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 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.

scholarly journals Reliability Analysis of Two Unit Standby Model with Controlled and Uncontrolled Failure of Unit and Replacement Facility Available in the System

2021 ◽  
pp. 625-632
Author(s):  
Nafeesa Bashir ◽  
JPS Joorel ◽  
T R Jan
Keyword(s):  
Present Model ◽  
Design Strategy ◽  
Replacement Policy ◽  
System Failure ◽  
Reliability Measures ◽  
Primary Interest ◽  
Efficient System ◽  
Regenerative Point ◽  
Regenerative Point Technique ◽  
Preventive Repair

Planning a highly reliable and efficient system has always been a primary interest for reliability engineers by devising the powerful design strategy and employing effective repair and replacement policy. Keeping in view this, the basic aim of this paper is to analyze the reliability of a system which comprised of two units A and B in which unit A is functional and B is held standby. Unit A after failure may be controlled or uncontrolled. The failed unit undergoes for repair in the controlled unit. If the repair of a unit is not controlled then it is replaced by a new one.  Upon the breakdown of operational unit A, unit B come becomes active instantaneously. Unit B after failure is repaired by regular repairmen. System failure takes place when both the units quit serving. The unit serves as good as a fresh after preventive repair and replacement policy. The regenerative point technique has been used to obtain the expression for several reliability measures. Finally, the graphical behavior of MTSF and profit of the present model has been observed for arbitrary values of parameters and costs.

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 Probabilistic Assessment of Two-Unit Parallel System with Correlated Lifetime under Inspection Using Regenerative Point Technique

2019 ◽  
Vol 2 (1) ◽  
pp. 5-14
Author(s):  
VIJAY VIR SINGH ◽  
PRAVEEN KUMAR POONIA
Keyword(s):  
Mathematical Formulation ◽  
Practical Importance ◽  
Joint Probability ◽  
General Distribution ◽  
Regenerative Point ◽  
Negative Exponential Distribution ◽  
Parallel Configuration ◽  
Regenerative Point Technique ◽  
Repair Facility ◽  
Negative Exponential

This paper deals with the reliability analysis of a complex system consisting ofa two dissimilar unit’ in a parallel configuration with correlated lifetime distribution. The system stops functioning when both units stop working. Both units are inspected periodically as well as being examined before assigning to repair facility. Under consideration of the system have two states: Normal and failed. Regenerative point technique has been used for the mathematical formulation of the model. The system is analyzed using Laplace transforms to solve the mathematical equations. Reliability, Availability, MTSF, Busy Period of repairmen and Cost-effectiveness of the system has been computed. The computed results have been demonstrated by tables and graphs. The repair time of both the units follows the negative exponential distribution with different parameters in a joint probability density function. The inspection times are assumed to follow the general distribution. Some particular cases of the system have also been derived from seeing the practical importance of the model.

Stochastic Analysis of a Computer System with Unit Wise Cold Standby Redundancy and Priority to Hardware Repair Subject to Failure of Service Facility

2020 ◽  
pp. 2150013
Author(s):  
S. C. Malik ◽  
R. K. Yadav
Keyword(s):  
Computer System ◽  
Stochastic Analysis ◽  
Busy Period ◽  
System Model ◽  
Profit Function ◽  
Reliability Measures ◽  
Service Facility ◽  
Time Treatment ◽  
Regenerative Point ◽  
Semi Markov Process

The use of semi-Markov process and regenerative point has been made for determining reliability measures of a computer system. The stochastic model is developed by considering the ideas of unit wise redundancy and failure of service facility. The treatment to the failed service facility is given in order to resume the jobs with full efficiency. The system is analyzed at different time points in the steady state. The profit of the system model has been obtained under the following two policies: In first policy, the profit is evaluated by taking cost per unit time for busy period of the service facility and cost per unit time treatment of the service facility. In second policy, the profit is evaluated by taking cost per unit hardware repair, per unit time software up-gradation and cost per unit time treatment of the service facility. The behavior of some reliability measures, such as MTSF, availability and profit function, has been shown graphically for arbitrary values of the parameters.

Analysis of discrete-time semi-Markov model for a two-unit warm standby system subject to degradation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Neama Temraz
Keyword(s):  
Markov Model ◽  
Weibull Distribution ◽  
Discrete Time ◽  
Content Type ◽  
Regenerative Point ◽  
Semi Markov Process ◽  
Regenerative Point Technique ◽  
The Mathematical Model ◽  
Mean Time ◽  
Warm Standby

PurposeThe present paper analyzed a model consisting of one unit with a warm standby unit where the main unit has three states: up, degraded and down.Design/methodology/approachThe semi-Markov model under the regenerative method is used to construct the mathematical model for the system.FindingsThe effectiveness measures of the system are discussed such as availability, reliability, steady-state availability and mean time to system failure. The life and repair times of the system units are assumed to be discrete follow discrete Weibull distribution. Also, the parameters of the discrete Weibull distribution are assumed to be fuzzy with bell-shaped membership function. An application is introduced to show the results obtained for the system and the profit of the presented model.Originality/valueRarely papers in literature treated the topic of the discrete-time semi-Markov process using a regenerative point technique.

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