Monika Saini

Cost -Benefit Analysis of a Single-Unit System with Preventive Maintenance and Weibull Distribution for Failure and Repair Activities

Abstract This paper deals with a reliability model developed for a single-unit system which goes for preventive maintenance after a pre-specific time ‘t’ up to which no failure occurs. There is a single server who takes some time to arrive at the system for doing repair activities. The unit does not work as new after repair at complete failure and so called the degraded unit. The degraded unit is replaced by new one after its failure with some replacement time. The failure time, preventive maintenance time, replacement time and repair time of the unit are taken as Weibull distributed with common shape parameter and different scale parameters. The switching devices are perfect. The system is observed at suitable regenerative epochs to obtain various measures of system effectiveness of interest to system designers and operation managers.

Comparison of Various Reliability Measures of a Computer System with the Provision of Priority

In this study the comparative analysis of various reliability measures of a computer system is carried out under the concepts of maximum repair time, maximum operation time, and priority. An immediate repair facility is provided to the system. The system consists of two identical unit one in operative mode and other in cold standby mode. For the derivation of various reliability measures, two stochastic models are developed hereby using the concept of priority. Priority to preventive maintenance over h/w repair in Model II whereas no priority is given in Model I. The failure time distribution of the s/w and h/w follows exponential while other random variables are taken as arbitrary. Graphs are drawn with respect to preventive maintenance to analyze the mean time to system failure and profit function of both models comparatively.

Analysis of a redundant system with priority and Weibull distribution for failure and repair

Abstract The main objective of the present study is to analyse a redundant system under the concept of priority and Weibull distribution for all random variables with different scale parameter and common shape parameter. For this purpose, by using semi-Markovian approach and regenerative point technique a reliability model is developed for a two non-identical unit system. A single repair facility is provided to the system to perform all repair activities. After a pre-specified time to enhance the performance and efficiency of the system the unit goes for preventive maintenance (PM). Priority to the repair of original unit is given over the PM of duplicate unit. Numerical results for the mean time of system failure, availability and profit function have been derived for a particular case to highlight the importance of the study.

Profit Analysis of a Computing Machine with Priority and s/w Rejuvenation

The main concentration of the present study is to carry out the profit analysis of a computing machine using the concepts of priority to software rejuvenation over hardware component’s preventive maintenance and hardware repair. For this purpose, a stochastic model is designed which comprises of two identical units. Cold standby redundancy technique is used in the development of the model. A single repair facility remains available with the system to do all repair activities, and he takes the system for preventive maintenance after a specific period of time. All repair and maintenance are perfect. The random variables are all Weibull-distributed. Using semi-Markov processes, Laplace transformation, and regenerative point technique recurrence relations and numerical results are obtained for various measures of system effectiveness.

Probabilistic Analysis of Performance Measures of Redundant Systems Under Weibull Failure and Repair Laws

The aim of the present paper is to analyze probabilistically various performance measures of two redundant systems under Weibull failure and repair activities using semi-Markov processes and regenerative point technique. Two stochastic models comprise of one original and one duplicate units are developed with the provision of a single repair facility and priority. All repairs and preventive maintenance, after a pre-specific time, are perfect. Recurrence relations of availability, mean time to system failure and profit function for both the models are derived. To highlight the importance of the system, numerical and graphical results for the difference of both models are obtained with respect to failure rate of original unit.

Ratio estimators for the finite population mean under simple random sampling and rank set sampling

This paper proposes ratio estimators for the population mean by using auxiliary information efficiently under simple random sampling (SRS) and rank set sampling (RSS). We obtain the bias and mean square error for the proposed estimators and show that the proposed estimator under RSS is more efficient than the estimator under SRS. The results have been illustrated numerically through simulation study.

Analysis of some reliability measures of single-unit systems subject to abnormal environmental conditions and arbitrary distribution for failure and repair activities

Abstract This article analyzes the effect of abnormal environmental conditions on various reliability measures. After the continuous operation of single-unit systems for a long duration of time these systems cannot be restored again in a younger state after the failure of the system. The unit does not remain as new after repair. This phenomenon is known as degradation and the unit after repair is called degraded unit. Preventive maintenance is a proactive method to tackle and overcome from these types of problems. For this purpose, a stochastic model is developed for single-unit systems by using semi-Markov process. There is a single server who inspects the failed unit after failed to check the feasibility of repair and replacement. If repair is not feasible then unit is replaced with some replacement time. The failed unit after repair becomes degraded and degraded failed unit is replaced by new one. All time distributions are arbitrary distributed like Weibull distribution with common shape parameter and different scale parameters. The switching devices are instantaneous. The system is observed at suitable regenerative epochs to obtain various measures of system effectiveness of interest to system designers and operation managers.

Analysis of a Single-Unit System with Weibull Failure and Repair densities Subject to Server Failure

The main concentration in the present paper is to analyze a single- unit system using the concepts of inspection, degradation, preventive maintenance, and server failure. A single repair facility inspect the original and degraded unit upon failure to check the feasibility of repair. The repair facility may fail during maintenance, repair and inspection and undergoes for treatment with Weibull probability density function. The unit after repair becomes degraded. Switch devices are perfect. All random variables like repair time, failure time, inspection time and treatment rate are independent and statistically independent. For the analysis of the system various measures of system effectiveness are obtained by using semi-Markov processes and regenerative point technique. With the help of numerical and graphical results for MTSF, availability and profit functions it is concluded that present system is more reliable, available and profitable, when random variables have less vale of shape parameters. Keywords: System, Availability, Inspection, Degradation and Preventive Maintenance

Stochastic Analysis of a Redundant System with Maximum Repair Time and Priority for Operation over Preventive Maintenance

The main goal of the present study is to analyze a redundant system by using the concept of priority to operation over Preventive Maintenance (PM) and Maximum Repair Time (MRT). For this purpose, two stochastic models are developed. The concept of MRTis studied in the second model in addition to the assumptions of first model. There is a single server who visits the system immediately as and when required. The server takes the unit under preventive maintenance after a maximum operation time at normal mode if one standby unit is available for operation. If the repair of the failed unit is not possible up to an MRT, failed unit is replaced by new one. The failure time, maximum operation time and MRT distributions of the unit are considered as exponentially distributed while repair and maintenance time distributions are considered as arbitrary. Various measures of system effectiveness are obtained by using the technique of semi-Markov process and RPT. To compare the performance of stochastic models graphs for several reliability measures are drawn.

Some Estimators for Population Mean under Estimated Multi-auxiliary Informationat SSU Level

Abstract This paper deals with the newdifference, regression and predictive estimators for two stage sampling by usingdouble sampling technique in which multi-auxiliary informationis estimated at SSU level and analyzes their properties. The efficiency of suggested estimators has been compared empirically.