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The purpose of this paper is to evaluate the reliability indices such as reliability, mean time to failure and sensitivity analysis.

A non-repairable multi-state complex system with two subsystems, namely, S₁ and S₂, is studied. The subsystems S₁ and S₂ are multi-state weighted r-out-of-n: G and s-out-of-m: G systems, respectively. Every component of the sub-system S₁ consists of linear (f, l, k): G system, and the sub-system S₂ consists of circular (f, l, k): G system. The subsystems are connected in series arrangement and components of these subsystems are arranged in parallel.

Markov stochastic process has been applied to obtain probability of components of the subsystems and various results discuss such as reliability, mean time to failure and sensitivity analysis with the help of the universal generating function.

In this work, reliability measures of the purpose system can be enhanced under the high profit.

To find the reliability characteristics of repairable weighted (u, v)- out-of-(x, y) system using the interval valued universal generating function (IUGF).

In this paper (u, v)-out-of-(x, y) system is an extension of the k-out-of-n system. Here, the interval valued universal generating function (UGF) is present and the corresponding operators are defined.

The present paper proposes a interval valued universal generating function (IUGF) to compute the reliability indices of the considered system. The current study investigates the reliability and sensitivity of the proposed system with respect to system parameters by applying Markov process with the help of the interval valued UGF approach.

In this work, the considered system, i.e. repairable weighted (u, v)-of-the- (x, y) is the extension of k-out-of-n system for the assessment of reliability characteristics using the interval valued UGF.