical models. data analysis and test plans. New York: Wiley; 1990. [7] G.O. Silva, E.M. Ortega and G.M. Cordeiro. The beta modified Weibull distribution. Lifetime Data Analysis, 16(3):409-430, 2010. [8] G.M. Cordeiro, E.M. Hashimoto and E.M. Ortega and . The McDonald Weibull model. Statistics, 48(2):256-278, 2014. [9] N. Singla, K. Jain and S. Kumar Sharma. The beta generalized Weibull distribution: properties and applications. Reliability Engineering and System Safety, 102:5-15, 2012. [10] A. Saboor, H.S. Bakouch and M.N. Khan. Beta Sarhan–Zaindin modified Weibull distribution. Applied Mathematical Modelling, 40: 6604, 2016. [11] B. He and W. Cui. An additive modified Weibull distribution. Reliability Engineering and System Safety, 145:28-37, 2016. [12] F. Prataviera E.M. Ortega, G.M. Cordeiro, R.R. Pescim and B.A.W. Verssania. A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems. Reliability Engineering and System Safety, 176:13–26, 2018. [13] A.A. Ahmad and M.G.M. Ghazal. Exponentiated additive Weibull distribution. Reliability Engineering and System Safety, 193:106663, 2020. [14] S.J. Almalki and J. Yuan. The new modified Weibull distribution. Reliability Engineering and System Safety, 111:164-170, 2013. [15] S.J. Almalki. Reduced new modified Weibull distribution. Communications in Statistics - Theory and Methods, 47:2297-2313, 2018. [16] W. Kuo and M.J. Zuo. Reduced new modified Weibull distribution. Optimal reliability modeling: principles and applications. Wiley; 2001. [17] N. Eugene and F. Famoye. Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 31:497-512, 2002. [18] B.C. Arnold and H.N. Nagarajah. A first course in order statistics. New York: John Wiley, 2008. [19] I.S. Gradshteyn and I.M. Ryzhik. Table of integrals, Series and Products. Academic Press, New York; 2000. [20] R.G. Miller, G. Gong and A. Muñoz. Survival analysis. New York: John Wiley and Sons; 1981. [21] M.V. Aarset. How to identify a bathtub hazard rate. EEE Transactions on Reliability, 36(1):106-108, 1987. [22] W.Q. Meeker and L.A. Escobar. Statistical methods for reliability data. New York: Wiley; 1998. [23] Y. Liu and A.I. Abeyratne. Practical applications of bayesian reliability. New York: John Wiley and Sons; 2019.

show abstract

Exponentiated additive Weibull distribution

Cited by 53 publications

References 30 publications

Development of an aqueous ultrasound‐assisted extraction process of bioactive compounds from beet leaves: a proposal for reducing losses and increasing biomass utilization

Development of an aqueous ultrasound‐assisted extraction process of bioactive compounds from beet leaves: a proposal for reducing losses and increasing biomass utilization

Experimental and Analytical Investigation into the Synergistic Mechanism and Failure Characteristics of the Backfill-Red Sandstone Combination

The Beta Reduced Modified Weibull Distribution with Applications to Reliability Data

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