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For a system that is subject to shocks, it is assumed that the distribution of the magnitudes of shocks changes after the first shock of size at least d1, and the system fails upon the occurrence of the first shock above a critical level d2 (> d1). In this paper, the distribution of the lifetime of such a system is studied when the times between successive shocks follow matrix-exponential distribution. In particular, it is shown that the system's lifetime has matrix-exponential distribution when the intershock times follow Erlang distribution. The model is extended to the case when the system fails upon the occurrence of l consecutive critical shocks.

There are different ways of improving reliability characteristics of manufactured items. The most common methodology adopted in industry is burn-in, which is a method of ‘elimination’ of initial failures (infant mortality). As was mentioned previously, the ‘sufficient condition’ for employing the traditional burn-in is the initially decreasing failure rate. For example, when a population of items is heterogeneous, and therefore consists of subpopulations with ordered failure (hazard) rates, it obviously contains weaker (with larger failure rates) subpopulations. As the weakest populations are dying out first, the failure rate of this population is often initially decreasing and burn-in can be effectively applied.

We modify a mathematical model of photosynthesis to quantify the perturbations that high energy muons could make on aquatic primary productivity. Then, we apply this in the context of the extragalactic shock model, according to which Earth receives an enhanced dose of high-energy cosmic rays when it is at the galactic north. We obtain considerable reduction in the photosynthesis rates, consistent with potential drops in biodiversity.

We study a reliability system subject to shocks generated by a renewal point process. When a shock occurs, components fail independently of each other with equal probabilities that are random numbers drawn from a distribution that may differ from shock to shock. We first consider the case of a parallel system and derive closed expressions for the Laplace-Stieltjes transform and the expectation of the time to system failure and for its density in the case that the distribution function of the renewal process possesses a density. We then treat a more general system structure, which has some very important special cases, such as k-out-of-n:F systems, and derive analogous formulae.

Lifetime distributions for multicomponent systems are developed through the interplay of ageing and stress shocks to the system. The ageing process is explicitly modeled by an exponential function with rate affected by the magnitude of stresses from a compound Poisson process shock model. Applications of these life distributions and associated failure rates towards the study of multicomponent system survival are discussed. In particular, we illustrate the behavior of these survival functions in relevant subsets of the parameter space.

Some topics in the theory of jets are reviewed. These include jet precession, unconfined jets, the origin of knots, the internal shock model as a unifying theme from protostellar jets to Gamma-ray bursts, relations between the Blandford-Znajek and MHD disk-wind models, and jet collimation in magnetic acceleration models., Comment: To appear in Highly Energetic Physical Processes .... (IAU Symp 195) P. C. H. Martens and S. Tsuruta, eds

Conditions for a correlated cumulative shock model under which the system failure time is HNBUE are given. It is shown that the proof of a theorem given by Sumita and Shanthikumar (1985) relative to this property is not correct and a correct proof of the theorem is given.

Two kinds of multidimensional IFR distribution are defined by using a partial order in R n +, which is derived from a non-negative, strictly increasing function in R n +. Some closure properties under operations and an application to a shock model are discussed.

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate. SHOCK PROCESS; INCREASING FAILURE RATE; CUMULATIVE DAMAGE; LIFE DISTRIBUTIONS

In this paper we study some distribution properties of the system failure time in general shock models associated with correlated renewal sequences (X n, Y n) . Two models, depending on whether the magnitude of the nth shock X n is correlated to the length Y n of the interval since the last shock, or to the length of the subsequent interval to the next shock, are considered. Sufficient conditions under which the system failure time is completely monotone, new better than used, new better than used in expectation, and harmonic new better than used in expectation are given for these two models.

In this paper we define and analyze a general shock model associated with a correlated pair (Xn, Yn ) of renewal sequences, where the system fails when the magnitude of a shock exceeds (or falls below) a prespecified threshold level. Two models, depending on whether the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length Yn of the subsequent interval until the next shock, are considered. The transform results, an exponential limit theorem, and properties of the associated renewal process of the failure times are obtained. An application in a stochastic clearing system with numerical results is also given.

A number of extensions of the class preservation results in the Esary, Marshall and Proschan shock model have been investigated by various authors in recent years, most recently by Ghosh and Ebrahimi. In this note, generalizations are obtained using different methods for the IFR and NBUE cases when the shocking process is a regular continuous-time Markov process with stationary transition probabilites.

A shock model in which the time intervals between shocks are in the domain of attraction of a stable law of order less than 1 or relatively stable is considered. Weak limit theorems are established for the cumulative magnitude of the shocks and the first time the cumulative magnitude exceeds z without any assumption on the dependence between the intershock interval and shock magnitude.

A non-homogeneous Poisson shock model has a continuous mean function Λ(t). The kth shock Sk causes simultaneous failure of the components j ∊ J ∊ {1, ···, n} with probability pJ (Sk ). If Tj is the lifetime of component j, it is shown that (T 1, · ··, Tn ) belongs to various multivariate non-parametric life classes depending on the life class of .

Suppose that a device is subjected to shocks and that denotes the probability of surviving k shocks. Then is the probability that the device will survive beyond t, where is the counting process which governs the arrival of shocks. A-Hameed and Proschan (1975) considered the survival function H(t) under what they called the pure birth shock model. In this paper we shall prove that is IFRA and DMRL under conditions which differ from those used by A-Hameed and Proschan (1975).

First order Fermi acceleration is an efficient mechanism to produce relativistic particles in strong astrophysical shocks. We have developed a model using this theory to explain the non-thermal emission from non-relativistic jets in Quasars and AGNs. Fluid dynamical simulations of cosmic jets predict shock formation in them at quasi-periodic intervals. This is also suggested by observations of jets. We identify the shocks as the sites of reacceleration of the energetic particles required to explain the non-thermal emission of the jets. In order to facilitate the comparison with observations, we have done numerical simulations of the expected observational properties at high and low spatial resolution.