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M. Tirumala Devi ¹, T. S. Uma Maheswari ², K. Sandhya ¹, N. Swathi ¹

Affiliations
1 Department of Mathematics, Kakatiya University, A.P., IN
2 Kakatiya University, A.P., IN

Abstract

Failure of a system may occur due to certain type of stresses or loading acting on the system. If these stresses does not exceed a certain threshold value (minimum strength k) the system may work for a long period. On the other hand, if the stresses exceed the threshold they may fail within no time. For this reason pareto distribution can be used to find the reliability for stress-strength model and cascade redundancy system. Comparison with five different distributions (Geometric, Weibull, Rayleigh, Pareto, and Lognormal) pareto distribution is the best fit in the context of system reliability. Pareto distribution is used for decreasing hazard model. In this paper the reliability has been derived for cascade redundancy stress-strength system when stress and strength follow pareto distribution of the first kind. It is observed by the computations that if k_i* = 1 then the reliability for n-cascade system when stress and strength follow pareto distribution of the first kind is same as the reliability for exponential distribution even though the means are not same for these distributions.

Keywords

Cascade Redundancy System, Pareto Distribution, Reliability, Stress-Strength Model.

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N. Swathi ¹, T. Sumathi Uma Maheswari ², M. Tirumala Devi ²

Affiliations
1 Department of Mathematics, Kakatiya University, A.P., IN
2 Department of Mathematics, Kakatiya University, A.P., IN

Abstract

In certain situations and with certain types of equipments time-to-failure may not be quantity of interest. The systems may work practically for an infinite period of time if all the factors are within the prescribed tolerances. Their failure occurs due to certain types of stresses acting on them. If these stresses do not exceed a certain threshold value, they may work for a very long period; If the stresses exceed the threshold, they fail in no time, these models are stress dependent models. Stress and strength are time varying in many real-life systems. In this article reliability analysis of time dependent stress strength system is carried out by considering each of stress variables are deterministic and strength variables are random independent and vice versa for deterministic and random cycles. In case1 if stress and strength follow Exponential and Rayleigh distributions, it is observed that, for deterministic cycles, strength parameter(μ) and number of cycles(n) increases, reliability value decreases and for random cycles parameter value(α) and time(t) increases reliability decreases and in case2 stress strength follow Exponential and Rayleigh distributions, no. of cycles(n) and parameter value(α) increases, Reliability decreases and stress parameter(λ) and strength (y₀) increases Reliability increases. It is also observed from the computations that deterministic model is more reliable than Random model.

Keywords

Deterministic Model, Exponential Distribution, Rayleigh Distribution, Random Cycle, Stress-Strength Model.

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