scholarly journals SMOOTHING INTENSITIES OF COUNTING PROCESS BY USING POLYNOMIAL

2021 ◽  
Vol 18 (2) ◽  
pp. 209-230
Author(s):  
Ratheesan K. ◽  
Anilkumar P.
Keyword(s):  
Counting Process

Statistical approach for describing failures and lifetimes of water mains

1998 ◽  
Vol 38 (6) ◽  
pp. 209-217 ◽  
Author(s):  
Jianhua Lei ◽  
Sveinung Sægrov
Keyword(s):  
Data Base ◽  
Ductile Iron ◽  
Counting Process ◽  
Statistical Approach ◽  
Process Models ◽  
Average Lifetime ◽  
Maintenance Practice ◽  
Water Mains ◽  
Near Future

This paper demonstrates the statistical approach for describing failures and lifetimes of water mains. The statistical approach is based on pipe inventory data and the maintenance data registered in the data base. The approach consists of data pre-processing and statistical analysis. Two classes of statistical models are applied, namely counting process models and lifetime models. With lifetime models, one can estimate the probability which a pipe will fail within a time horizon. With counting process models one can see the deteriorating (or improving) trend in time of a group of “identical” pipes and their rates of occurrence of failure (ROCOF). The case study with the data base from Trondheim municipality (Norway) demonstrates the applicability of the statistical approach and leads to the following results: 1). In the past 20 years, Trondheim municipality has experienced approximately 250 to 300 failures per year. However, the number of failures per year will significantly increase in the near future unless better maintenance practice is implemented now. 2). Unprotected ductile iron pipes have a higher probability of failures than other materials. The average lifetime of unprotected ductile iron pipes is approximately 30 to 40 years shorter than the lifetime of a cast iron pipe. 3). Pipes installed 1963 and 1975 are most likely to fail in the future; 4) The age of a pipe does not play a significant role for the remaining lifetime of the pipe; 5). After 2 to 3 failures, a pipe enters a fast-failure stage (i.e., frequent multiple between failures).

Estimation on conditional restricted mean survival time with counting process

2020 ◽  
pp. 1-15
Author(s):  
Junshan Qiu ◽  
Dali Zhou ◽  
H.M. Jim Hung ◽  
John Lawrence ◽  
Steven Bai
Keyword(s):  
Survival Time ◽  
Counting Process ◽  
Mean Survival Time ◽  
Restricted Mean Survival Time

scholarly journals Generalized fractional Poisson process and related stochastic dynamics

2020 ◽  
Vol 23 (3) ◽  
pp. 656-693 ◽  
Author(s):  
Thomas M. Michelitsch ◽  
Alejandro P. Riascos
Keyword(s):  
Poisson Process ◽  
Continuous Time ◽  
Counting Process ◽  
Stochastic Dynamics ◽  
Waiting Times ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Fractional Operators ◽  
Fractional Poisson Process ◽  
Erlang Process

AbstractWe survey the ‘generalized fractional Poisson process’ (GFPP). The GFPP is a renewal process generalizing Laskin’s fractional Poisson counting process and was first introduced by Cahoy and Polito. The GFPP contains two index parameters with admissible ranges 0 < β ≤ 1, α > 0 and a parameter characterizing the time scale. The GFPP involves Prabhakar generalized Mittag-Leffler functions and contains for special choices of the parameters the Laskin fractional Poisson process, the Erlang process and the standard Poisson process. We demonstrate this by means of explicit formulas. We develop the Montroll-Weiss continuous-time random walk (CTRW) for the GFPP on undirected networks which has Prabhakar distributed waiting times between the jumps of the walker. For this walk, we derive a generalized fractional Kolmogorov-Feller equation which involves Prabhakar generalized fractional operators governing the stochastic motions on the network. We analyze in d dimensions the ‘well-scaled’ diffusion limit and obtain a fractional diffusion equation which is of the same type as for a walk with Mittag-Leffler distributed waiting times. The GFPP has the potential to capture various aspects in the dynamics of certain complex systems.

New Graft Dispenser to Simplify Hair Transplantation

1997 ◽  
Vol 14 (2) ◽  
pp. 201-202
Author(s):  
Isabel M. Banuchi
Keyword(s):  
Stainless Steel ◽  
Counting Process ◽  
Open Channel ◽  
Saline Solution ◽  
Hair Transplantation ◽  
Multiple Channel ◽  
Loading Process ◽  
New Instrument ◽  
Disposable Plastic

The Banuchi graft dispenser is an instrument for transplanting a plurality of hair grafts into preformed holes that facilitates and reduces the time of the implant procedure. The graft dispenser is an elongated hollow tube having both proximal and distal ends open to facilitate the hair graft loading process. It has an open channel extending along the length of the tube that holds the grafts, simplifying the counting process during the procedure. This instrument offers many advantages. The most attractive advantage for both patients and surgeons is that it reduces the time of implantation significantly. This reduction in time is due to the fact that with the graft dispenser, the surgeon can use the instrument not only to hold the grafts, but to dilate the preformed incisions and make the insertion more accurately and quickly. The new instrument has been designed in stainless steel and soon will be available in disposable plastic for further convenience. A multiple-channel instrument with a common funnel has been tested and proven to be very useful. A special tray to keep the loaded grafts in saline solution has also been designed.

Partially observable semi-Markov reward processes

1993 ◽  
Vol 30 (3) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda
Keyword(s):  
Markov Process ◽  
Counting Process ◽  
Probabilistic Interpretation ◽  
Real Domain ◽  
Semi Markov Process ◽  
Reward Process ◽  
Markov Reward ◽  
Partially Observable ◽  
Joint Behavior

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.

The coincidence approach to stochastic point processes

1975 ◽  
Vol 7 (1) ◽  
pp. 83-122 ◽  
Author(s):  
Odile Macchi
Keyword(s):  
Poisson Process ◽  
Probability Space ◽  
Point Processes ◽  
Counting Process ◽  
Regular Point ◽  
General Point ◽  
Completely Regular ◽  
Photon Process ◽  
Stochastic Point Processes

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.

The Algorithm for Graphic Method of Rain-Flow Counting in Programming

2011 ◽  
Vol 225-226 ◽  
pp. 1157-1161 ◽  
Author(s):  
Qing Deng ◽  
Hong Jie Yuan
Keyword(s):  
Computer Program ◽  
Execution Time ◽  
Counting Process ◽  
Load Cycle ◽  
Mean Value ◽  
Graphic Method ◽  
Counting Method ◽  
Starting Point ◽  
Mechanical Basis

In this article, a new algorithm for rain-flow counting method in computer program is introduced. In the whole counting process, this algorithm entirely follows the principle of graphic method of rain-flow counting method, and so it can embodies the mechanical basis of extracting load cycle in rain-flow counting method; during the processing of counting, the information of every load cycle can be accurately recorded, such as starting and ending time, the time of peak or valley, the value of starting point and peak (or valley), mean value and amplitude. Besides, the counting result is in full accordance with the result from graphic method. Compared to four peak-valley method, this algorithm has shorter execution time and higher efficiency.

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