Analysis of <inline-formula><math display="inline"><semantics><mrow><mo mathvariant="bold">ℝ</mo><mo mathvariant="bold">=</mo><mi mathvariant="bold-italic">P</mi><mo stretchy="false">[</mo><mi mathvariant="bold-italic">Y</mi><mo mathvariant="bold"><</mo><mi mathvariant="bold-italic">X</mi><mo mathvariant="bold"><</mo><mi mathvariant="bold-italic">Z</mi><mo stretchy="false" mathvariant="bold">]</mo></mrow></semantics></math></inline-formula> Using Ranked Set Sampling for a Generalized Inverse Exponential Model

Abstract

In many real-world situations, systems frequently fail due to demanding operating conditions. In particular, when systems reach their lowest, highest, or both extremes operating conditions, they usually fail to accomplish their intended functions. This study considers estimating the stress–strength reliability, for a component with a strength (X) that is independent of the opposing lower bound stress (Y) and upper bound stress (Z). We assumed that the strength and stress random variables followed a generalized inverse exponential distribution with different shape parameters. Under ranked set sampling (RSS) and simple random sampling (SRS) designs, we obtained four reliability estimators using the maximum likelihood method. The first and second reliability estimators were deduced when the sample data of the strength and stress distributions used the sample design (RSS/SRS). The third reliability estimator was determined when the sample data for Y and Z were received from the RSS and the sample data for X were taken from the SRS. The fourth reliability estimator was derived when the sample data of Y and Z were selected from the SRS, while the sample data of X were taken from the RSS. The accuracy of the suggested estimators was compared using a comprehensive computer simulation. Lastly, three real data sets were used to determine the reliability.

Keywords

• stress-strength model
• generalized inverse exponential distribution
• ranked set sample
• maximum likelihood method