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We consider a parallel-connected configuration comprised of multiple k-out-of-m load sharing subsystems, employing proportional conditional failure rates and the unequal load-sharing principle to model component failures. Our study focuses on estimating load sharing parameters using censored Type-I and Type-II failure data, considering both Exponential and Weibull baseline distributions. We examine two scenarios: n parallel subsystems with a 1-out-of-2 setup and with a 2-out-of-4 setup. The accuracy of parameter estimation methods is evaluated through simulation studies and validated using a real-world dataset. This approach is adaptable to configurations with varied load sharing setups, including those in series or a p-outof-q steup

KEYWORDS: k-out-of-m system, Load sharing system, Order statistics, Proportional conditional failure rate, Reliability modeling, Type-I and Type-II censoring.

Acceptance sampling plans are essential in industries like manufacturing as they aid in making decisions on whether to accept or reject a lot, depending on samples of the population. The reliability single sampling plan is typically used for estimating time characteristics and optimizing sample size when reliability is a critical quality factor. This article implements a reliability sampling plan using the implementation of bivariate Poisson distribution and lifetime distribution. In appropriate circum-stances, the bivariate Poisson distribution may be utilized as a basis for identifying items with defects, and lifetime distributions will be used to determine the defec-
tiveness. In the case of consumer risk, the minimum sample size is needed to attain the specified life percentile. An acceptable lot's expected percentile time and operat-ing characteristic values are given. Thus, this paper is concerned with developing a new structure and modus operandi for estimating percentiles using bivariate Poisson distribution with its application in one-shot syringes data quality management.

KEYWORDS: Bivariate Poisson distribution; minimum sample size; operating characteristic function; producers risk; consumers risk; percentile time.

This work presents a novel group of univariate distributions formed by integrating the Marshall-Olkin and the Topp-Leone Nadarajah-Haghighi G families. This new family, designed to enhance  exibility and applicability in data analysis, exhibits unique structural properties that make it suitable for various statistical applications. We discuss three notable members of the proposed family, each demonstrating dis-tinct characteristics and potential use cases with a special case identified within the family. When considering submodels, the densities, as well as hazard rate plots, re-veal a range of shapes, showcasing the versatility of the proposed family. A thorough analysis of certain structural characteristics is carried out. Additionally, a charac-terization derived from truncated moments is presented. Estimating parameters is conducted through maximum likelihood estimation and the ecacy of the same is evidenced through extensive simulation studies. Subsequently, with a specific family member already identied (the baseline distribution being the exponential distribu- tion), a comprehensive analysis has been conducted to apply this novel model using real-life data. Compared to other leading competing models, the new model excels in all evaluated statistical criteria and tests.

KEYWORDS: Data analysis; Marshall-Olkin transformation; Marshall-Olkin Nadarajah-Haghighi Topp-Leone-G family; Maximum likelihood method; Nadarajah-Haghighi distribution; Nadarajah-Haghighi Topp-Leone-G family

In this paper, we consider an extended version of the exponential Poisson distribution and examine its theoretical properties. We derive expressions for the cumulative distribution function, survival function, failure rate function, pdf of the order statistics and raw moments. We also discuss the maximum likelihood estimation procedures and the Expectation-Maximization algorithm for estimating the parameters of this distribution. Additionally, a statistical test is proposed to assess the significance of the additional parameter introduced in the model. To demonstrate its practical utility, we provide certain real-life data applications. Furthermore, with the help of simulated datasets, it is shown that as the sample size increases, the average bias and mean squared errors of the maximum likelihood estimators decrease in a consistent manner.

KEYWORDS: EM algorithm; Gamma distribution; Maximum likelihood estimation; Poisson distribution

In this article, we consider a new class of bimodal symmetric distributions and study some of its important statistical properties. The estimation of parameter is attempted and illustrated with the help of certain real life data sets. A simulation study is carried out to examine the performance of the estimator of parameter of the distribution.

KEYWORDS: Bimodal distribution; Maximum likelihood estimation; Model selection; Simulation.

The Power Generalized DUS transformation provides improved  exibility when deal-ing with lifetime and reliability data. It provides parsimonious model and is a pow-erful tool for statistical modeling and analysis of a parallel system or maximum random variable. The empirical success and adaptability of the PGDUS transforma-tion further highlight its value in diverse applications. The Power Generalized DUS powered inverse Rayleigh distribution (PGDUS-PIR) is a new distribution that we introduced in this paper and that was derived by using the PGDUS transforma-tion on a baseline distribution, the powered inverse Rayleigh (PIR) distribution. Its statistical features are discussed in detail. The unknown parameters are estimated using the maximum likelihood method and the maximum product spacing method. To better understand the behavior and applicability of the PGDUS-PIR distribu-tion, a simulation study was carried out, which led to more accurate and reliable statistical modeling and analysis. Two sets of real data are used to compare the per-formance of the proposed distribution with some distributions that are currently in use. Stress-strength reliability is an essential aspect of lifetime data analysis, provid-ing a systematic approach to evaluate the reliability and durability of components
and systems under varying stresses. This concept is essential to ensure the safety, quality and durability of products in many industries. We derived the single- and multicomponent stress-strength reliability of the PGDUS-PIR (; ; ) distribution.

KEYWORDS: Powered inverse Rayleigh distribution; PGDUS transformation; Maximum likelihood estimation; Maximum Product Spacing estimation; Stress-Strength Reliability.