S. C. Malik

Reliability and profit analysis of two single-unit models with three modes and different repair policies of repairmen who appear and disappear randomly

Abstract Cost-benefit analysis of a single-unit system with three possible modes of the unit—normal (N), partial failure (P) and complete failure (F)—is carried out. The paper consists of two models: in model 1, the unit goes under repair (if a repairman is available) the moment it fails partially, whereas in model 2 the unit goes under repair at complete failure. The repairman appears in, and disappears from, the system randomly. A comparison between these two models after calculating MTSF and profit has also been made.

Profit analysis of a 2-out-of-2 redundant system with single standby and degradation of the units after repair

The purpose of this paper is to carry out the profit analysis of a three unit redundant system in which two units work in parallel and one unit is kept as spare in cold standby. Each unit has direct complete failure from normal mode. There is a single repairman (called server) who visits the system immediately to do repair, inspection and replacement of the units. The unit does not work as new after repair and so called a degraded unit. The degraded unit at its further failure undergoes for inspection to see the feasibility of its repair. If the repair is not feasible, it is replaced immediately by new unit. The system is considered in up-state if any two of original and/or degraded units are operative. The time to failure, repair and inspection of the units are taken as arbitrary with different probability density functions. By adopting semi-Markov process and regenerative point technique, the results for some measures of system effectiveness are obtained in steady state.

Analysis of a single-unit system with degradation and maintenance

Abstract A single-unit system is analyzed by considering the concepts of degradation and maintenance subjected to random shocks. A single server is called immediately to do repair activities. The maintenance of system is done by the server if it is suffered by the impact of shock. However, upon failure server repairs the unit. Repair of the unit is not perfect and it does not work as new after repair so called a degraded unit. The degraded unit is replaced by new one in case it is affected by the impact of shock. Server conducts inspection of degraded failed unit upon its failure to check the possibility of its repair. If repair of the unit is not possible, it is replaced by new one with some replacement time. Repair, maintenance, inspection, and replacement times all are arbitrary distributed whereas failure and shock times of the unit are exponentially distributed. Using regenerative point technique and semi-Markov process recurrence relations for several reliability measures are obtained. The numerical results for MTSF, steady state availability and profit functions are obtained with respect to shock rate.

Stochastic Modelling of a Computer System with Hardware Redundancy

this paper, an effort for the stochastic analysis of a computer system has been made considering the idea of hardware redundancy in cold standby. The hardware and software failures occur independently in the computer system with some probability. A single server is employed immediately to conduct hardware repair and software up- gradation on need basis. The repair and up-gradation activities performed by the server are perfect. The time to hardware and software failures follows negative exponential distribution, whereas the distributions of hardware repair and software up- gradation times are taken as arbitrary with different probability density functions. The expressions for various reliability measures are derived in steady state using semi- Markov process and regenerative point technique. The graphs are drawn for arbitrary values of the parameters to depict the behaviour of some important performance measures of the system model. up-gradation when needed. The repair and up-gradation activities performed by the server are perfect. The time to hardware and software failures follows negative exponential distribution while the distributions of hardware repair and software up-gradation times are taken as arbitrary with different probability density functions. The expressions for various reliability measures such as transition probabilities and mean sojourn times, mean time to system failure (MTSF), availability, busy period of the server due to hardware repair and software up-gradation, expected number of hardware repairs and software up-gradations and profit function are derived in steady state using semi-Markov process and regenerative point technique. The cost-benefit analysis has been made using these measures. The graphs are drawn for arbitrary values of the parameters to depict the behaviour of MTSF, availability and profit function of the system model.

A system with pre-inspection and two types of repairman

Abstract The present paper deals with a two-unit cold standby system with pre-inspection and two types of repairman—one regular and the other expert. The regular repairman first inspects every unit that fails to ascertain whether he is able to repair it or not. If he can repair it, it is alright, otherwise an expert repairman is called who comes immediately. The system has been analysed to determine the various reliability measures by using semi-Markov and regeneration processes. Graphs are also plotted for a special case.

Profit Analysis of a Computer System with H/W Repair and S/W Replacement

The main intension of this paper is to make profit analysis of a computer system of two identical units in which one unit is operative and other is kept as cold standby. In each unit, h/w and s/w components fail independently from the normal mode. A single server visits the system immediately whenever needed to carry out repair and replacement of the components. If there is a h/w failure in the unit, then that unit goes immediately under repair. However, only replacement of the s/w in the unit is made by new one whenever s/w fails to meet out the requirements. The failure time of the unit is exponentially distributed while the distributions of repair rate of h/w and replacement rate of the s/w are taken as arbitrary with different probability density functions (pdf). The expressions for several reliability characteristics are derived by making use of semi-Markov process and regenerative point technique. Graphs are drawn for a particular case to highlight the behaviour of some measures of system effectiveness. The results of the present model have also been compared with the results obtained for the model proposed by Malik and Anand [4].

Fuzzy Reliability Evaluation of a Fire Detector System

Reliability has vital significance to engineers and designers in a safety system. Consequently, failures free operation of components or sub-systems is of their key concern. To assess the reliability of such systems quantitatively, failure data of the components or sub-systems is essentially required. In general, such data is either not pre-recorded or present in linguistic form (good, bad etc). For quantitative evaluation of reliability the usual probabilistic considerations seems to be inadequate. Therefore, in this paper, conventional fault tree analysis (FTA) approach integrated with fuzzy theory has been used to evaluate the reliability of a fire detector system using fuzzy failure possibilities of components (or subsystems).