scholarly journals Profit Analysis of a Standby Repairable System with Priority to Preventive Maintenance and Rest of Server Between Repairs

2021 ◽  
Author(s):  
Chhama Aggarwal ◽  
Nitika Ahlawat ◽  
S.C. Malik
Keyword(s):  
Preventive Maintenance ◽  
Failure Time ◽  
Random Variable ◽  
Productivity Level ◽  
Reliability Characteristics ◽  
Profit Analysis ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
The Cost ◽  
Efficiency And Productivity

The paper aims to bring out the profit analysis of a system with cold standby redundancy of two identical units. In the system, we keep one unit productive and the other is to backup the operation. The system requires preventive maintenance after a specific time. In addition to that, the server is allowed to rest between two consecutive repairs. The repairs are done to increase the efficiency and productivity level of the system. The repair and rest times follow arbitrary distributions while the random variable related to failure time of the unit follows negative exponential distribution. The provision of priority has been made for the preventive maintenance over repairs. Some important reliability characteristics are studied in steady state by using the approach of stochastic processes. The revenue per unit time and the cost per unit time for which server is busy in repairs and maintenances are considered for determining the profit incurred to the system.  The results are shown graphically and numerically to highlight the effect of different parameters on some significant reliability characteristics.

scholarly journals Reliability and Sensitivity Analysis of a Repairable System with Warranty and Administrative Delay in Repair

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mohamed S. El-Sherbeny ◽  
Zienab M. Hussien
Keyword(s):  
Performance Metrics ◽  
Failure Time ◽  
Relative Sensitivity ◽  
Sensitivity Analyses ◽  
Inspection Time ◽  
Industrial Systems ◽  
Negative Exponential Distribution ◽  
Product Warranty ◽  
Negative Exponential ◽  
The Cost

The purpose of this study is to analyze the behavior of some industrial systems in light of the cost-free warranty policy. According to this policy, we assume that the repairman is not always present in the system. When the active unit fails, the repairman will be called to visit the system; however, administrative procedures may delay the visit for some time. Once on the system, the repairman first inspects whether the fault is caused by the user or not and whether it is repairable or not. According to product warranty laws, the repairman carries out the repair or replacement of the faulty unit. The failure time, administrative delay time, inspection time, and repair time are assumed taken as a negative exponential distribution. The system model is analyzed by the supplementary variable technique and Laplace transform, as various performance metrics of system efficiency have been obtained. The sensitivity and relative sensitivity analyses for the system parameters have also been performed. Finally, an illustrative example is taken to illustrate the efficiency of the system.

RELIABILITY MEASURES OF A COLD STANDBY SYSTEM WITH PREVENTIVE MAINTENANCE AND REPAIR

2013 ◽  
Vol 20 (06) ◽  
pp. 1350022 ◽  
Author(s):  
S. C. MALIK ◽  
SUDESH K. BARAK
Keyword(s):  
Preventive Maintenance ◽  
Failure Time ◽  
Reliability Measures ◽  
Maintenance And Repair ◽  
Regenerative Point ◽  
Cold Standby ◽  
Semi Markov Process ◽  
Standby System ◽  
Regenerative Point Technique ◽  
Negative Exponential

The purpose of the present study is to determine reliability measures of a two-unit cold standby system with preventive maintenance and repair. The units are identical in nature subject to constant failure from normal mode. Preventive maintenance of the operative unit is carried out after a pre-specific time "t" up to which no failure occurs. However, repair of the unit is done at its failure. The unit works as new after repair and preventive maintenance. The switch devices are perfect. The distributions of failure time and the time by which unit undergoes for preventive maintenance are taken as negative exponential while that of preventive maintenance and repair times are assumed as arbitrary with different probability density functions. The random variables associated with failure, preventive maintenance and repair times are statistically independent. The semi-Markov process and regenerative point technique are adopted to derive the expressions for system performance measures in steady state. The graphical behavior of MTSF, availability and profit function have been observed with respect to preventive maintenance rate for particular values of other parameters and costs.

Analytic characterization of the optimal control of a queueing system

1970 ◽  
Vol 7 (03) ◽  
pp. 617-633 ◽  
Author(s):  
S. Zacks ◽  
M. Yadin
Keyword(s):  
Optimal Control ◽  
Queueing System ◽  
Control Policy ◽  
Random Variable ◽  
Management Policy ◽  
Homogeneous Poisson Process ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Arrival Intensity

Summary In a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.

scholarly journals Gain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching

2011 ◽  
Vol 467 (2134) ◽  
pp. 2825-2851 ◽  
Author(s):  
Mark D. McDonnell ◽  
Alex J. Grant ◽  
Ingmar Land ◽  
Badri N. Vellambi ◽  
Derek Abbott ◽  
...  
Keyword(s):  
Information Asymmetry ◽  
Exponential Distribution ◽  
Random Variable ◽  
Mathematical Finance ◽  
Positive Random Variable ◽  
Optimal Switching ◽  
Switching Strategy ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The two-envelope problem (or exchange problem) is one of maximizing the payoff in choosing between two values, given an observation of only one. This paradigm is of interest in a range of fields from engineering to mathematical finance, as it is now known that the payoff can be increased by exploiting a form of information asymmetry. Here, we consider a version of the ‘two-envelope game’ where the envelopes’ contents are governed by a continuous positive random variable. While the optimal switching strategy is known and deterministic once an envelope has been opened, it is not necessarily optimal when the content's distribution is unknown. A useful alternative in this case may be to use a switching strategy that depends randomly on the observed value in the opened envelope. This approach can lead to a gain when compared with never switching. Here, we quantify the gain owing to such conditional randomized switching when the random variable has a generalized negative exponential distribution, and compare this to the optimal switching strategy. We also show that a randomized strategy may be advantageous when the distribution of the envelope's contents is unknown, since it can always lead to a gain.

scholarly journals Censored Negative Exponential Distribution as a Mixed Distribution and Derivation of Its Moments

2013 ◽  
Vol 14 (1) ◽  
pp. 167-176
Author(s):  
Srijan Lal Shrestha
Keyword(s):  
Exponential Distribution ◽  
Failure Time ◽  
Three Dimensional ◽  
Time Data ◽  
Exponential Distributions ◽  
Discrete Random Variables ◽  
Negative Exponential Distribution ◽  
Doubly Censored ◽  
Mean And Variance ◽  
Negative Exponential

Censored negative exponential distribution is treated as a mixed type distribution having two distinct types of components. These components give arise to continuous as well as discrete random variables. Moments (mean and variance) are derived for the doubly censored, right censored, and left censored negative exponential distributions (NEDs) along with separations of continuous and discrete components and their respective means and variances. Moments obtained for the censored NEDs are then compared to the corresponding values of the uncensored NEDs and the changes in the proportions of the moments due to censoring are examined and assessed. Plots of moments of the censored distributions including a three dimensional scatter plot are presented considering different hypothetical values at which censoring may occur. These distributions are widely applied in fitting and modeling failure time data in survival and reliability analyses. Nepal Journal of Science and Technology Vol. 14, No. 1 (2013) 167-176 DOI: http://dx.doi.org/10.3126/njst.v14i1.8937

scholarly journals The Negative Exponential Distribution and Average Excess Claim Size

1979 ◽  
Vol 10 (3) ◽  
pp. 303-304
Author(s):  
G. C. Taylor
Keyword(s):  
Exponential Distribution ◽  
Motor Vehicle ◽  
Random Variable ◽  
Claim Size ◽  
Negative Exponential Distribution ◽  
Claim Size Distribution ◽  
Average Size ◽  
Negative Exponential ◽  
Image Position ◽  
Damage Claim

Consider a claim size distribution with complementary d.f. H(.). Let E(x) denote the average claim payment under a policy subject to this claim size d.f. but with a deductible of x. That iswhere E is the expectation operator and X is the random variable claim size before application of the excess.It is well-known—see Benktander and Segerdahl (1960, p. 630)—that:It was shown by them that E(x) is a constant for all x ≥ o if and only if the claim size d.f. is negative exponential:This property of the negative exponential distribution is closely related to the fact that it is the only distribution with constant failure rate. See Kaufmann (1969, pp. 20-22).The constancy of average excess claim size with varying deductible can be useful in practice. For example, if the distribution of motor vehicle (property damage) claim sizes can be assumed roughly exponential, which will often be reasonable, then a variation in the deductible will not induce any variation in the average size of claims paid by the insurer, i.e. after application of the deductible. This will be a particularly useful piece of information if for example one is examining trends in average claim size over a period during which a change in deductible occurred.

Analytic characterization of the optimal control of a queueing system

1970 ◽  
Vol 7 (3) ◽  
pp. 617-633 ◽  
Author(s):  
S. Zacks ◽  
M. Yadin
Keyword(s):  
Optimal Control ◽  
Queueing System ◽  
Control Policy ◽  
Random Variable ◽  
Management Policy ◽  
Homogeneous Poisson Process ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Arrival Intensity

SummaryIn a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

EVALUATION OF THE RELIABILITY OF COMPLEX TECHNICAL RECONFIGURATION SYSTEMS BY STATISTICAL MODELING METHOD

2019 ◽  
pp. 84-88
Author(s):  
A.Yu. Kulakov
Keyword(s):  
Normal Distribution ◽  
Statistical Modeling ◽  
Quantitative Estimate ◽  
Failure Time ◽  
Modeling Method ◽  
System Failure ◽  
Similar System ◽  
Orbit Control ◽  
Reliability Characteristics ◽  
Complex Technical System

Goal. Assess the reliability of a complex technical system with periodic reconfiguration and compare the results obtained a similar system, but without reconfiguration. Materials and methods. In this article uses the method of statistical modeling (Monte Carlo) to assess the reliability of complex system. We using the normal and exponential distribution of failure time for modeling failures of system elements. Reconfiguration algorithm is the algorithm proposed for the attitude and orbit control system of spacecraft. Results. A computer program has been developed for assessing reliability on the basis of a statistical modeling method, which makes it possible to evaluate systems of varying complexity with exponential and normal distribution, as well as with and without periodic reconfiguration. A quantitative estimate of the reliability as a function of the probability of system failure is obtained. Conclusion. It has been demonstrated that a system with reconfiguration has the best reliability characteristics, both in the case of exponential and normal distribution of failures.

Ehrenfest urn models

1965 ◽  
Vol 2 (02) ◽  
pp. 352-376 ◽  
Author(s):  
Samuel Karlin ◽  
James McGregor
Keyword(s):  
Exponential Distribution ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Urn Models ◽  
Time Intervals ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 <p< 1).

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