An Efficient Stress–Strength Reliability Estimate of the Unit Gompertz Distribution Using Ranked Set Sampling

Abstract

In this paper, the estimation of the stress–strength reliability is taken into account when the stress and strength variables have unit Gompertz distributions with a similar scale parameter. The consideration of the unit Gompertz distribution in this context is because of its intriguing symmetric and asymmetric properties that can accommodate various histogram proportional-type data shapes. As the main contribution, the reliability estimate is determined via seven frequentist techniques using the ranked set sampling (RSS) and simple random sampling (SRS). The proposed methods are the maximum likelihood, least squares, weighted least squares, maximum product spacing, Cramér–von Mises, Anderson–Darling, and right tail Anderson–Darling methods. We perform a simulation work to evaluate the effectiveness of the recommended RSS-based estimates by using accuracy metrics. We draw the conclusion that the reliability estimates in the maximum product spacing approach have the lowest value compared to other approaches. In addition, we note that the RSS-based estimates are superior to those obtained by a comparable SRS approach. Additional results are obtained using two genuine data sets that reflect the survival periods of head and neck cancer patients.

Statistical analysis of the inverse power Zeghdoudi model: Estimation, simulation and modeling to engineering and environmental data

“…Two real data sets and comparisons with different distributions are used to graphically explain and display how effective the suggested distribution is for modeling data. Future studies will take into account an estimation of the IPZD's stress-strength reliability model [41][42][43][44].…”

Comparison of Estimation Methods for Reliability Function for Family of Inverse Exponentiated Distributions under New Loss Function

“…In a related study, Kumari et al [4] examined a single-component stress-strength model for this family of distributions. Similar works with respect to the stress and strength variables could also refer to some of the contributions by Temraz [5], de la Cruz et al [6], Alsadat et al [7], and EL-Sagheer et al [8]. Jamal et al [9] studied the type II general inverse exponential family of distributions.…”

Stress–Strength Reliability Analysis for Different Distributions Using Progressive Type-II Censoring with Binomial Removal

“…Numerous studies on the S-S model using complete and censored samples have been conducted by [2][3][4][5][6][7][8][9][10][11][12] and others. Some recent studies concerning SS models can be found in [13][14][15][16][17][18][19].…”