scholarly journals On selecting the most reliable components

1998 ◽  
Vol 2 (2) ◽  
pp. 133-145 ◽  
Author(s):  
Dylan Shi
Keyword(s):  
Markov Process ◽  
Death Process ◽  
Series System ◽  
Birth And Death Process ◽  
Retrograde Motion ◽  
The Past ◽  
Optimal Policies ◽  
Average Proportion ◽  
The Mean ◽  
Mean Time

Consider a series system consisting of n components of k types. Whenever a unit fails, it is replaced immediately by a new one to keep the system working. Under the assumption that all the life lengths of the components are independent and exponentially distributed and that the replacement policies depend only on the present state of the system at each failure, the system may be represented by a birth and death process. The existence of the optimum replacement policies are discussed and the ε-optimal policies axe derived. If the past experience of the system can also be utilized, the process is not a Markov process. The optimum Bayesian policies are derived and the properties of the resulting process axe studied. Also, the stochastic processes are simulated and the probability of absorption, the mean time to absorption and the average proportion of the retrograde motion are approximated.

On the parity of individuals in birth and death processes

1982 ◽  
Vol 14 (03) ◽  
pp. 484-501
Author(s):  
S. K. Srinivasan ◽  
C. R. Ranganathan
Keyword(s):  
General Model ◽  
Death Process ◽  
Birth And Death Process ◽  
Birth Rates ◽  
Birth And Death Processes ◽  
Age Dependent ◽  
The Mean ◽  
Number Of Individuals ◽  
Number Of Births

This paper deals with the parity of individuals in an age-dependent birth and death process. A more general model with parity and age-dependent birth rates is also considered. The mean number of individuals with parity 0, 1, 2, ·· ·is obtained for the two models. The first moments of the total number of births in the population up to time t and the sum of the parities of the individuals existing at time t are obtained. A brief discussion on the parity of individuals in a population including ‘twins' is also given.

On Sieved Orthogonal Polynomials II: Random Walk Polynomials

1986 ◽  
Vol 38 (2) ◽  
pp. 397-415 ◽  
Author(s):  
Jairo Charris ◽  
Mourad E. H. Ismail
Keyword(s):  
Random Walk ◽  
Markov Process ◽  
Orthogonal Polynomials ◽  
Transition Probabilities ◽  
Death Process ◽  
Birth And Death Process ◽  
Stationary Markov Process ◽  
Image Position

A birth and death process is a stationary Markov process whose states are the nonnegative integers and the transition probabilities(1.1)satisfy(1.2)as t → 0. Here we assume βn > 0, δn + 1 > 0, n = 0, 1, …, but δ0 ≦ 0. Karlin and McGregor [10], [11], [12], showed that each birth and death process gives rise to two sets of orthogonal polynomials. The first is the set of birth and death process polynomials {Qn(x)} generated by

OPTIMAL REPAIR OF A SERIES SYSTEM WITH FIXED REPAIR TIMES

1999 ◽  
Vol 13 (4) ◽  
pp. 477-487
Author(s):  
Esther Frostig
Keyword(s):  
Series System ◽  
In Series ◽  
The Mean ◽  
Mean Time

Consider a system consisting of n components in series, subject to failures, with one repairman. No preemption is permitted during a repair. The repairman has a list of components and when he becomes available he repairs the failed component which is closest to the top of the list. The goal is to minimize the mean time until all the components operate—the mean down time. For systems consisting of two components, we assume that the operation and repair times are generally distributed and that the operation times are stochastically ordered. For systems consisting of n components we assume exponentially distributed operation times with rate λi and fixed repair times. We prove that lists in which the components are ordered in an increasing order of their expected operation times are optimal.

A model for blue-green algae and gorillas

1977 ◽  
Vol 14 (04) ◽  
pp. 675-688 ◽  
Author(s):  
Byron J. T. Morgan ◽  
B. Leventhal
Keyword(s):  
Exact Solutions ◽  
Green Algae ◽  
Death Rate ◽  
Death Process ◽  
Birth And Death Process ◽  
Mean Values ◽  
Blue Green Algae ◽  
Supercritical Case ◽  
The Mean ◽  
Runge Kutta

The linear birth-and-death process is elaborated to allow the elements of the process to live as members of linear clusters which have the possibility of breaking up. For the supercritical case, expressions, based on an approximation, are derived for the mean numbers of clusters of the various sizes as time → ∞. These expressions compare very well with exact solutions obtained by the method of Runge-Kutta. Exact solutions for the mean values for all time are given for when the death rate is zero.

A linear birth and death process under the influence of another process

1975 ◽  
Vol 12 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Prem S. Puri
Keyword(s):  
Markov Process ◽  
Closed Form ◽  
Limit Distribution ◽  
Explicit Solution ◽  
Negative Integer ◽  
Death Process ◽  
Birth And Death Process ◽  
Death Rates ◽  
Time To Extinction

Let {X1 (t), X2 (t), t ≧ 0} be a bivariate birth and death (Markov) process taking non-negative integer values, such that the process {X2(t), t ≧ 0} may influence the growth of the process {X1(t), t ≧ 0}, while the process X2 (·) itself grows without any influence whatsoever of the first process. The process X2 (·) is taken to be a simple linear birth and death process with λ2 and µ2 as its birth and death rates respectively. The process X1 (·) is also assumed to be a linear birth and death process but with its birth and death rates depending on X2 (·) in the following manner: λ (t) = λ1 (θ + X2 (t)); µ(t) = µ1 (θ + X2 (t)). Here λ i, µi and θ are all non-negative constants. By studying the process X1 (·), first conditionally given a realization of the process {X2 (t), t ≧ 0} and then by unconditioning it later on by taking expectation over the process {X2 (t), t ≧ 0} we obtain explicit solution for G in closed form. Again, it is shown that a proper limit distribution of X1 (t) always exists as t→∞, except only when both λ1 > µ1 and λ2 > µ2. Also, certain problems concerning moments of the process, regression of X1 (t) on X2 (t); time to extinction, and the duration of the interaction between the two processes, etc., are studied in some detail.

A model for blue-green algae and gorillas

1977 ◽  
Vol 14 (4) ◽  
pp. 675-688 ◽  
Author(s):  
Byron J. T. Morgan ◽  
B. Leventhal
Keyword(s):  
Exact Solutions ◽  
Green Algae ◽  
Death Rate ◽  
Death Process ◽  
Birth And Death Process ◽  
Mean Values ◽  
Blue Green Algae ◽  
Supercritical Case ◽  
The Mean ◽  
Runge Kutta

The linear birth-and-death process is elaborated to allow the elements of the process to live as members of linear clusters which have the possibility of breaking up. For the supercritical case, expressions, based on an approximation, are derived for the mean numbers of clusters of the various sizes as time → ∞. These expressions compare very well with exact solutions obtained by the method of Runge-Kutta. Exact solutions for the mean values for all time are given for when the death rate is zero.

Study of Hazard Rate Functions on the Cumulative Damage Phenomenon

2011 ◽  
Vol 27 (1) ◽  
pp. 47-55 ◽  
Author(s):  
K. S. Wang
Keyword(s):  
Hazard Rate ◽  
Failure Mechanisms ◽  
Operation Time ◽  
Cumulative Damage ◽  
Hazard Rates ◽  
Type B ◽  
The Past ◽  
Rate Functions ◽  
The Mean ◽  
Mean Time

ABSTRACTIn this paper different failure mechanisms which yield cumulative damage are investigated through two types of hazard rate functions. They have been studied during the past two decades. Type A was developed early by assuming the hazard rate as a function of reliability. There are two kinds of trend, one follows the negative logistic decay model, the other the negative Gompertz decay. Some modifications are suggested according to the failure tendency and convenience of fittings. Type B is developed recently by assuming the hazard rate as a function of the expected operation time, T, which is defined as the integration of reliability over the time, normalized by the mean-time-between-failure. In both types the proposed hazard rates grow with the time monotonically. Typical examples are taken to examine these models, meanwhile the comparisons with the Weibull-typed distribution are also made. The results show that the most of proposed relations are successful in the expression of cumulative damage phenomenon, especially the Type B is a better choice even compared with the Weibull-typed description in some respects. The advantages of the models are discussed based on the physical meanings involved in the parameters.

scholarly journals PROPOSALS FOR STRATEGIES IN THE CURRICULA OF TECHNICAL UNIVERSITIES

2017 ◽  
Vol 19 (4) ◽  
Author(s):  
VALENTIN ZICHIL ◽  
VALENTIN NEDEFF ◽  
CAROL SCHNAKOVSZKY ◽  
CĂTĂLIN DROB
Keyword(s):  
Birth Rate ◽  
Educational Activity ◽  
Product Analysis ◽  
New Techniques ◽  
The Past ◽  
The Mean ◽  
Technical High Schools ◽  
The University ◽  
Mean Time ◽  
Virtual Higher Education

<p>Into the past 20 years, in Romania is registered a continuous decrease of the birth rate. At this problem it has to be added the youth wish to work in economics and laws systems, where the length of time study is smaller (only 3 years), gaining the possibility to own rapidly a salary. In those conditions, technical universities have to challenge greater provocations. The paper propose a solution, partially applied in “Vasile Alecsandri” University  of Bacau, to solve some of these new problems using a few solutions such as: “virtual” higher education and distance learning methods in order to achieve as much as is possible from the goals presented in known theories of career development. In the mean time, the strategy of the staff is presented, to make the university attractive for the youth, in order to continue the educational activity and to form better and better qualified specialists, able to face the new techniques technologies in manufacturing and product analysis. A model of curricula for the first two academic years in technical high schools is proposed.</p>

A linear birth and death process under the influence of another process

1975 ◽  
Vol 12 (01) ◽  
pp. 1-17 ◽  
Author(s):  
Prem S. Puri
Keyword(s):  
Markov Process ◽  
Closed Form ◽  
Limit Distribution ◽  
Explicit Solution ◽  
Negative Integer ◽  
Death Process ◽  
Birth And Death Process ◽  
Death Rates ◽  
Time To Extinction

Let {X 1 (t), X 2 (t), t ≧ 0} be a bivariate birth and death (Markov) process taking non-negative integer values, such that the process {X 2(t), t ≧ 0} may influence the growth of the process {X 1(t), t ≧ 0}, while the process X 2 (·) itself grows without any influence whatsoever of the first process. The process X 2 (·) is taken to be a simple linear birth and death process with λ 2 and µ 2 as its birth and death rates respectively. The process X 1 (·) is also assumed to be a linear birth and death process but with its birth and death rates depending on X 2 (·) in the following manner: λ (t) = λ 1 (θ + X 2 (t)); µ(t) = µ 1 (θ + X 2 (t)). Here λ i, µi and θ are all non-negative constants. By studying the process X 1 (·), first conditionally given a realization of the process {X 2 (t), t ≧ 0} and then by unconditioning it later on by taking expectation over the process {X 2 (t), t ≧ 0} we obtain explicit solution for G in closed form. Again, it is shown that a proper limit distribution of X 1 (t) always exists as t→∞, except only when both λ 1 &gt; µ 1 and λ 2 &gt; µ 2. Also, certain problems concerning moments of the process, regression of X 1 (t) on X 2 (t); time to extinction, and the duration of the interaction between the two processes, etc., are studied in some detail.

Homeless men with psychosis are spending more time shelterless

2020 ◽  
pp. 103985622092886
Author(s):  
Daniel Burton ◽  
Simon Jones ◽  
Trevor Carlisle ◽  
Alex Holmes
Keyword(s):  
Affordable Housing ◽  
Low Cost ◽  
Housing First ◽  
Mental Health Team ◽  
Health Team ◽  
The Past ◽  
Homeless Men ◽  
The Mean ◽  
Mean Time

Objective: The objective of this study was to determine if homeless men with psychosis in central Melbourne have spent a greater proportion of the past 12 months in homeless settings as compared with the same group 15 years previously. Method: A 12-month accommodation history was collected from all men with psychosis assessed by a homeless outreach mental health team over a 12-month period commencing 2018 and compared with data from 2006. Results: Between 2006 and 2018, the percentage of time spent homeless in the previous 12 months rose from 50% to 80% ( p = 0.0001). The mean time spent shelterless increased from 72 days to 149 days ( p = 0.0001). Conclusions: The amount of time spent homeless has increased in men with psychosis assessed in central Melbourne. This finding suggests that men with psychosis are becoming increasingly entrenched in homeless settings. Addressing this trend requires an increased emphasis on assertive outreach, greater access to acute inpatient and long-term rehabilitation units, and more low cost affordable housing, including housing first facilities.

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