scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

scholarly journals Reliability and Availability Analysis of Arepairable System With Two Types of Failure

2015 ◽  
Vol 4 (1) ◽  
pp. 39
Author(s):  
M. A. El-Damcese ◽  
M. S. Shama
Keyword(s):  
System Reliability ◽  
Repairable System ◽  
Time To Failure ◽  
Repair Rate ◽  
System Parameters ◽  
Availability Analysis ◽  
Reliability Characteristics ◽  
The Mean ◽  
Mean Time ◽  
Reliability And Availability

This paper investigates reliability and availability of a repairable system with two types of failure. Let failure rate and repair rate of [type1, type2] components are assumed to be exponentially distributed. The expressions of availability and reliability characteristics such as the system reliability and the mean time to failure are derived. We used several cases to analyze graphically the effect of various system parameters on the reliability system and availability system.

scholarly journals The M/M/NRepairable Queueing System with Variable Breakdown Rates

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Shengli Lv ◽  
Jingbo Li
Keyword(s):  
Steady State ◽  
Queueing System ◽  
Probability Generating Function ◽  
Idle Time ◽  
Transform Method ◽  
Busy Time ◽  
Breakdown Rates ◽  
The Mean ◽  
System States ◽  
Steady State Probabilities

This paper considers the M/M/Nrepairable queuing system. The customers' arrival is a Poisson process. The servers are subject to breakdown according to Poisson processes with different rates in idle time and busy time, respectively. The breakdown servers are repaired by repairmen, and the repair time is an exponential distribution. Using probability generating function and transform method, we obtain the steady-state probabilities of the system states, the steady-state availability of the servers, and the mean queueing length of the model.

scholarly journals The steady-state behaviour of multistate monotone systems

1984 ◽  
Vol 21 (04) ◽  
pp. 826-835 ◽  
Author(s):  
Bent Natvig ◽  
Arnfried Streller
Keyword(s):  
Steady State ◽  
Explicit Formula ◽  
Point Process ◽  
Critical Level ◽  
Monotone Systems ◽  
State Behaviour ◽  
The Mean ◽  
Stationary Interval ◽  
Mean Time ◽  
Steady State Behaviour

In this paper the steady-state behaviour of multistate monotone systems of multistate components is considered by applying the theory for stationary and synchronous processes with an embedded point process. After reviewing some general results on stationary availability, stationary interval availability and stationary mean interval performance probabilities, we concentrate on systems with independently working and separately maintained components. For this case an explicit formula is given for the mean time which the system in steady state sojourns in states not below a fixed critical level.

The Model of Reliability for a Repairable System

2011 ◽  
Vol 474-476 ◽  
pp. 1715-1719
Author(s):  
Xin Xiao ◽  
Jing Bo Li ◽  
Li Ma
Keyword(s):  
Steady State ◽  
Idle Time ◽  
Repairable System ◽  
Steady State Distribution ◽  
State Distribution ◽  
Busy Time ◽  
Server Breakdown ◽  
Steady State Probabilities

In this paper we consider the system of M/M/N queue with service interrup-tions , therates of server breakdown are different between busy time and idle time, and thereis one repairman ite system. We give out the group of equations for the steady state distribution of the number of effective servers. We obtain the steady-state probabilities of the states and the steady-state availability of the system. This document

Bench-top comparison of thermometers used in newborn infants

2020 ◽  
pp. fetalneonatal-2020-320123
Author(s):  
Emma A Dunne ◽  
Katie Cunningham ◽  
Colm Patrick Finbarr O'Donnell ◽  
Lisa K McCarthy
Keyword(s):  
Steady State ◽  
Prospective Study ◽  
Newborn Infants ◽  
Mean Difference ◽  
Continuous Mode ◽  
Control Temperature ◽  
Steady State Temperature ◽  
The Mean ◽  
A Prospective Study ◽  
Mean Time

We wished to determine the accuracy of thermometers used to measure temperature in newborn infants. We measured the temperature of a water bath with three types of thermometer set at 0.5°C increments between 32.5°C and 38.5°C and compared the values to a control. We recorded the time to display steady-state temperature. The Microlife thermometer most closely approximated control temperature (mean difference <0.1°C (SD<0.1°C)) and displayed a reading in a mean time of 29 s (SD 2 s). Used in ‘predictive’ (default) mode, the Welch Allyn SureTemp Plus 692 thermometer differed from the control by a mean of 0.6°C (SD 0.3°C), displaying a temperature at 15 s (SD 3 s). This device consistently overestimated temperature. In ‘continuous’ mode, the mean difference was <0.1°C (SD<0.1°C) at 5 min. The Phillips probe differed from the control by a mean of 0.4°C (SD 0.2°C). Thermometers used to measure temperature in newborn infants may underestimate hypothermia. A prospective study in newborn infants is needed.

A MARKOV REPAIRABLE SYSTEM INVOLVING AN IMPERFECT SERVICE STATION WITH MULTIPLE VACATIONS

2005 ◽  
Vol 22 (04) ◽  
pp. 555-582 ◽  
Author(s):  
JAU-CHUAN KE ◽  
CHUEN-HORNG LIN
Keyword(s):  
Repairable System ◽  
System Failure ◽  
Service Station ◽  
System Parameters ◽  
Failure Frequency ◽  
The Mean ◽  
Repair Facility ◽  
Markov Repairable System ◽  
Mean Time ◽  
Reliability And Availability

The main purpose of this paper is to study the reliability and availability of a system with M operating devices, m spares, and an imperfect service station that takes vacations. Specifically, once there are no failed devices in the system, the service station takes consecutive vacations until there is at least one failed device upon its return from vacation. The service station may break down and require repair at a repair facility. This paper derives the reliability, the mean time to system failure, the availability, and failure frequency of the K-out-of-M + m system. Numerical simulation of the impacts of system parameters as well as sensitivity analysis for the reliability, the mean time to system failure, the availability and failure frequency is performed.

A Note on the Transient Solution of Stokes' Second Problem with Arbitrary Initial Phase

2006 ◽  
Vol 22 (4) ◽  
pp. 349-354 ◽  
Author(s):  
C.-M. Liu ◽  
I.-C. Liu
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Initial Phase ◽  
Transient State ◽  
Wall Stress ◽  
Transform Method ◽  
Transient Solutions ◽  
Stokes Second Problem ◽  
Oscillating Plate ◽  
Steady State Solutions

AbstractThe flow of a viscous fluid disturbed by an oscillating plate of arbitrary initial phase is studied in present note. The exact solutions of the velocity and the shear stress are solved using a Laplace transform method. The velocity is derived in terms of complementary error functions and the shear stress on the boundary is given in the form of Fresnel integrals. Since the steady-state solutions are well known, our discussions are focused on the transient solutions. The transient state will disappear faster for the wall stress than that for the velocity field. Comparing the results corresponding to different initial phases, the cosine case reaches to the steady state more rapidly than the sine case.

Model-independent aspects of tracer chromatography theory

1973 ◽  
Vol 333 (1592) ◽  
pp. 89-98 ◽  
Keyword(s):  
Steady State ◽  
Thermodynamic Properties ◽  
Residence Time ◽  
Mean Residence Time ◽  
Chromatographic Determination ◽  
System Response ◽  
Chromatographic Process ◽  
The Mean ◽  
Population Balances ◽  
Mean Time

A theory of tracer chromatography is developed on the basis of population balances in the steady state. As well as to tracer systems the theory applies to chromatography with a carrier gas if the system response is linear. It is shown that the time of passage of a tracer peak can properly be taken to be the mean residence time of the tracer and that the mean time is directly related to thermodynamic properties. Many results of chromatography theory may be established easily without the need for the assumptions usually employed. Thus the methods already developed for the chromatographic determination of thermodynamic properties are more powerful, and there is more freedom in the design of experiments, than had been realized. The mean residence time of species i in the steady state is equal to the ratio of the holdup of i in the system to the rate of transmission of i through the system. By invoking the hypothesis that in the steady state the system is in equilibrium with its feed, the mean time can be related to thermodynamic properties contained in an expression for the holdup. This provides a powerful strategy for developing theoretical results without the need for a mathematical model of the chromatographic process.

A Method for the Calculation of the Mean Time To Failure (MTTF) of Repairable System

2008 ◽  
Vol 44-46 ◽  
pp. 813-820 ◽  
Author(s):  
Jian Xin Zhu ◽  
Li J. Wang ◽  
Shi Yi Bao ◽  
W.P. Wang ◽  
Zeng Liang Gao
Keyword(s):  
Single Unit ◽  
Management Strategy ◽  
Great Influence ◽  
Repairable System ◽  
Time To Failure ◽  
Test Interval ◽  
Operating Cycle ◽  
Mean Time To Failure ◽  
The Mean ◽  
Mean Time

The ability of executing assigned function of repairable system under certain condition is quite different from that of single unit due to redundant configuration. It is well understood that proper management strategy can greatly prolong the mean time to failure (MTTF) of repairable system. By introducing operating cycle or partial test interval, repair time and maintenance efficiency, the MTTF of classic 1oo1, 1oo2 and 2oo3 redundant systems is studied in this paper. It is found that periodical maintenance can dramatically improve the availability of repairable system, while the efficiency of maintenance has great influence on the MTTF of repairable system.

scholarly journals The steady-state behaviour of multistate monotone systems

1984 ◽  
Vol 21 (4) ◽  
pp. 826-835 ◽  
Author(s):  
Bent Natvig ◽  
Arnfried Streller
Keyword(s):  
Steady State ◽  
Explicit Formula ◽  
Point Process ◽  
Critical Level ◽  
Monotone Systems ◽  
State Behaviour ◽  
The Mean ◽  
Stationary Interval ◽  
Mean Time ◽  
Steady State Behaviour

In this paper the steady-state behaviour of multistate monotone systems of multistate components is considered by applying the theory for stationary and synchronous processes with an embedded point process. After reviewing some general results on stationary availability, stationary interval availability and stationary mean interval performance probabilities, we concentrate on systems with independently working and separately maintained components. For this case an explicit formula is given for the mean time which the system in steady state sojourns in states not below a fixed critical level.

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