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The notion of signature has been widely applied for the reliability evaluation of technical systems that consist of binary components. Multi‐state system modeling is also widely used for representing real life engineering systems whose components can have different performance levels. In this article, the concept of survival signature is generalized to a certain class of unrepairable homogeneous multi‐state systems with multi‐state components. With such a generalization, a representation for the survival function of the time spent by a system in a specific state or above is obtained. The findings of the article are illustrated for multi‐state consecutive‐k‐out‐of‐n system which perform its task at three different performance levels. The generalization of the concept of survival signature to a multi‐state system with multiple types of components is also presented. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 593–599, 2017

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In this paper; survival (non-ruin) probability after a definite time period of an insurance company is studied in a discrete time model based on nonhomogenous claim occurrences. Furthermore, distributions of the minimum and maximum levels of surplus in compound binomial risk model with nonhomogeneous claim occurrences are obtained and some of its characteristics are given.

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SURVIVAL PROBABILITIES FOR COMPOUND BINOMIAL RISK MODEL WITH DISCRETE PHASE-TYPE CLAIMS ALTAN TUNCELAbstract. Due to having useful properties in approximating to the other distributions and mathematically tractable, phase type distributions are commonly used in actuarial risk theory. Claim occurrence time and individual claim size distributions are modelled by phase type distributions in literature. This paper aims to calculate the survival probabilities of an insurance company under the assumption that compound binomial risk model where the individual claim sizes are distributed as discrete Phase Type distribution.

In this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well.