In this paper, we study the stress–strength reliability of a failure profile in which, the components of the system are affected by the internal environmental factors. The internal environmental factors commonly change the random strength of a failure profile and have different effects on the random strength of profile components. Throughout this study, we investigated the effect of internal environmental factors under the various scenarios and computed the stress–strength reliability of a failure profile of order [Formula: see text]. Particularly, the stress–strength reliability of a [Formula: see text]-out-of-[Formula: see text] system has been evaluated based on several stochastic orders. In addition, the sensitivity analysis of the stress–strength reliability and the mean cost rate of failure profiles have been performed in the exponential model.
In this paper, the system reliability in a stress–strength model, when the distributions of the stress and the strength random variables are replaced by two distorted distributions, is considered. The conditions to increase the reliability under several distortion functions are studied. Furthermore, the changes in the residual stress–strength reliability, the mean remaining strength and the number of working components of a system are investigated when the original distributions have been affected by distortion functions. Some of the previous results in the literatures can be achieved as special cases of our results.
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