Stress–Strength Reliability Estimation for Gamma Distributions in a Noisy System.

When assessing the reliability of a system or the viability of a material, it is necessary to consider the stress conditions of the operating system. Let <italic>X</italic> be the strength of the system and <italic>Y</italic> be the stress of the system caused by the environment. In a stress–strength model, the system’s reliability is defined as P(X>Y), and due to ignoring environmental shocks or human failure, it is usually overestimated. To underestimate reliability, we assume that when <italic>X</italic> goes to the environmental conditions, the system’s strength reduces to ZX, where <italic>Z</italic> is a random variable on (0,1). We propose a modified reliability model with Ru=P(ZX>Y) for the gamma distribution. In this model, stress <italic>Y</italic> and the scale mixture of the strength of the gamma distribution, ZX, are modeled as independent random variables. The proposed model is compared with the traditional model through a simulation study. Additionally, the asymptotic distribution is used to construct an asymptotic confidence interval for Ru. Finally, we use two real datasets to demonstrate the practical applicability of our proposed method. [ABSTRACT FROM AUTHOR]