Limit theorems for general shock models with infinite mean intershock times

1987 ◽  
Vol 24 (2) ◽  
pp. 449-456 ◽  
Author(s):  
Kevin K. Anderson
Keyword(s):  
Limit Theorems ◽  
Maximum Magnitude ◽  
Shock Model ◽  
Time Intervals ◽  
Shock Models ◽  
First Time

A general shock model in which the time intervals between shocks have infinite expectation is considered. Limit theorems for the first time the magnitude of a shock exceeds a and the historical maximum magnitude are given.

Limit theorems for general shock models with infinite mean intershock times

1987 ◽  
Vol 24 (02) ◽  
pp. 449-456 ◽  
Author(s):  
Kevin K. Anderson
Keyword(s):  
Limit Theorems ◽  
Maximum Magnitude ◽  
Shock Model ◽  
Time Intervals ◽  
Shock Models ◽  
First Time

A general shock model in which the time intervals between shocks have infinite expectation is considered. Limit theorems for the first time the magnitude of a shock exceeds a and the historical maximum magnitude are given.

A note on cumulative shock models

1988 ◽  
Vol 25 (01) ◽  
pp. 220-223 ◽  
Author(s):  
Kevin K. Anderson
Keyword(s):  
Limit Theorems ◽  
Domain Of Attraction ◽  
Weak Limit ◽  
Shock Model ◽  
Time Intervals ◽  
Stable Law ◽  
Shock Models ◽  
Weak Limit Theorems ◽  
First Time ◽  
Intershock Interval

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 note on cumulative shock models

1988 ◽  
Vol 25 (1) ◽  
pp. 220-223 ◽  
Author(s):  
Kevin K. Anderson
Keyword(s):  
Limit Theorems ◽  
Domain Of Attraction ◽  
Weak Limit ◽  
Shock Model ◽  
Time Intervals ◽  
Stable Law ◽  
Shock Models ◽  
Weak Limit Theorems ◽  
First Time ◽  
Intershock Interval

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.

Reliability analysis of an extended shock model

2021 ◽  
pp. 1748006X2098779
Author(s):  
Mohammad Hossein Poursaeed
Keyword(s):  
Discrete Time ◽  
Probability Generating Function ◽  
Reliability Function ◽  
Time Interval ◽  
Shock Model ◽  
Critical Levels ◽  
Shock Models ◽  
The Mean ◽  
First Time ◽  
Mean Time

Suppose that a system is subject to a sequence of shocks which occur with probability p in any period of time [Formula: see text], and suppose that [Formula: see text] and [Formula: see text] are two critical levels ([Formula: see text]). The system fails when the time interval between two consecutive shocks is less than [Formula: see text], and the time interval bigger than [Formula: see text] has no effect on the system activity. In addition, the system fails with a probability of, say, [Formula: see text], when the time interval varies between [Formula: see text] and [Formula: see text]. Therefore, this model can be regarded as an extension of discrete time version of [Formula: see text]-shock model, and such an idea can be also applied in the extension of other shock models. The present study obtains the reliability function and the probability generating function of the system’s lifetime under this model. The present study offers some properties of the system and refers to a generalization of the new model. In addition, the mean time of the system’s failure is obtained under reduced efficiency which is created when the time between two consecutive shocks varies between [Formula: see text] and [Formula: see text] for the first time.

scholarly journals CHANGES IN THE DNA SYNTHESIS PATTERN OF PARAMECIUM WITH INCREASED CLONAL AGE AND INTERFISSION TIME

1974 ◽  
Vol 61 (3) ◽  
pp. 591-598 ◽  
Author(s):  
Joan Smith-Sonneborn ◽  
Michael Klass
Keyword(s):  
Cell Cycle ◽  
Dna Synthesis ◽  
Unicellular Organism ◽  
Time Intervals ◽  
Synchronized Cells ◽  
Different Ages ◽  
Self Fertilization ◽  
Autoradiographic Analysis ◽  
S Period ◽  
First Time

The clonal age in paramecia refers to the total number of vegetative divisions a clone has undergone since its origin at autogamy (self-fertilization). As clonal age increases, the interfission time usually increases. The DNA synthesis pattern of cells of different ages was compared by autoradiographic analysis of the DNA synthesis of synchronized cells at various time intervals during the cell cycle (from one division to the next). The study showed that the G1 period (the lag in DNA synthesis post division) was constant, irrespective of interfission time or clonal age; but the duration of the DNA synthesis period increased with increased interfission time or clonal age. Therefore, we have shown for the first time that the G1 period is fixed, and the S period is increased in a eukaryotic unicellular organism as a function of interfission time and clonal age.

Limit theorems for first-passage times in linear and non-linear renewal theory

1984 ◽  
Vol 16 (04) ◽  
pp. 766-803 ◽  
Author(s):  
S. P. Lalley
Keyword(s):  
Limit Theorems ◽  
Large Deviation ◽  
Local Limit Theorem ◽  
Renewal Theory ◽  
Local Limit ◽  
Linear Boundary ◽  
First Passage ◽  
Non Linear ◽  
First Time ◽  
Passage Times

A local limit theorem for is obtained, where τ a is the first time a random walk Sn with positive drift exceeds a. Applications to large-deviation probabilities and to the crossing of a non-linear boundary are given.

Failure distributions of shock models

1980 ◽  
Vol 17 (03) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

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.

Reliability assessment of system under a generalized cumulative shock model

2019 ◽  
Vol 234 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Min Gong ◽  
Serkan Eryilmaz ◽  
Min Xie
Keyword(s):  
Reliability Assessment ◽  
Shock Model ◽  
External Shocks ◽  
Phase Type Distribution ◽  
Internal Factors ◽  
Reliability Characteristics ◽  
Shock Models ◽  
The One ◽  
Random Shocks ◽  
Real Practice

Reliability assessment of system suffering from random shocks is attracting a great deal of attention in recent years. Excluding internal factors such as aging and wear-out, external shocks which lead to sudden changes in the system operation environment are also important causes of system failure. Therefore, efficiently modeling the reliability of such system is an important applied problem. A variety of shock models are developed to model the inter-arrival time between shocks and magnitude of shocks. In a cumulative shock model, the system fails when the cumulative magnitude of damage caused by shocks exceed a threshold. Nevertheless, in the existing literatures, only the magnitude is taken into consideration, while the source of shocks is usually neglected. Using the same distribution to model the magnitude of shocks from different sources is too critical in real practice. To this end, considering a system subject to random shocks from various sources with different probabilities, we develop a generalized cumulative shock model in this article. We use phase-type distribution to model the variables, which is highly versatile to be used for modeling quantitative features of random phenomenon. We will discuss the reliability characteristics of such system in some detail and give some clear expressions under the one-dimensional case. Numerical example for illustration is also provided along with a summary.

Time sensitive blog retrieval using temporal properties of queries

2016 ◽  
Vol 43 (1) ◽  
pp. 103-121 ◽  
Author(s):  
MohammadSadegh Zahedi ◽  
Abolfazl Aleahmad ◽  
Maseud Rahgozar ◽  
Farhad Oroumchian ◽  
Arastoo Bozorgi
Keyword(s):  
Experimental Analysis ◽  
Experimental Results ◽  
Temporal Property ◽  
Time Intervals ◽  
Efficient Approach ◽  
Temporal Properties ◽  
Time Sensitivity ◽  
Retrieval Algorithms ◽  
First Time ◽  
The Web

Blogs are one of the main user-generated contents on the web and are growing in number rapidly. The characteristics of blogs require the development of specialized search methods which are tuned for the blogosphere. In this paper, we focus on blog retrieval, which aims at ranking blogs with respect to their recurrent relevance to a user’s topic. Although different blog retrieval algorithms have already been proposed, few of them have considered temporal properties of the input queries. Therefore, we propose an efficient approach to improving relevant blog retrieval using temporal property of queries. First, time sensitivity of each query is automatically computed for different time intervals based on an initially retrieved set of relevant posts. Then a temporal score is calculated for each blog and finally all blogs are ranked based on their temporal and content relevancy with regard to the input query. Experimental analysis and comparison of the proposed method are carried out using a standard dataset with 45 diverse queries. Our experimental results demonstrate that, using different measurement criteria, our proposed method outperforms other blog retrieval methods.

General shock models associated with correlated renewal sequences

1983 ◽  
Vol 20 (3) ◽  
pp. 600-614 ◽  
Author(s):  
J. G. Shanthikumar ◽  
U. Sumita
Keyword(s):  
Limit Theorem ◽  
Renewal Process ◽  
Threshold Level ◽  
Numerical Results ◽  
Shock Model ◽  
Failure Times ◽  
Clearing System ◽  
Shock Models ◽  
Subsequent Interval

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.

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