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AbstractThe line transect survey method is commonly used to estimate the population size. However, recent developments in this field have tended to prefer practical mathematical models for this purpose. In this study, a new model called the weighted Weibull detection model was introduced to specifically address certain criteria related to line transect data. This study thoroughly explored the characteristics of this new model, including its shapes, moments, and probability density functions. The maximum likelihood estimation and Bayesian estimation methods were employed to ensure accurate parameter estimation. To gauge the performance of this model, population size estimates were generated and compared with various existing parametric estimation methods that are commonly used in the field. Through simulations, the resulting estimates were assessed and compared to widely adopted approaches for estimating population size. Additionally, this mathematical model was applied to real-world data involving perpendicular distances, allowing for a direct comparison of its performance against both traditional and contemporary methods using various measures of goodness of fit. Moreover, the study calculates statistical metrics, such as the variance–covariance matrix, parameter confidence intervals, and estimated population size, were obtained using the proposed detection model. These metrics provide valuable insights into the precision and uncertainty associated with estimated parameters and population size estimates. Confidence intervals offer a range of plausible parameter values, whereas the variance–covariance matrix quantifies the relationships and uncertainties between the estimated parameters.

AbstractThis study focuses on implementing a group acceptance sampling plan (GASP) for simultaneous inspection of objects with complex lifespan patterns described by the odd exponential logarithmic (OEL) Fréchet distribution. The inspiration from the proposed model stems from the challenges posed by the objects that exhibited right-skewed, j-shaped, reversed j-shaped and nearly symmetric densities, along with decreasing and increasing hazard rates. A mathematical function is derived to identify key points in the distribution, crucial for designing the inspection process based on factors like testing duration and acceptable risk levels. Performance is assessed across various quality levels, with a simulation study providing insights into parameter changes. The results are clarified via visual representations. The minimum ratios of actual to expected lifespan at specific risk levels, utilizing real-world data to validate the approach are computed. Finally, a comparison is driven in the quest of highlighting the efficacy and versatility of the proposed acceptance sampling plan (ASP) under the inverse log-logistic and generalized exponential (GE) models.

AbstractBackground The exhaustive information about non-communicable diseases associated with COVID-19 and severe acute respiratory syndrome corona virus-2 (SARS-CoV-2) are getting easier to find in the literature. However, there is a lack of knowledge regarding tuberculosis (TB) and chronic obstructed pulmonary disease (COPD), with numerous infections in COVID-19 patients.Objectives Priority is placed on determining the patient’s prognosis based on the presence or absence of TB and COPD. Additionally, a comparison is made between the risk of death and the likelihood of recovery in terms of time in COVID-19 patients who have either COPD or TB.Methodology At the DHQ Hospital in Muzaffargarh, Punjab, Pakistan, 498 COVID-19 patients with TB and COPD were studied retrospectively. The duration of study started in February 2022 and concluded in August 2022. The Kaplan–Meier curves described time-to-death and time-to-recovery stratified by TB and COPD status. The Wilcoxon test compared the survival rates of people with TB and COPD in two matched paired groups and their status differences with their standard of living.Results The risk of death in COVID-19 patients with TB was 1.476 times higher than in those without (95% CI: 0.949–2.295). The recovery risk in COVID-19 patients with TB was 0.677 times lower than in those without (95% CI: 0.436–1.054). Similarly, patients with TB had a significantly shorter time to death (p=.001) and longer time to recovery (p=.001).Conclusions According to the findings, the most significant contributor to an increased risk of morbidity and mortality in TB and COPD patients was the COVID-19.KEY MESSAGESSARS-Cov-19 is a new challenge for the universe in terms of prevention and treatment for people with tuberculosis and chronic obstructive pulmonary disease, among other diseases.Propensity score matching to control for potential biases.Compared to hospitalized patients with and without (TB and COPD) had an equivalently higher mortality rate.

AbstractIn this paper, we propose a tractable Kumaraswamy Bell exponential (KwBE) distribution as a submodel of the Kumaraswamy Bell-G family of distributions. Several well-established properties are obtained for the KwBE distribution, such as the linear functional representation, [Formula: see text]th moment, incomplete moment, moment generating function using Wright generalized hyper-geometric function, conditional moment and Réyni entropy. Based on the KwBE model, a group acceptance sampling plan (GASP) for the truncated life test is presented using median life as a quality index. Moreover, the essential design parameters are derived by defining the consumer risk and the test termination duration. The comparative study of GASP with ordinary sampling plan (OSP) is performed. A simulation study is performed to highlight the behavior of the estimates. On the inferential side, the associated parameters are estimated using a well-established maximum likelihood estimation method. The detailed model’s comparison analysis, graphical as well as numerical evidence to real-data applications, supports the theoretical work.

AbstractIn this study, we presented a group acceptance sampling plan for situations in which the lifetime of an item followed a flexible new Kumaraswamy exponential distribution for applications to quality control reliability. This study includes a detailed analysis of the operating characteristic function values, producer risk, and minimum required group size for the acceptance number, which are determined by three shape parameters. To determine the quality index, we used the median and tested various parametric values to obtain the optimized values. These optimized values are presented in the tables and graphically for a better understanding. In addition, we explain the results of our study using two real-life datasets and an example. Comparison has been also made between GASP and OSP.

AbstractIn the present study, a group-acceptance sampling plan was presented when the lifetime of an item followed an alpha power transformation-inverted perks distribution. The median is used as a quality index to attain design parameters, such as the acceptance number and minimum group size, which are determined when the test termination and consumer risk are specified. The operating characteristic values are presented both graphically and in the form of tables. Two real-life datasets are used as examples to illustrate the tables.

Abstract Background Accessibility to the immense collection of studies on noncommunicable diseases related to coronavirus disease of 2019 (COVID‐19) and severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) is an immediate focus of researchers. However, there is a scarcity of information about chronic obstructed pulmonary disease (COPD), which is associated with a high rate of infection in COVID‐19 patients. Moreover, by combining the effects of the SARS‐CoV‐2 on COPD patients, we may be able to overcome formidable obstacles factors, and diagnosis influencers. Materials and Methods A retrospective study of 280 patients was conducted at DHQ Hospital Muzaffargarh in Punjab, Pakistan. Negative binomial regression describes the risk of fixed successive variables. The association is described by the Cox proportional hazard model and the model coefficient is determined through log‐likelihood observation. Patients with COPD had their survival and mortality plotted on Kaplan–Meier curves. Results The increased risk of death in COPD patients was due to the effects of variables such as cough, lower respiratory tract infection (LRTI), tuberculosis (TB), and body‐aches being 1.369, 0.693, 0.170, and 0.217 times higher at (95% confidence interval [CI]: 0.747–1.992), (95% CI: 0.231–1.156), (95% CI: 0.008–0.332), and (95% CI: −0.07 to 0.440) while it decreased 0.396 in normal condition. Conclusion We found that the symptoms of COPD (cough, LRTI, TB, and bodyaches) are statistically significant in patients who were most infected by SARS‐CoV‐2.

In the present study, the group acceptance plan is examined when the lifetime of an item follows the odd Perks exponential distribution, and a large number of items regarded as a group are evaluated simultaneously. The crucial parameters are derived from the consumer risk and the test termination period. The operating characteristics function values are generated for various quality levels. An optimized group acceptance plan and comparison of group acceptance sampling plan with the ordinary sampling plan are also presented. Additionally, a graphical illustration of operating characteristics for diverse groups and parametric values is provided. The minimum ratios of the actual average life to the stipulated average life are likewise computed at the prescribed producer’s risk. Examples are used to illustrate the outcomes via our algorithm under the odd Perks exponential distribution setting. It is explained using a quality control dataset to establish its practical versatility.

The generalized viscosity implicit rules of nonexpansive asymptotically mappings in Hilbert spaces are considered. The strong convergence theorems of the rules are proved under certain assumptions imposed on the sequences of parameters. An application of it in the convex minimization problem is considered. The results presented in this paper improve and extend some recent corresponding results in the literature.

Let E be a 2 uniformly smooth and convex real Banach space and let a mapping A: E → E∗ be lipschitz and strongly monotone such that A−1(0)≠∅. For an arbitrary ({x1}, {y1})∈E, we define the sequences {xn} and {yn} by yn = xn − θnJ−1(Axn), n≥1 xn+1 = yn − λnJ−1(Ayn), n≥1 where λn and θn are positive real number and J is the duality mapping of E. Letting (λn, θn)∈(0, 1), then xn and yn converges strongly to ρ∗, a unique solution of the equation Ax = 0. We also applied our algorithm in convex minimization and also proved the convergence of it in Lp, lp or Wm,p. At the end we proposed the algorithm of it in Lp(Ω) and its inverse Lq(Ω).