Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Lins, Isis Didier; Moura, Márcio das Chagas; Droguett, Enrique López; Corrêa, Thaís Lima

doi:10.3390/e20040223

Cited by 4 publications

(1 citation statement)

References 36 publications

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“…The q-Weibull distribution includes an additional r parameter, and in the cases r = 1 and r = 2 we recover the q-exponential and q-Gaussian distributions, respectively. The q-Weibull distribution also has been used in a variety of contexts in complex systems [56,57,58], and it is closely linked to the Tsallis statistics [59,60,61,62]. We finally propose to fit the I-V curves with the q-Weibull cdf, shown in Eq.…”

Section: Using the Q-weibull Distribution Function: Plasma Potential ...mentioning

confidence: 99%

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Gonzalez

González

Soler

et al. 2022

Plasma Res. Express

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We describe a procedure to obtain the plasma parameters from the {\bf I-V} Langmuir curve by using the Druyvesteyn equation. We propose to include two new parameters, $q$ and $r$, to the usual plasma parameters: plasma potential ($V_p$), floating potential ($V_f$), electron density ($n$), and electron temperature ($T$). These new parameters can be particularly useful to represent non-Maxwellian distributions. The procedure is based on the fit of the {\bf I-V} Langmuir curve with the $q$-Weibull distribution function, and is motivated by recent works which use the $q$-exponential distribution function derived from Tsallis statistics. We obtain the usual plasma parameters employing three techniques: the numerical differentiation using Savitzky Golay (SG) filters, the $q$-exponential distribution function, and the $q$-Weibull distribution function. We explain the limitations of the $q$-exponential function, where the experimental data $V>V_p$ needs to be trimmed beforehand, and this results in a lower accuracy compared to the numerical differentiation with SG. To overcome this difficulty, the $q$-Weibull function is introduced as a natural generalization to the $q$-exponential distribution, and it has greater flexibility in order to represent the concavity change around $V_p$. We apply this procedure to analyze the measurements corresponding to a nitrogen $N_2$ cold plasma obtained by using a single Langmuir probe located at different heights from the cathode. We show that the $q$ parameter has a very stable numerical value with the height. This work may contribute to clarify some advantages and limitations of the use of non-extensive statistics in plasma diagnostics, but the physical interpretation of the non-extensive parameters in plasma physics remains not fully clarified, and requires further research.

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Section: Using the Q-weibull Distribution Function: Plasma Potential ...mentioning

confidence: 99%

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Gonzalez

González

Soler

et al. 2022

Plasma Res. Express

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Pre-operative mapping and structured reporting of pelvic endometriotic lesions on dynamic ultrasound and its correlation on laparoscopy using the #ENZIAN classification

Bindra

Nori²,

Mohanty³

et al. 2022

Arch Gynecol Obstet

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Purpose: The objective of this study was to evaluate and compare the diagnostic performance of ultrasonography (USG) assessment using structured reporting with intraoperative laparoscopic assessment in deep in ltrating endometriosis (DIE) using the recent update of the #ENZIAN classi cation.Methods: This was a retrospective study conducted in Tertiary Multi-disciplinary Endometriosis Care Hospital over a period of 8 months which included 50 patients who underwent a planned laparoscopic endometriosis excisional surgery after a dedicated USG assessment using International Deep Endometriosis Analysis (IDEA) protocol and #Enzian score (updated Enzian classi cation), between Feb 2021 to Sept 2021 at Apollo Hospitals, Hyderabad. The pre-operative USG ndings were reported in a structured reporting format and intraoperative ndings were classi ed using the standard #ENZIAN classi cation. No prospective interventions were done. A review of pre-operative ultrasound and laparoscopic ndings as per the #Enzian.Results: Sensitivity and the negative predictive value of ultrasound were 86% and 84.2% for peritoneal lesions, 97% and 93.3 % for left ovarian lesions, 93% and 91.6% for right ovarian lesions, 91% and 84% for left tubal lesions, 90% and 86.3 % for right tubal lesions, 93% and 75 % for uterosacral ligaments, 93.3 % and 97% for rectal lesions and sensitivity and negative predictive values were 100 % for rectovaginal lesions, adenomyosis, and ureteric lesions as con rmed on laparoscopy.Conclusion: Dynamic ultrasound assessment with a structured report based on IDEA protocol and #ENZIAN score is accurate for mapping of pelvic endometriosis in all forms, and it correlates with laparoscopic ndings, thus helps surgeon for better planning and providing a road map for surgeons. From a clinical perspective, a uniform and shared reporting system across imaging and therapeutic modalities will simplify communication, improving patient management by conservative or surgical treatments, avoiding multiple repeat surgeries, and improving quality of treatment.

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A tool for evaluating repairable systems based on Generalized Renewal Processes

Oliveira

Firmino

Cristino

2019

Reliability Engineering & System Safety

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Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Cited by 4 publications

References 36 publications

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Pre-operative mapping and structured reporting of pelvic endometriotic lesions on dynamic ultrasound and its correlation on laparoscopy using the #ENZIAN classification

A tool for evaluating repairable systems based on Generalized Renewal Processes

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