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

This paper deals with the availability, MTTF and the cost analysis of a single server complex system consisting of two classes A and B with three possible states, viz. good, degraded, failed and suffers two types of failure, viz. unit failure and failure due to critical human errors.Sub-system A has two dissimilar units arranged in parallel whereas sub-system B has three non-identical units arranged in series. Failure and repair times have exponential and general distributions respectively. There is only one repair facility when the system is in failed state due to failure of sub-system B. Several parameters of interest are obtained using the supplementary variable method. A numerical example has been appended. Five graphs have also been given in the end.     

Reliability and MTTF analysis of a non repairable parallel redundant complex system under hardware and human failures

This paper deals with the evaluation of point-wise availability and M.T.T.F., of a two-unit standby redundant electronic equipment, incorporating the concept of human failures. Single service facility is available for the service of constant failure. Using the supplementary variable technique, general equations are set up for deriving the above two measures. In addition, steady state availability is also derived and some important graphs have been sketched in the end.     

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.     

Cost analysis of a three-state parallel redundant complex system

This paper deals with the cost analysis of a three state system consisting of two independent units in parallel redundancy. The failure and repair times for the system follow exponential and general distributions respectively. The Laplace-transforms of various state probabilities have been derived and steady state behaviour of the system has also been examined. A few particular cases have also been discussed at the end to highlight the utility of the model.     

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.     

Reliability analysis of a three-state multi-component warm standby redundant complex system with waiting for repair

Investigations have been carried out with the help of Laplace transforms and supplementary variable techniques for the evaluation of reliability analysis of a three-state multi-component warm standby redundant complex system suffering three types of failures, namely minor, major, and human due to critical human errors incorporating the concept of waiting for repair.     

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.     

Cost analysis, availability and MTTF of a three state standby complex system under common cause and human failures

The paper deals with the pointwise availability, steady state availability, MTTF and variance of the time to failure of 3 state, 1-out-of-2 unit systems with cold standby, under common cause and human failures. The cost function analysis is also to get the expected gain over the time. Several graphs are presented to interpret the results.     

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

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.     

A two non-identical three-state units redundant system with common-cause failures and one standby unit

This paper presents a mathematical model for predicting a two non-identical three-state active units redundant system with common-cause failures and one standby unit. The units may fail in either of two mutually exclusive failure modes or by the occurrence of common-cause failures. System is only repaired when all the units fail (including the standby unit). The failure rates of units are constant and system repair times are arbitrarily distributed. Laplace transforms of the state probabilities are derived.     

N-unit parallel redundant system with multiple correlated failures

This paper deals with mathematical models of an N-unit parallel redundant system with one repair facility and multiple correlated failures. These models are generalized on the basis of the results obtained previously and related to a system subject to a process of single failures and double and N-unit correlated failures. The method of the supplementary variable in two models differing by the repair policy is used. We obtain the following results: for both models the stationary availability, and for the second model the Laplace transform (L.T.) of the system reliability, L.T. of the pointwise a vailability, and the mean time to system failure (MTSF).     

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.     

Cost analysis of a three-state standby redundant electronic equipment

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.     

A k-out-of-N:G three-state unit redundant system with common-cause failures and replacements

A mathematical model for predicting a k-out-of-N:G three-state unit redundant system with common-cause failures and failed system with replacement units has been developed. Laplace transforms of the state probabilities are derived. The steady-state probabilities, frequency of encountering and the average duration of residence in a state are also reported.     

Reliability analysis of a repairable parallel system with standby involving human error and common-cause failures

This paper presents two analytical models of special multiple-state devices with repair. The failure rates are constant and the repair rates between failure states are constant, while the repair rate times between failure state and good state are arbitrarily distributed. Laplace transform of the state probabilities and steady-state availability are derived.     

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.     

Availability of a man-machine system with critical and non-critical human error

This paper presents a newly developed probabilistic model representing two units in parallel and one on standby system with critical and non-critical human error. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. A general formula for the system steady-state availability is developed with the aid of the method of supplementary variables, the Markov approach and Laplace transforms. Specific plots and tables are shown to demonstrate the impact of critical and non-critical human errors on system steady-state availability.     

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.     

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.