Abstract
Linear and circular consecutive models play a vital role to study the mechanical systems emerging in various fields including survival analysis, reliability theory, biological disciplines, and other lifetime sciences. As a result, analysis of reliability properties of consecutive k − out − of − n : F systems has gained a lot of attention in recent years from a theoretical and practical point of view. In the present article, we have studied some important stochastic and aging properties of residual lifetime of consecutive k − out − of − n : F systems under the condition n − k + 1, k ≤ n and all components of the system are working at time t. The mean residual lifetime (MRL) and its hazard rate function are proposed for the linear consecutive k − out − of − n : F (lin/con/k/n:F) and circular consecutive k − out − of − n : F (cir/con/k/n:F) systems. Furthermore, several mathematical properties of the proposed MRL are examined. Finally, the Weibull distribution with two parameters is used as an example to explain the theoretical results.
Highlights
Introduction and methodologyIn a dynamic era today, from the perspective of developers and consumers, it is important for engineering systems such as computers, automobiles, airplanes, etc. to be highly reliable
We found that the reliability function of any coherent system can be expressed as a linear combination with non-negative coefficients of the reliability functions of k − out − of − n : F systems, implying that the coherent system is a mixture of k − out − of − n : F systems
We have addressed consecutive k − out − of − n : F systems which are a special class of coherent systems
Summary
Introduction and methodologyIn a dynamic era today, from the perspective of developers and consumers, it is important for engineering systems such as computers, automobiles, airplanes, etc. to be highly reliable. Investigated the failure distributions of these consecutive systems under independent and identical components. For the lifetime of these consecutive systems, Boland and Samaniego (2004) gave some stochastic ordering results by assuming that the components of the system are independent and identical.
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