Estimation methods for the probability density function and the cumulative distribution function of the Pareto-Rayleigh distribution

Jebeli, Maleki; Deiri, Einolah

doi:10.1080/02331888.2019.1689979

Cited by 10 publications

(7 citation statements)

References 10 publications

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“…CDF is a widely used statistical analysis function that describes the probability of discovery of an investigated variable 27 , 28 . To explore the degradation in PR, we plotted the CDF for the affected PID PV strings as shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

Field study on the severity of photovoltaic potential induced degradation

Badran

Dhimish

2022

Sci Rep

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Photovoltaic (PV) systems can be affected by different types of defects, faults, and mismatching conditions. A severe problem in PV systems has arisen in the last couple of years, known as potential-induced degradation (PID). During the early installation stage of the PV system, the PID may not be noticed because it appears over time (months or years). As time passes, it becomes more apparent since the output power may drop dramatically. We studied PV modules over the course of three years that were affected by PID. An electroluminescent and thermal imaging technique helped discover the PID. PID appeared in PV modules after being in different fields for 4–8 months, resulting in a 27–39% drop in power. An anti-PID box was fitted during the second year of the PV operation to recover the PID. Accordingly, it has stabilized the power degradation, but it could not restore the performance of the affected PID modules as compared with healthy/non-PID modules.

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Section: Resultsmentioning

confidence: 99%

Field study on the severity of photovoltaic potential induced degradation

Badran

Dhimish

2022

Sci Rep

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“…Prior to proceed with the Bayesian EWMA monitoring of the shape parameter of the IGD based on the real data, it is of prime importance to assess the goodness of fit of the model to the observed data. We may use the model selection criteria to evaluate the goodness of fit of the model to the observed data and compare different models, [ 68 ]. So we may use Akaike information criterion (AIC), [ 69 ] and Bayesian information criterion (BIC, also known as Schwarz criterion), which are respectively defined as and …”

Section: Real Data Applicationmentioning

confidence: 99%

Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process

Javed,

Abbas,

Abbas

2024

PLoS ONE

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Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results.

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“…To estimate drilling machine lifetime, [ 34 ] used the Lomax-G generator to derive Lomax-Rayleigh distribution and applied it to drilling machine data. Different types of estimators of Pareto-Rayleigh distribution are given by [ 35 ]. Different traditional and heuristic methods of estimation for the Lomax-Rayleigh distribution generated by the Lomax-X generator are given by [ 36 ].…”

Section: New Lomax Rayleigh Distributionmentioning

confidence: 99%

Application of the multiple dependent state sampling strategy to late adolescent suicide rates

Kolli,

Rosaiah,

Rao

et al. 2023

BMC Med Res Methodol

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A multiple dependent state sampling plan (MDSSP) is designed when the lifetimes of the variables follow New Lomax Rayleigh Distribution (NLRD). The decision to accept or reject a lot in the proposed methodology is based on the quality of the given present or previous lots. A binomial model-based operating characteristic curve (OC curve) for continuous lots of variables under similar settings in healthcare is used in finding the probability of acceptance, acceptance number, rejection number, and the number of preceding (succeeding) lots to consider. Time truncated life test based on the specified median of the NLRD is used in designing the current acceptance sampling plan. For specified values of the parameters of NLRD, quantile ratios, consumer’s risk and producer’s risk, average sampling number (ASN) and probability of acceptance of a lot are reported in tables. Real data on worldwide suicide rates of 15–19 years in the year 2019 from the World Health Organization (WHO) website is considered to illustrate this methodology. The minimum sample size required from the selected data to comment on worldwide suicide rates in late adolescents is explained with MDSSP. The results of the proposed acceptance sampling method are compared with the single-stage sampling plan.

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Estimation methods for the probability density function and the cumulative distribution function of the Pareto-Rayleigh distribution

Cited by 10 publications

References 10 publications

Field study on the severity of photovoltaic potential induced degradation

Field study on the severity of photovoltaic potential induced degradation

Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process

Application of the multiple dependent state sampling strategy to late adolescent suicide rates

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