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 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 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.     

Stochastic behaviour of a standby redundant system with three modes

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system in which each unit works in three different modes-normal, partial failure and total failure. Failure-time distributions of units are exponential, whereas repair-time distributions are arbitrary. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure and steady state availability of the system are obtained. A few particular cases are discussed.     

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 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.     

Some characteristics of a two-dissimilar-unit cold standby redundant system with three modes

This paper deals with the stochastic behaviour of a two-dissimilar-unit cold standby redundant system in which each unit works in three different modes—normal, partial failure and total failure. It is assumed that the failure and repair times are stochastically independent random variables each having an arbitrary distribution. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Explicit expressions for the Laplace-Stiektjes transforms of the distribution function of the first passage time, mean time to system failure, pointwise availability and steady state availability of the system are obtained. Certain important results have been derived as particular cases.     

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.     

Analysis of a two unit standby redundant fail-safe system

This paper evaluates reliability and fail-safety of a two unit cold standby fail-safe redundant system. Three modes of failure—(1) failure due to human error, (2) failure due to unit faults and (3) failure due to switchover faults—are considered. The complete failure states of the system are divided into two categories, fail-safe state and fail-dangerous state. Several fail-safety measures of interest to a fail-safe system designer are defined and evaluated, such as safety function, safety ratio and danger ratio.     

Stochastic behaviour of a two-unit cold standby redundant system with administrative delay and two types of repairs

In this paper we consider a two-unit cold standby redundant system in which each unit works in three modes—normal, partial failure and total failure with two types of repairs (major and minor) after partial failure mode, with administrative delay to locate expert repair man for major repair. The administrative time distribution is assumed to be exponential, whereas the repair and failure time distributions are exponential and arbitrary. The technique of regenerative processes is applied to obtain various reliability characteristics of interest to system designers.     

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.     

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.     

Reliability analysis of a complex system with a deteriorating standby unit under common-cause failure and critical human error

This paper presents a stochastic model representing two units and one as a standby unit with critical human error and common cause failure. The deteriorating effect of the standby unit on the system is studied. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. The analysis is carried out using supplementary variable techniques and various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.     

Stochastic behaviour of a two-unit (dissimilar) hot standby system with three modes

A hot standby system composed of two non-identical units is analysed under the assumption that each unit works in three possible modes—normal, partial failure and total failure. For each unit the failure time distribution is negative exponential and the repair time distribution is arbitrary. Breakdown of the system occurs when both the units are in total failure mode. There is only one repair service and when both the units are in the same mode, priority is given to the first unit in the matter of operation as well as repair. Several reliability characteristics of interest to system designers and operations managers have been evaluated.     

Stochastic behavior of a two-dissimilar-unit standby redundant system with repair maintenance

A standby redundant system of two dissimilar units is considered under the assumptions that both the failure and the repair time distributions are arbitrary. The system states are defined corresponding to the failure of the specified units. The first passage time distributions, the expected numbers of visits to a certain state, the transition probabilities, and the limiting probabilities are obtained using the unique modifications of the regeneration point techniques in Markov renewal processes. Two particular cases are finally presented.     

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.     

Stochastic behaviour of a two-unit cold standby system with three modes and allowed down time

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system under two very general sets of conditions: (i) each unit of the system having three different modes of working—normal, partial failure and total failure; (ii) breakdown of the system occurring when with both the units in total failure mode, the system is not regarded as failed (the system fails only when the breakdown does not terminate within the allowed down time). Failure-time distributions of units are exponential, whereas repair time distributions are arbitrary. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

Stochastic analysis of a warm standby system with repair in the presence of chance of multiple critical errors

The paper presents a stochastic analysis of a k active and N warm standby system with r repair facilities in the presence of chance of multiple critical errors. The system is in a failed state when N+1 (active and/or warm) units have failed or any one of the multiple critical errors has occurred. Failed units will be repaired with constant repair rate. The failed system due to critical errors will be repaired with constant repair rate to state with N+1 failed units. Laplace transforms of the reliability and the availability and the steady-state availability of the system are given.     

Optimal maintenance of a two-unit standby redundant system with a generalized cost structure

To maintain a system there are generally several alternatives available to a decision maker. In this paper a usual 2-unit standby system is considered with exponential distribution for life-time of units and arbitrary distribution for repair time. A generalized cost structure with different earning rates in different states, transition rewards and discounting, has been superimposed upon the semi-Markov process generated by the system model. An optimal maintenance policy for the system is the one that maximizes profit rate of the system. A solution algorithm, based on Howard's policy iteration method, is developed. An illustration is presented at the end.