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.     

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.     

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 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.     

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.     

A reliability model for a k-out-of-N:G redundant system with multiple failure modes and common cause failures

The paper presents a reliability model of a k-out-of-N:G redundant system with M mutually exclusive failure modes and common cause failures. Failed system repair times are arbitrarily distributed. The system is in a failed state when (N−k+1) units failed or a common cause failure occurred. Laplace transforms of the state probabilities and the availability of the system are derived. Finally, the system steady-state availability is also reported.     

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.     

Cost analysis of a two-unit electronic parallel redundant system with overloading effect

A two-unit parallel redundant repairable electronic system with exponential failure-time distribution and overloading effect is considered. The system is to be in any of the three states: good, degraded and failed. One repair facility is available when the system is either in degraded or failed state. 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 operational availability of the system at any time. Using supplementary variable technique, Laplace transforms of various state probabilities have been evaluated. Making use of Abel's theorem, various time independent probabilities have been computed. Also the overloading effect for the expected profit on the operational availability of the complex system has been studied.     

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.     

A k-out-of-N:G redundant system with cold standby units and common-cause failures

This paper presents a k-out-of N:G redundant system with M cold standby units, r repair facilities and common-cause failures. The constant failure rates of the operating and cold standby units are different. Failed system repair times are arbitrarily distributed. The system is in a failed state when (N+M?k+1) units failed or a common-cause occurred. Laplace transforms of the state probabilities, the availability of the system and the system steady-state availability are derived.     

Robotic systems probabilistic analysis

This paper presents probabilistic analysis of a system comprised of a robot and its associated safety mechanism. The system can have various modes of failures and is repaired upon failure. The system failure rates other than the common-cause failure rate are assumed constant and the failed system repair times are assumed arbitrarily distributed. Three techniques are combined to perform analysis: Markov, the device of stages method, and the supplementary variable approach. Expressions along with plots for the robot system availability and state probabilities are presented.     

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.     

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.     

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.     

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.     

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.     

Availability analysis of a repairable standby human-machine system

This paper presents a model representing a two units active and one unit on standby human-machine system with general failed system repair time distribution. In addition, the model takes into consideration the occurrence of common-cause failures. The method of linear ordinary differential equation is presented to obtain general expressions for system steady state availability for failed system repair time distributions such as Gamma, Weibull, lognormal, exponential, and Rayleigh. Generalized expressions for system reliability, time-dependent availability, mean time to failure, and system variance of time to failure are also presented. Selected plots are presented to demonstrate the impact of human error on system steady state availability, reliability, time-dependent availability, and mean time to failure.     

A two-unit duplicating standby system with correlated failure-repair/vbreplacement times

This paper considers the stochastic analysis of a two-unit (original and duplicate) cold standby system model with preventive maintenance and replacement of the failed duplicate unit. The failed duplicate unit is non-repairable but its replacement is considered with an identical duplicate unit which is available instantaneously. Joint distributions of failure and repair/replacement times of original/duplicate units are bivariate exponential with different parameters. Various reliability characteristics of the system model under study are obtained by using regenerative point technique. Mean time to system failure and steady state availability have also been studied through graphs.     

Some large availability models: computation and bounds

A dynamic analytic solution is described for a 2^N state general availability model with N components having constant failure and repair rates. From this model, a family of models is developed using truncation and/or attenuation of transition rates. Expressions are derived for steady-state solutions. Then spread-sheet programs are: (1) given for obtaining these solutions, and (2) compared with BASIC programs yielding the same results. State probabilities of these truncation and level-attenuation models are either greater than or less than comparable states in the general model. Thus the states of the general model become either lower bounds or upper bounds for states in these two model types. Other bounds can be constructed from single exponentials based on steady-state probabilities. From this family of models, bounds should exist on state probabilities in models of similar structure but different constraints on failure and repair rates. A specific model is pursued where failures are restricted to any 2 components; and the failure rate of one component is assumed to change on second level of failure. Under these conditions, dynamic bounds on state-probabilities of the initial-state and some, but not all, steady state bounds on the other state probabilities can be found. Examples illustrate various bounds     

Reliability analysis of a k-out-of-n:G vehicle fleet

This paper presents a reliability analysis of a k-out-of-n:G on-surface vehicle fleet. The transit system is in a failed state when (n − k + 1) vehicles failed. Laplace transforms of state probabilities and reliability of the transit system are derived. The transit system steady-state probabilities and availability formulas are also developed.