Journal of Reliability and Statistical Studies

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

2026-03-06T19:37:36+01:00

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

2026-02-07T06:48:28+01:00

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

2026-03-28T07:24:18+01:00

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

2026-05-12T14:19:32+02:00

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.