R.K. Sharma

Reliability analysis of a two state repairable parallel redundant system under human failure

Abstract In this paper, the investigations have been carried out for the MTTF and reliability analysis of a repairable two-unit redundant electronic equipment having two states under human failures. The two-unit repairable parallel redundant system suffers two types of failures; viz; unit failure and human failure. Human failure brings the system to a complete failure stage. There is only one server who is always available. Laplace transforms of the probabilities of the complex system being in up and down states have been derived and have been inverted to obtain time dependent probabilities. Two graphs have also been given in the end.

Availability and MTTF analysis of a three-state parallel redundant multi-component system under critical human failures

Abstract This paper deals with the availability and mean time to failure of a single server complex system made up of two classes A and B under critical human errors. Sub-system A has two identical components arranged in parallel whereas B has N non-identical components arranged in series. The complex redundant system has three states, viz. good, degraded, failed and suffers two types of failures, viz. unit failure and failure due to critical human errors. The failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of the probabilities of the complex system being in various states have been obtained along with steady state behaviour of the equipment. A numerical example has also been appended in the end to highlight the important results. There is only one repair facility, which is availed only when the system is in failed state due to failure of sub-system B.

Cost analysis of a three-state repairable redundant complex system under various modes of failures

Abstract In this paper, a mathematical model for the evaluation of expected profit during the time interval (0, t] and availability at an instant t under human failure has been set up. The model consists of two subsystems arranged in parallel having three states for operation. The first subsystem consists of two identical units in series whereas the second subsystem has only one unit. Failure and repair times for the system follow exponential and general distributions respectively. Repair is undertaken only when the system is in a reduced efficiency state. Using supplementary variable and Laplace transforms techniques, time dependent probabilities of the complex system being in various states have been computed along with the steady state behaviour of the system. A particular case has also been discussed to highlight the important results.

Cost analysis of a three-state standby redundant electronic equipment

Abstract In this paper, the investigations have been carried out for the cost function analysis of a standby redundant system having three states. The two-unit standby redundant system suffers two types of failures: viz. minor and major, which bring the system to degraded or a complete failure stage. There is only one server and is always available. Failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of the probabilities of the complex system being in various states have been derived, which have been inverted further so as to obtain time dependent probabilities. To highlight the important results, two graphs have also been given in the end.

Cost analysis of a two unit, three state standby redundant complex system with two types of repair facilities under waiting

Abstract This paper deals with the cost analysis of a two unit, three state standby redundant complex system, incorporating the concept of two types of repair facilities, viz. minor and major repair. The concept of waiting time for the major repair of the failed system has also been introduced. The system can suffer from two types of failures, namely catastrophic and partial. Failure and waiting times of units follow exponential time distribution, whereas repair of units follows general time distribution. Using the supplementary variable technique, Laplace transforms of probabilities of the complex system being in various states have been computed. In addition, using Abels lemma, steady state behaviour has also been examined. Some important graphs have been sketched at the end to highlight the important results.

Evaluation of MTTF and reliability of a power plant by BF technique

In this paper, investigations have been carried out for the evaluation of reliability and MTTF (mean time to failure) of a parallel redundant complex system; viz. a power plant. The object of the system is to supply power generated by generators from a power house to a very important consumer, connected by cables and switches. The reliability and MTTF have been evaluated by using Boolean Function (BF) technique. Failure times for the various components of the complex system follow arbitrary distribution. A numerical example has also been appended to highlight the important results. Two graphs on reliability and MTTF have also been given in the end to forecast the operable behaviour of the system at any time.

Reliability and MTTF analysis of a power plant consisting of four generators by Boolean function technique

Abstract This paper investigates the reliability behaviour of a non-repairable parallel redundant complex system which is nothing but a power plant. The object of the system is to supply power generated by three generators from a power house to a very critical consumer, connected by cables and switches etc. The reliability of the power supply to the critical consumer has been obtained by using the Boolean Function technique. Moreover, an important parameter of reliability, viz . M.T.T.F. (mean time to failure), has also been computed for exponential failure rates of components. A numerical example with graphs has also been appended in the end to highlight the important results.

Cost analysis of a 2-unit standby redundant electronic system with critical human errors

Abstract In this paper, investigations have been carried out for the evaluation of availability and expected profit during the operable stage of a standby redundant, electronic system, incorporating the concept of human failure. The system can be in any of the three states: good, degraded and failed. One repair facility is available for the repair of a unit in failed or degraded state. The system cannot be repaired when it fails due to critical human errors. The repair of the system in any state follows general distribution. To make the system more applicable to practical life problems, time dependent probabilities have been evaluated so as to forecast the expected profit and the operational availability of the system at any time.

An algebraic method for reliability calculations

Abstract This paper evaluates the reliability behaviour of a complex system consisting of three sub-systems G1, G2 and G3 connected in parallel redundancy (1-out-of-3: G). These sub-systems are nothing but three power generators in a power house which are connected with switching devices. By the application of Boolean function technique and the theorem of summation of probabilities of compatible events, a symbolic expression for reliability of such a complex system has been evaluated by considering that failure times for various components of the complex system follow arbitrary distributions. In particular, reliability has been evaluated for exponential and Weibull distributions. Moreover, an important parameter, viz. MTTF, has also been computed for exponential failure rates of the units comprising the system. A numerical example, along with graphs, is discussed at the end to highlight the important results.

Evaluation of reliability and M.T.T.F. of a power plant with the aid of Boolean function expansion algorithm

Abstract In this paper, investigations have been carried out for the evaluation of reliability behaviour of a power plant with the aid of Boolean function expansion algorithm. The complex system under consideration consists of two power generators in a power house. The object of the system is to supply power from a power house (generated by generators) to critical consumers fed from an output main switch and, consequently, the reliability of the power supply has been calculated by considering that failure times for various components, viz. cables, generators and main switch boards, etc., follow arbitrary distribution. In particular, system mean time to failure (M.T.T.F.) has also been calculated for exponential failure time distribution. Some graphs have also been plotted to highlight the utility of the model.