Journal of Reliability and Statistical Studies

Stress and Strength Reliability Estimation for the Inverse Family of Distributions using Bayesian Analysis

Kuldeep Singh Chauhan — 2026-04-28

A Bayesian model to study stress-strength reliability P=P(Y<X), which makes use of parameters in the family of the inverse distributions. For the reliability function and for the stress-strength parameter, Bayes estimators are obtained under SELF and GELF. When this is appropriate, conjugate priors will be introduced into estimators, which will be constituted using different powers of the unknown parameters. Performance of these estimators is determined by a simulation-based methodology and large numbers of bootstrap replications. The findings show that, especially in small-sample circumstances, the Bayesian estimators based on SELF perform better than those based on GELF. The performance difference closes as the sample sizes grow. The exploration of this paper displays that the inverse family can be altered for several common distributions, which have more significant practical implications when analyzing reliability.

On Complete Diallel Cross Plans

Maengseok Noh — 2026-06-16

A diallel cross is a pairing strategy commonly employed by animal husbandry scientists and botanists to explore the genetic interactions and inheritance patterns among a set of l inbred lines. A commonly used diallel cross design is a complete diallel cross (CDC) plan where each line is crossed with the remaining (l−1) distinct lines, resulting in l(l−1)/2 number of crosses in the entire design.

In this investigation, we present a method for constructing complete diallel cross schemes based on balanced incomplete block design (BIBD) of series t=b=l,r=k=l−1, and λ=l−2. Here, crosses are made in such a way that one line will cross with other line within a block. Two methods viz, (i) binary complete diallel cross plan and (ii) non-binary CDC plans are developed from the same series of BIBD to suggest which plans should be accepted by the breeder for their experiment. The construction of CDC plan is demonstrated though appropriate examples. We compute the efficiency of the CDC plan and compare it with randomized complete block design. It is shown that the constructed CDC plan is universally optimal. Robustness of CDC plan is examined in relation to the loss of one block.

A Quasi Poisson-Rama Distribution with Properties and Applications

Rama Shanker — 2026-06-16

A quasi Poisson-Rama distribution has been introduced which is the Poisson compound of quasi Rama distribution. The moments based descriptive properties have been discussed. The proposed distribution is unimodal, has increasing hazard rate and over-dispersed. The estimation of parameters has been studied using the method of moments and the method of maximum likelihood. A simulation study has been done to test the performance of maximum likelihood estimators of parameters. Finally, the goodness of fit of the proposed distribution has been discussed with two discrete datasets, the first from biological sciences and the second from thunderstorms and compared with the goodness of fit of Poisson-Lindley distribution, Poisson-Akash distribution, Poisson-Sujatha distribution, Poisson-Rama distribution, quasi Poisson-Lindley distribution, quasi Poisson-Akash distribution and quasi Poisson-Sujatha distribution.

Improving Finite Population Mean through Ranked Sets

Poonam Singh — 2026-06-16

In the field of sampling theory, simple random sampling (SRS) has been widely used and proven to be effective for drawing samples to estimate population parameters. However, in certain situations, obtaining observations on the study variable is more challenging than ranking the units. In such cases, ranked set sampling (RSS) becomes very useful in the estimation of population parameters. We offer two new estimators under RSS to estimate the finite population mean out of which one estimator is equivalent to the many estimators existing in the literature, Therefore it can be used as the alternatives to the existing ones while the other one performs better than the recent estimator Khalid et al., (2024) in terms of mean squared error (MSE) and percentage relative efficiency (PRE), under RSS framework. Among the two proposed estimators, One of these estimators combines log and exponential, while the other combines regression and exponential.We found that second estimator turns out to be most efficient among the estimators studied in this study under RSS. The MSE and PRE are employed to evaluate the performance of the proposed estimators in comparison with traditional estimators discussed in this study. Analytical expressions for the MSE and bias are derived, along with the conditions under the proposed estimators demonstrate improved efficiency. To substantiate the theoretical findings, both empirical and simulation studies are conducted. The results indicate that the proposed estimators provide better performance compared to traditional estimators.

On a Flexible Three-Parameter Lifetime Model: Theoretical Properties and Real-Data Applications

Aafaq A. Rather — 2026-07-02

This paper introduces a new three-parameter lifetime model, called the Sujatha Power Series (SPS) distribution, motivated by the need for more flexible distributions in reliability and survival analysis. The model is constructed by compounding the Sujatha distribution with a family of power-series distributions, allowing it to accommodate various density and hazard rate shapes, including the important bathtub form. Key distributional properties are derived, and parameter estimation is performed using maximum likelihood methods. The practical performance of the SPS distribution is demonstrated through applications to two real lifetime datasets and comparisons with established competing models. The results indicate that the proposed model provides superior or comparable fits, highlighting its usefulness as an effective and flexible tool for modeling lifetime data in reliability and survival studies.

Statistical Inference for Harmonic New Better Than Renewal Used in Expectation Class of Life Distributions Under Random Progressive Censoring

Gamal R. Elkahlout — 2026-07-21

This paper extends the theoretical framework and testing methodology for the Harmonic New Better (or Worse) than Renewal Used in Expectation classes of life distributions. We revisit and refine empirical test statistics under random censoring, incorporating progressive Type II censoring schemes to enhance applicability. Modern lifetime distributions, including Lognormal, Gumbel, and Weibull models, are incorporated into the power analysis, with results strengthened through Monte Carlo simulations, bootstrap confidence intervals, and variance estimates. The findings highlight the robustness and practical value of the proposed methods, particularly in small-sample scenarios, and provide guidance for implementation through readily available software tools.

Comparing Classical and Sequential Parameter Estimation in Power Rayleigh Distribution

Prem Lata Gautam — 2026-07-21

This study explores the novel application of the performance characteristics of sequential probability ratio test (SPRT) for estimation the scale parameter (θ) of the power Rayleigh distribution, focusing on its scale parameters (θ) that are the fundamental to defining its properties and shaping the statistical characteristics. For testing the null hypothesis H₀:θ=θ₀ versus H₁:θ=θ₁, a stop rule method is utilized to optimize the sample size. Through this approach, we derive approximations for key performances metrics, including the operating characteristic (OC) function and the average sample number (ASN). The study also confirms the existence of the function L(θ), necessary to meet the ASN requirements in sequential testing. The new method is comprised of the efficiency of the SPRT compared to the classical Neyman-Pearson (N-P) technique. A comprehensive simulation study shows that the proposed method of SPRT significantly reduces the sample size required for the hypothesis testing by 65.99% to 77.49% compared to the Neyman-Pearson (N-P) test without compromising accuracy.

A Novel Neutrosophic Fuzzy Approach for Stress-Strength Reliability Analysis of Ailamujia Distributions Under Parameter Uncertainty

Naser Ahmad Odat — 2026-08-07

In this study, a hybrid framework is proposed that combines fuzzy logic with neutrosophic statistics to deal with the issue of parameter uncertainty in stress-strength reliability analysis of systems that are governed by the Ailamujia distribution. The proposed framework is an extension of the conventional binary reliability model in that it incorporates a fuzzy reliability concept that considers the degree of exceedance of strength over stress rather than the conventional binary concept of exceedance/non-exceedance. To deal with the indeterminate scale parameters that arise in practice, the proposed framework is extended to a neutrosophic framework to arrive at interval estimates of reliability that reflect the imprecise nature of real-world problems. The objectives of this study are to arrive at the fuzzy reliability model, extend it to a neutrosophic framework, and finally examine the performance of the proposed framework through extensive simulation studies. Additionally, the practicality of the proposed model is also examined through a case study of component reliability in mechanical systems.

The Unit Omega Distribution as an Alternative to the Beta Distribution for the Modeling to the Infrared Thermography Temperature Data

Alia A. Alkhathami — 2026-08-07

Proportion data is significant in many disciplines, including as economics, finance, reliability engineering, medicine, biology, and chemistry, since it serves as the basis for identifying trends, expediting procedures, and making well-informed conclusions that result in advances and innovations. For the representation and analysis of proportional data, the beta distribution is a standard model. In this paper, we explore the unit omega distribution [15] and their ordered properties such as the exact expressions, as well as recurrence relations, for the single moments of the order statistics (OSs) and record values. Additionally, various L-moment characteristics based on OS moments and record values were analyzed. The applicability of the unit omega distribution over beta distribution was demonstrated through its successful fit to the original IRT temperature dataset. For comparative assessment, the performance of the unit omega distribution was evaluated against the commonly used beta distribution using the Kolmogorov–Smirnov (KS) goodness-of-fit test. The results indicate that the unit omega distribution yields a smaller KS test statistic and a larger associated p-value compared to the Beta distribution, suggesting a superior fit to the observed data. These findings highlight the flexibility and effectiveness of the unit omega distribution in modelling bounded data. Furthermore, the study provides a strong foundation for future research, particularly in extending the analysis to generalized order statistics and progressive censoring schemes associated with the unit omega distribution.

AI and Telemedicine in Elderly Healthcare: A Statistical Analysis

S. Srinivasan — 2026-08-07

The manuscript examines the role of Artificial Intelligence (AI) and telemedicine in Improving healthcare access and services for older adults. The study focuses on digital consultations and early diagnosis and employs a descriptive research design. Data were collected from 120 older adults in rural and urban areas of Dehradun, Uttarakhand. The analysis uses statistical techniques including descriptive statistics, regression analysis, ANOVA, and chi-square tests through SPSS to evaluate telemedicine usage, challenges, and satisfaction levels among older adults.

In-Between Landscape Transformations and Tourism Development: Investigating Latent Trends in Long-term Wildfires’ Patterns, Greece (1955–2024)

Ioannis Konaxis — 2026-08-07

Global environmental change has increasingly reshaped wildfire dynamics resulting in heightened ecological and socioeconomic risks worldwide. While fire suppression and technical prevention remain central to wildfire and landscape management, broader land-use and governance frameworks are recognized as influential determinants of fire impacts at landscape scales. The present study investigates a long-time series (1955–2024) of wildfire basic indicators (burnt area, fire density, average fire size) with the final aim at deriving latent information clarifying change processes associated with climatic stressors, land-use change, and rapidly evolving socioeconomic conditions in Greece, a Mediterranean country with specific land-use trajectories, social dynamics, economic performances, and governance-related factors. Using an empirical approach based on multivariate statistics, this study evaluates the relative contribution of temporal variability in wildfire pattern as an indirect reflection of anthropogenic pressure. In this perspective, insights from existing literature and field-based observations are integrated to support interpretation of the quantitative results based on official statistics and landscape analysis. Wildfire risk seems to grow in the recent decades, both for fire size and frequency. These results underscore the relevance of integrated landscape management policies safeguarding agroforestry systems, and cross-sectoral measures fostering resilient and functional Mediterranean landscapes.

Applied Statistical Modelling and Reliability Assessment of Digital Transformation Effects on Sustainable Business Model Performance: Panel Data Evidence from China’s Manufacturing Sector

Jiao Zhe — 2026-08-07

This paper examines how digital transformation affects sustainable business model performance in Chinese listed manufacturing firms from 2019 to 2023. A composite measurement system is built for digital maturity, green business practices, green finance, and sustainable performance. Reliability testing, descriptive statistics, Pearson correlations, two-way fixed-effects panel regression, robustness checks, mediation and moderation models, Sobel and Bootstrap tests, and structural equation modelling are jointly employed. The results show a positive association between digital transformation and sustainable business model performance (β=0.369, p < 0.01). Green business practices partially mediate this relationship and explain 30.89% of the total effect, while green financial support strengthens the link (interaction β=0.087, p < 0.05). The findings provide statistically reliable evidence that digital capability, green operations, and external finance jointly improve sustainable business outcomes.