Regenerative Point Technique Research Articles

Stochastic Model on Three-Similar Units Three Phased Mission System with FCFS Repairs Pattern

The paper allocates a stochastic model on threesimilar units three-phased mission system. The developed system consists of units working in parallel, series and parallel configurations respectively. Initially, the three similar units are operational. Each component has only three states: good, degraded and failed. In this case, the single repair facility that repairs the units in first come first serve (FCFS)pattern has been thought of. Using Semi-Markov Process and regenerative point techniques, various measures of the system performance at each phase are obtained. The system has been analyzed graphically taking a particular case. Various conclusions are made regarding the reliability and cost consideration of the system at each phase as well as for the whole system(as combined Phase I, Phase II, Phase III).

Stochastic Analysis of a Priority Standby System under Preventive Maintenance

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.

Performance evaluation of a hybrid series–parallel system with two human operators using Gumbel–Hougaard family copula

PurposeThis study deals with the reliability analysis of a hybrid series–parallel system consisting of two subsystems A and B with two human operators. Subsystem A has two units in active parallel while subsystem B consists of two-out-of-four units. Both units have exponential failure and repair time. The system under consideration has two states: partial failure state and complete failure state. The mathematical equations associated with the transition diagram have been formulated using regenerative point techniques. The system is analysed using Laplace transforms to solve the mathematical equations. Some important measures of reliability such as availability of system, reliability of the system, mean time to failure (MTTF), sensitivity for MTTF and cost analysis have been discussed. Some particular cases have also been derived and examined to see the practical effect of the model. The computed results are demonstrated by tables and graphs. Furthermore, the results of the designed model are beneficial for system engineers and designers, reliability and maintenance managers.Design/methodology/approachThis paper considered a hybrid series–parallel system consisting of two subsystems A and B with two human operators. The performance of the system is studied using the supplementary variable technique and Laplace transforms. The various measures of reliability such as availability, reliability, mean time to system failure (MTSF), sensitivity for MTTF and cost analysis have been computed for various values of failure and repair rates. Maple 13 software has been used for computations.FindingsIn this research paper, the authors have computed various measures of reliability such as availability, reliability, MTSF, sensitivity for MTTF and cost analysis for various values of failure and repair rates and find that failure due to human operators are more responsible for successful operation of the system and also regular repair should be invoked to improve system performance.Originality/valueThis research paper is the original work of authors. The references are well cited based on the importance of study. Nothing has been detached from any research paper or books.

Modelling and Reliability Analysis of Power Cables Used as a Two Unit Hot Standby System with Preference of Repair over Replacement in the Metro Railways

In this study we aim to do an analysis of the profitability and reliability of a system used primarily in Metro Train Networks consisting of a power cable rated for 33KV. The wires for the feed to each substation are laid in loops. As a starting point, two cables of the same voltage are laid with one being operational and another being a hot standby for backup. The moment the primary operational cable fails the backup cable immediately becomes operational. In the situation of a cable failure, it is considered if repairing the damaged cable can be done as opposed to repairing it. The moment both the operational as well as the back-up cables fail, the system is brought to a complete halt. Cable failures are categorized in two groups viz. irreparable failures & repairable failures. Regenerative Point Technique & Semi-Markov Processes are the methodologies used to derive the data that depicts real-failure situations or any other parameters of system effectiveness. This analysis is being done to enable multiple cases to detect and realize essential profit-analysis results for the system in question.

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

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.

Analysis of Two Non-Identical Unit Cold Standby System in Presence of Prior Information

Characteristics of a two non-identical unit system with a cold standby facility are studied from Bayesian point of view with different type of priors assumed for unknown parameters. Time to failure and time to repair of the operating units are assumed to follow Lindley distribution. Several measures of system effectiveness, such as reliability, MTSF, steady state availability, expected profit etc. are obtained by using regenerative point technique. At the end, a numerical illustration is also carried out, for validation of the proposed system model.

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

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.

Three reliability models of a building cable manufacturing plant: a comparative analysis

In this paper, comparative analysis between the profits of three reliability models of a building cable manufacturing plant is carried out. To facilitate the analysis, real maintenance data of the plant are collected. Three case specific reliability models of the plant are developed. Semi-Markov processes and regenerative point techniques are used to estimate optimized reliability indices of the plant; such as; mean time to plant failure, plant availability, expected number of plant repairs, expected busy period of the repairman and profit incurred to the plant. Comparison between the profits is demonstrated through graphical analysis.

A standby repairable system with rest of server between repairs

A cold standby repairable system of two identical units has been analyzed stochastically in detail by considering the idea of rest of the server between repairs. The unit has two modes – normal and complete failure. There is a single server who is allowed to take rest before starting repair of the unit which was waiting for the repair. The random variables associated with repair and rest time of the server follow arbitrary distribution with different probability density functions while the failure rate of the unit is considered as constant. The semi-Markov process and regenerative point technique are used to derive the expressions for mean time to system failure (MTSF), availability, busy period of the server due to repair, expected number of repairs and profit function. The profit analysis of the system model has been carried out for particular values of the parameters. The profit of the system model has also been observed for change in the revenue per unit time, change in the cost for which server is busy due to repair and change in the cost per repair per unit time.

Reliability analysis of a two-unit cold standby system with arbitrary distributions and change in units

The objective of this paper is to improve systems’ reliability by the change between units of the industrial systems at random times. In this paper, we deal with the study of the industry system consisting of two dissimilar units; one of them is the active unit while the other unit is a cold standby unit. After a random amount of time $$ \tau_{0} $$ from the starting of the system operation, the cold standby unit replaces the active unit and the active unit is converted to a cold standby. All-time distributions are considered to be arbitrary. Various measures of the reliability of the system are obtained using the regenerative point technique. All these measures are also derived based on time $$ \tau_{0} $$ . Finally, a simulation study is obtained to explain the result.

RELIABILITY AND COST ANALYSIS COMPARISON BETWEEN TWO-UNIT PARALLEL SYSTEMS WITH NON-IDENTICAL AND IDENTICAL CONSUMABLE UNITS

In this paper, reliability and cost analysis of two different two-unit parallel redundant systems with non identical and identical consumable units respectively have been done by employing Semi – Markov Processes and Regenerative Point Technique and a comparison is made between both the systems. The systems being considered are two inkjet printers with different cartridge arrangements. The first system contains two non-identical consumable units, colour and black cartridges, wherein, failure of one unit results in system being operative under reduced efficiency. However, the second system contains two identical consumable units, both colour cartridges, wherein, failure of any one of the units does not affect efficiency of system. The system may also fail due to other technical failures. Various system efficiency indicators such as Mean Time to System Failure (MTSF), Availability and Expected Down-Time of the System, Busy Time Period of Repairman, and Average Number of (damaged) Unit Replacements are estimated. Using data collected from industry, the parameters are used to estimate reliability parameters of both the printers and a comparison of profits of both systems with respect to time has been done. Subsequently, the differences in behavior of Availability and Profitability of both systems due to variations in its parameters have been analyzed.

A Reliability Model for a Two Dissimilar Units Series System with Repair Time-Dependent Standby

The present paper stochastically analyze a system comprising two dissimilar units (unit-1/unit-2) working in series configuration. System fails completely when either of the units gets failed. The repair time of unit-2 is considered to be much more as compared to the repair time of unit-1. So, to minimize the breakdown period of the system, a standby unit is provided against the second unit. Regenerative point technique (RPT) is used to develop a semi-markovian reliability model for the mentioned system. Optimum cut-off points concerning the profitability of the system have also been obtained. The model has applications in industries, particularly in aluminum industry.

Stochastic Modelling of an Aircraft Considering the Possibility of Precautionary Landing Due to Fuel Filter Clogging

The present work deals with the stochastic and cost - benefit analysis of a helicopter taking into account the situation of precautionary landing caused by blockage in its fuel - filter. The system has been analysed by developing a model and finding the various indices of system effectiveness like mean time to filter clogging, expected up (flying) time, expected number of precautionary landings etc. The regenerative point technique has been used for the purpose. The obtained measures have been further used to analyse the profit generated by the system. Graphical study of the proposed model has also been done. The suggested methodology finds its application in commercial aviation sector.

Stochastic analysis of a three-unit non-identical repairable system with priority to main unit for operation and repair

Here, stochastic analysis of a three-unit repairable system is carried out with one main unit (class I unit) and two cold standby identical secondary units (class II units). The secondary units are less efficient than the main unit and neither can bear the load of the main unit. However, the secondary units can work simultaneously at the failure of the main unit. The priority is given to the class I unit for operation and repair. Repair activities are handled by a single server and assumed to be perfect. Failures of class I unit and class II units are different but constant. The repair distributions of both types of units are taken as general. The expressions for reliability measures and profit function are derived using Semi-Markov Process (SMP) and regenerative point technique. The application of the proposed model can be visualised in a power supply system.

Stochastic analysis of a three-unit non-identical repairable system with priority to main unit for operation and repair

Here, stochastic analysis of a three-unit repairable system is carried out with one main unit (class I unit) and two cold standby identical secondary units (class II units). The secondary units are less efficient than the main unit and neither can bear the load of the main unit. However, the secondary units can work simultaneously at the failure of the main unit. The priority is given to the class I unit for operation and repair. Repair activities are handled by a single server and assumed to be perfect. Failures of class I unit and class II units are different but constant. The repair distributions of both types of units are taken as general. The expressions for reliability measures and profit function are derived using Semi-Markov Process (SMP) and regenerative point technique. The application of the proposed model can be visualised in a power supply system.

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

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.

Profit analysis of a warm standby non-identical unit system with single server performing in normal/abnormal environment

A system/unit is called working in normal environment if it is operating within prescribed conditions set by the manufacturer, otherwise the system is called working in abnormal environment. For example; a hydraulic machine having capacity uplifting the weight of 500 tons exceeds its capacity is termed as working in abnormal environment conditions. In this paper, profit analysis of a warm standby non-identical unit system with single server subject normal/abnormal environment conditions has been discussed. There is a single server who is allowed to do job in normal weather condition only and while performing its job it adopts FCFS (first come first serve) policy. The system model consists of two non-identical units—one is operative and the other kept as warm standby. The main unit may fail directly from normal mode, while failure of warm standby unit takes place owing to remaining unused for a longer period of time. The time taken for repair activity by the server follows negative exponential distribution. The expressions of various reliability measures are analyzed in steady state using semi-Markov process and regenerative point technique. Also, take the arbitrary values for the parameters (i.e., λ, μ, ϕ and θ) to delineate the behavior of some important performance measures to check the efficacy of the system model under such situations shown in the graphs.

Probabilistic Analysis of a Ceramic Tile Production System Considering Various Redundant Subsystems and Inspection

The present paper gives analysis of a stochastic model for a ceramic tile production system considering its five main subsystems viz. Ball Mill, Spray Dryer, Hydraulic Press, Glaze Line and Kiln and a storage system, Silo. It was considered that the failure of Ball Mill and Spray Dryer subsystems depends upon Silo while failure of other subsystems are independent of Silo. Also the storage in Silo is consumed during the repair/replacement of the failed subsystems then the system goes to failure otherwise it is operative. During the occurrence of failure in subsystems Hydraulic Press, Glaze Line and Kiln, leads to the failure in other subsequent subsystem and the repairman first inspects in which redundant unit of the subsystem has a fault and then accordingly repair/replacement is carried out. The system has been analysed using Markov process and regenerative point techniques. Various conclusions for the system regarding its reliability and availability are drawn by plotting several graphs for a particular case.

Stochastic behavior of dissimilar units cold standby system waiting for repair

Investigation of the time behavior of repairable systems spans a very large class of stochastic processes. The repetition of the same events connects the theory of reliability with Markov and semi-Markov processes. Exploiting this theory, the present study deals with two repairable dissimilar units’ cold standby system waiting for repair facility after failure of system units. Also, the regenerative point technique has been employed to obtain various reliability measures for the assumed system. Next, a particular case with exponential failures, arbitrary waiting and arbitrary repair rate is simulated followed by conclusions in the last section.

Modelling and analysis of two-unit hot standby database system with random inspection of standby unit

Stochastic model for a two-unit hot standby database system comprising of one operative (primary unit) and one hot standby unit has been developed. The primary unit acts as production unit which is synchronised with hot standby unit through online transfer of archive redo logs. The data being saved in the primary unit gets simultaneously stored in the hot standby unit. The different modes of failure of primary database have been considered. To avoid loss of data, random inspection of the standby unit is carried out by a database administrator (DBA) to see as to whether redo log files are created/updated in standby unit or not. The repair of the failed unit and creation/updation of redo log files are also done by the DBA. The system is analysed using semi-Markov process and regenerative point technique. Mathematical expressions for various performance measures of the system have been obtained along with cost-benefit analysis of the system. Numerical analysis has been done to validate the derived results. Bounds for various parameters have also been obtained with regard to profitability of the system.