Analysis of incorporating modified Weibull model fault detection rate function into software reliability modeling.

When software systems are introduced, they are typically deployed in field environments similar to those used during development and testing. However, these systems may also be used in various other locations with different environmental conditions, making it challenging to improve software reliability. Factors such as the specific operating environment and the location of bugs in the code contribute to this difficulty. In this paper, we propose a new software reliability model that accounts for the uncertainty of operating environments. We present the explicit closed-form mean value function solution for the proposed model. The model's goodness of fit is demonstrated by comparing it to the nonhomogeneous Poisson process (NHPP) model based on Weibull model, using four sets of failure data sets from software applications. The proposed model performs well under various estimation techniques, making it a versatile tool for practitioners and researchers alike. The proposed model outperforms other existing NHPP Weibull based in terms of fitting accuracy under two different methods of estimation and provides a more detailed and precise evaluation of software reliability. Additionally, sensitivity analysis shows that the parameters of the suggested distribution significantly impact the mean value function.

A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling.

In survival and stochastic lifespan modeling, numerous families of distributions are sometimes considered unnatural, unjustifiable theoretically, and occasionally superfluous. Here, a novel parsimonious survival model is developed using the Bilal distribution (BD) and the Kavya-Manoharan (KM) parsimonious transformation family. In addition to other analytical properties, the forms of probability density function (PDF) and behavior of the distributions' hazard rates are analyzed. The insights are theoretical as well as practical. Theoretically, we offer explicit equations for the single and product moments of order statistics from Kavya-Manoharan Bilal Distribution. Practically, maximum likelihood (ML) technique, which is based on simple random sampling (SRS) and ranked set sampling (RSS) sample schemes, is employed to estimate the parameters. Numerical simulations are used as the primary methodology to compare the various sampling techniques.

Statistical inference for Nadarajah-Haghighi distribution under unified hybrid censored competing risks data.

Nadarajah and Haghighi distribution (NHD) inferences problem has been discussed under unified hybrid censoring scheme (UHCS) in the existence of competing risks model. Competing risks model is defined by time-to-failure under more than one cause of failure, which can be dependent or independent. This study focuses on discussing the case of failure partially observed causes of failure competing risks model. We obtain various inferences: we first obtain the MLE, in addition, we construct approximate confidence intervals (ACIs). Second, we obtain the Bayes estimator via SELF and related highest posterior density (HPD) using Markov Chain Monte Carlo (MCMC). Finally, an electrical appliances data set and simulation studies have been analyzed for further illustrations.

Statistical inference with joint progressive censoring for two populations using power Rayleigh lifetime distribution.

In this study, point and interval estimations for the power Rayleigh distribution are derived using the joint progressive type-II censoring technique. The maximum likelihood and Bayes methods are used to estimate the two distributional parameters. The estimators' approximate credible intervals and confidence intervals have also been determined. The Markov chain Monte Carlo (MCMC) method is used to provide the findings of Bayes estimators for squared error loss and linear exponential loss functions. The Metropolis-Hasting technique uses Gibbs to generate MCMC samples from the posterior density functions. A real data set is used to show off the suggested approaches. Finally, in order to compare the results of various approaches, a simulation study is performed.

A new versatile modification of the Rayleigh distribution for modeling COVID-19 mortality rates.

The aim of this paper is to specify a new flexible statistical model to analyze COVID-19 mortality rates in Italy and Canada. A new versatile lifetime distribution with four parameters is proposed by using the exponentiated generalized class of distributions and the gull alpha power Rayleigh distribution to form the exponentiated generalized gull alpha power Rayleigh (EGGAPR) distribution. This new distribution is characterized by a tractable cumulative distribution function. To estimate the unknown parameters of the proposed distribution the maximum likelihood estimation method is used. In evaluating the effectiveness of the MLE method graphical displays of the Monte Carlo simulation are presented. The EGGAPR distribution is compared to its sub-models which include the exponentiated gull alpha Rayleigh distribution, the gull alpha Rayleigh distribution, exponentiated generalized Rayleigh distribution, exponentiated Rayleigh distribution and the Rayleigh distribution. Different measures of goodness-of-fit are used to investigate whether the EGGAPR distribution is more flexible and fit than its sub-models in modeling COVID-19 mortality rates.