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

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.     

Cost analysis of an electronic repairable redundant system with critical human errors

In this paper, an electronic system consisting of two subsystems connected in series has been considered. One subsystem consists of two identical units connected in parallel while the other subsystem has only one unit. The system is to be in any of the three states: good, degraded and failed. The system suffers two types of failures, viz; unit failure and failure due to critical human error. The system can be repaired when it fails due to the failure of the units in the subsystems and cannot be repaired when it fails due to critical human errors. The repair for 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.     

Cost analysis of a 3-state 2-unit reparable system

This paper presents the cost analysis of a 2-unit system with 3 states: good, degraded and failed. The units suffer from two types of failure: partial and catastrophic. The partial failure brings a unit to degraded state, whereas the catastrophic failure breaks down a unit completely. There is one repair facility, which is availed only when the system is either degraded or failed. The failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of various probability states have been obtained along with steady-state behaviour of the system. Inversions have also been computed so as to obtain time dependent probabilities, which determine expected profit as well as availability of the system at any time.     

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

In this paper investigations have been carried out for the availability and mean time to failure analysis of a three unit repairable electronic equipment having three states; viz; good, degraded and failed under critical human errors. The three states three units repairable electronic equipment suffers two types of failures; viz; unit failure and failure due to critical human errors. Entire system can fail 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 are obtained along with steady state behaviour of the equipment. A numerical example has also been appended to highlight the important results. Three graphs have also been given in the end. There is only one repair facility, which is availed only when the system is in either degraded or failed state due to unit failure.     

Stochastic behaviour of a two-unit cold standby redundant electronic equipment under human failure

This paper presents a mathematical model to evaluate availability and M.T.T.F. of a two-unit cold standby system with three possible states of each unit; viz. good, partially failed and failed, incorporating the concept of human failure. The model has been developed for exponential failures and general repairs. Single service facility is available in each state during the operational stage of the electronic equipment. Laplace transforms of the various state probabilities have been obtained. Steady-state probabilities, steady-state availability and mean time to failure have been derived.     

Cost analysis of a multi-component parallel redundant complex system with overloading effect and waiting under critical human error

The cost analysis of a multi-component parallel redundant complex system is considered, incorporating the concept of overloading effect and waiting time for repair under critical human error. Failure and waiting times follow an exponential time distribution, whereas repair time follows a general distribution. Using the supplementary variable technique, Laplace transforms of the probabilities of the complex system being in various states have been computed. Some graphs have been plotted to highlight the main results.     

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

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.     

MTTF and availability evaluation of a two-unit, two-state, parallel redundant complex system with constant human failure

This paper deals with MTTF and availability analysis of a two-state complex general repairable system consisting of two units arranged in parallel. Single service facility is available for the service of unit failure. The failure and repair times for the system follow exponential and general distributions respectively. Laplace-transforms of the various state probabilities have been derived and steady state behaviour of the system has also been examined. Availability at any time is obtained by the inversion process. To make the system more compatible with the physical situation, MTTF for the system has also been evaluated and various graphs have been plotted to highlight the utility of the model.     

Availability analysis of a repairable system with common-cause failure and one standby unit

This paper investigates the mathematical model of a system consisting of two non-identical parallel redundant active units, with common-cause failure, and a cold standby unit. The failed units are repaired one at a time or are repaired together, if they fail due to common cause failure. All repair time distributions are arbitrary and different. The analysis is carried out under the assumption of having a single service facility for repair and replacement.Applying the supplementary variable technique, Laplace transforms of the various state probabilities are developed. Explicit expressions for the steady state probabilities and the steady state availability are derived.Some well known results are obtained as special cases. A numerical example is given to illustrate the effect of the repair policy on the steady state probabilities and the availability of the system.     

Reliability and availability analysis of a k-out-of-N:G redundant system with repair in the presence of chance of multiple critical errors

The paper presents a reliability and availability analysis of a k-out-of-N:G redundant system with repair facilities in the presence of chance of multiple critical errors. The system is in a failed state when N−k+1 units have failed or any one of the multiple critical errors has occurred. Failed units and failed system will be repaired with constant repair rate to state with N−k+1 failed units. Laplace transforms of the state probabilities, the reliability and the availability of the system are derived. The system steady-state availability is also given.     

Operational behaviour of a three state standby redundant electronic equipment under critical human errors

This paper deals with the operational behaviour of a cold-standby redundant system incorporating the concept of three states, with four types of failures, namely major unit failure, minor unit failure, partial failure due to critical human errors and complete failure due to critical human errors, under only one repair facility. Failure and repair times for the complex system follow exponential and general distributions, respectively. Repair is undertaken only when the system is either in degraded state or in failed state. Laplace transforms of the probabilities of being in various states as well as in up and down states are computed, along with the steady state behaviour of the system. A particular case of such a system has also been appended to highlight the important results.     

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

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 Abel's lemma, steady state behaviour has also been examined. Some important graphs have been sketched at the end to highlight the important results.     

Reliability and MTTF evaluation of a repairable complex system under waiting

This paper deals with the reliability and mean time to failure (MTTF) evaluation of a complex system under waiting incorporating the concept of hardware failure and human error. Failure rates of the complex system follow exponential time distributions, whereas repair follows a general repair time distribution. Laplace transforms of various state probabilities have been evaluated and then reliability is obtained by the inversion process. A formula for variance of time to failure has also been developed. A particular case is also given to highlight some important results. Moreover, various plots have been sketched at the end.     

A multicomponent two-unit cold standby system with three modes

This paper investigates a mathematical model of a two-unit cold standby redundant system with three possible states of each unit—normal, partially failed and failed. Each unit has n components, each having a constant failure rate and a repair rate, an arbitrary function of the time spent. These vary from component to component. Steady-state probabilities, steady-state pointwise availability, mean time to system failure and Laplace transforms of various transient probabilities have been obtained. Several earlier results are verified as special cases.     

Cost analysis of a system with common cause failure and two types of repair facilities

A mathematical model to predict the cost involved to run an n-component single unit system which can fail in n-mutually exclusive ways of total failure or due to common cause, has been developed. Each component has two modes (normal and failure) with two types of repair facilities. Repair rates are arbitrary functions of the time spent. All other transition rates are constant. Laplace transform of the state probabilities are developed along with steady-state behaviour of the system. Inversions are computed to determine the expected profit and availability of the system at any time.     

Reliability analysis of a k-out-of-N:G parallel redundant system with multiple critical errors

This paper presents a reliability and availability of a k-out-of-N:G parallel redundant system with multiple critical errors while failed unit is not repaired. The system is in a failed state when a critical error occurred or k units have failed. Failed system repair times are arbitrarily distributed. Laplace transforms of state probabilities and reliability of the system are derived. The steady-state availability is also given.     

Stochastic behaviour of a two-unit paralleled system

This paper deals with a two-unit paralleled system with a single repair facility. Most papers on this subject assumed that at least one of the life time and repair time distribution is exponential. However the above assumption is violated by this paper. Then the various state probabilities (densities) have derived by employing the method of supplementary variables. We obtain the stochastic behaviour from these probabilities; (1) the long-run availability, (2) the idleness probability for the repair crew, and (3) the expected number (per unit time in long run) of system failures. Also comparison between the constant failure rate and non-constant failure rate is shown by numerical example.     

Stochastic behaviour of a three-state complex repairable system with three types of failures

This paper deals with the operational availability of a three-state complex repairable system consisting of n distinct units arranged in series. Single service facility is available for three types of failures of the complex system. A mathematical model for the complex system under severe restrictions has been developed for exponential failures and general repairs. Laplace transforms of various state probabilities have been evaluated and availability is then obtained by the inversion process. Few graphical illustrations are also given in the end so as to explain the practical utility of the model.     

Availability analysis of a robot with safety system

This paper presents availability analysis of a system composed of a robot and its associated safety system. The failed robot system is repairable and its associated repair rates could be constant or non-constant. The supplementary variable and Markov techniques were employed to obtain expressions for steady state availability, state probabilities, and Laplace transform of the state probabilities. Various plots are presented.     

Reliability and availability analysis of a system with warm standby and common cause failures

This paper presents reliability and availability analyses of a two unit parallel system with warm standby and common-cause failures. The standby and switching mechanisms are subject to failure. The failed system repair times are assumed to be arbitrarily distributed. Expressions for Laplace transforms of system state probabilities, steady state system availability, system reliability, and mean time to failure are developed.