scholarly journals Stochastic Analysis of a Priority Standby System under Preventive Maintenance

2021 ◽  
Vol 11 (9) ◽  
pp. 3861
Author(s):  
Khalaf S. Sultan ◽  
Mohamed E. Moshref
Keyword(s):  
Preventive Maintenance ◽  
Stochastic Analysis ◽  
Failure Modes ◽  
Reliability Measures ◽  
Partial Failure ◽  
Regenerative Point ◽  
Cold Standby ◽  
Total Failure ◽  
Standby System ◽  
Regenerative Point Technique

In this paper, we propose a system of two dissimilar units: one unit prioritizes operation (priority unit), and the other unit is kept as a cold standby (ordinary unit). In this system, we assume that the failures, repairs, and preventive maintenance (PM) times follow arbitrary distributions for both units, except for the fact that the repair time of the ordinary unit follows an exponential distribution. The priority unit has normal, partial failure or total failure modes, while the ordinary unit has normal or total failure modes. The PM of the system can be started after time t when (i) the priority unit is in the normal or partial failure modes up to time t and (ii) the standby unit is available up to time t. PM can be achieved in two types: the costlier type with probability p and the cheaper type with probability (1−p). Under these assumptions, we investigate the reliability measures of the system using the regenerative point technique. Finally, we show a numerical example to illustrate the theoretical findings and show the effect of preventive maintenance in the reliability measures of the proposed 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.

scholarly journals Stochastic Analysis of a Three-Unit Non-Identical Repairable System with Simultaneous Working of Cold Standby Units

2021 ◽  
Author(s):  
S. Kadyan ◽  
Suresh Chander Malik ◽  
Gitanjali
Keyword(s):  
Power Supply ◽  
Stochastic Analysis ◽  
Transition Probabilities ◽  
Repairable System ◽  
Single Server ◽  
Solar Panels ◽  
Reliability Measures ◽  
Expected Number ◽  
Cold Standby ◽  
Regenerative Point Technique

Here, stochastic analysis of a repairable system of three units has been carried out by taking one unit in operation (called main unit) and two identical units (called duplicate units) in cold standby. The switch device is used to convert the standby units into operative mode. A single server is hired to handle repair activities of the units who visits the system instantly whenever needed. The repair done by the server is perfect and thus the repaired unit follows the same lifetime distribution as the original. The constant failure rates are considered for both main and the duplicate units while their repair time distributions are taken as arbitrary. Some important reliability measures including mean sojourn times (MST), transition probabilities (TP), mean time to system failure (MTSF), availability, expected number of repairs for both kinds of units separately, expected number of visits by the server and busy period analysis of the server due to repair are determined using semi-Markov process (SMP) and regenerative point technique (RPT). The arbitrary values of the parameters are considered to examine the behaviour of some significant reliability measures through graphs. The possible application of the system model can be visualized in a power supply system of a house where a set of solar panels are kept in spare for their simultaneously working when main power supply is discontinued.

scholarly journals Stochastic Analysis of a Two-Unit Cold Standby System Wherein Both Units May Become Operative Depending upon the Demand

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Reetu Malhotra ◽  
Gulshan Taneja
Keyword(s):  
Markov Processes ◽  
Stochastic Analysis ◽  
The Other ◽  
Regenerative Processes ◽  
Cold Standby ◽  
Standby System ◽  
Semi Markov Processes ◽  
System Effectiveness

The present paper analyzes a two-unit cold standby system wherein both units may become operative depending upon the demand. Initially, one of the units is operative while the other is kept as cold standby. If the operative unit fails or the demand increases to the extent that one operative unit is not capable of meeting the demand, the standby unit becomes operative instantaneously. Thus, both units may become operative simultaneously to meet the increased demand. Availability in three types of upstates is as follows: (i) when the demand is less than or equal to production manufactured by one unit; (ii) when the demand is greater than whatever produced by one unit but less than or equal to production made by two units; and (iii) when the demand is greater than the produces by two units. Other measures of the system effectiveness have also been obtained in general case as well as for a particular case. Techniques of semi-Markov processes and regenerative processes have been used to obtain various measures of the system effectiveness.

Stochastic analysis of a multi-unit cold standby system working in orbit form

1990 ◽  
Vol 30 (5) ◽  
pp. 845-850
Author(s):  
L.R. Goel ◽  
Rakesh Gupta ◽  
S.E. Moafi B
Keyword(s):  
Stochastic Analysis ◽  
Cold Standby ◽  
Standby System
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