On a two-dissimilar-unit standby system with three modes and administrative delay in repair

This paper considers a two-dissimilar-unit cold standby redundant system with three modes of each unit under the assumption that there is an administrative delay in getting the repair man at the system location. The system is analyzed by the semi-Markov process technique, assuming that the failure time, repair time and administrative time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Further, special cases of the results of this paper coincide with earlier results obtained by Pandey and by Gupta.     

Reliability analysis of a two-unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby redundant system subject to a single repair facility with exponential failure and general repair time distribution. Each unit can work in three different modes — normal, partial failure and total failure. There is a perfect switch to operate the standby unit on total failure of the operative unit. The system has been analysed to determine the reliability parameters e.g. mean time to system failure (MTSF), steady state availability, mean recurrence to a state and expected number of visits to a state, first two moments of time in transient state, by using the theory of Semi-Markov Process. Howard's reward structure has been super-imposed on the Semi-Markov Process to obtained expected profit of the system. A number of results obtained earlier are derived as particular cases.     

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.     

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 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.     

One unit reliability system subject to random shocks and preventive maintenance

In this paper we consider two systems each consisting of one unit. The operating unit is subject to random shocks which occur at random times. Due to the shock the following may happen: (i) The unit is not at all affected by the shock; (ii) the failure rate of the unit increases from λ₀ to λ₁; (iii) the unit fails. The failure time of the unit is exponentially distributed. The repair, shock and preventive maintenance times follow general distributions. In System 2 there is provision of preventive maintenance, whereas in System 1 there is no provision of preventive maintenance. There is one repair man available in each system. In this paper the mean time to system failure, steady state availablities and the impact of shocks on these are studied. In System 2 the effect of the preventive maintenance on MTSF and steady-state availabilities is investigated.     

Reliability Analysis of Systems Comprised of Units with Arbitrary Repair-Time Distributions

This work demonstrates the feasibility of reliability modeling of systems with repair capability using a semi-Markov process. A two-unit system with exponential failure times but general repair times is studied. Formulas for state-transition probabilities, waiting-time distribution functions, and mean time in each state are developed. These quantities are expressed in terms of the Laplace transform of repair time distribution functions. Once these quantities are known, mean time to system failure and system availability, as well as other system parameters, can be found using matrix manipulations. In addition, time-dependent results may be obtained. A numerical example varying the parameter in a repair-time law is presented. The formulas developed can be extended to larger systems with repair capability for only one unit at a time and exponential failure times.     

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 two-unit cold standby system with two types of operation and repair

This paper deals with the cost analysis of a single-server two-identical unit cold standby system and two types of repair—minor and major. The unit requires minor repair if it fails for the first time. The major repair is required only when the unit fails after the minor repair. Upon minor repair the unit does not work as a normal unit but as a quasi-normal unit which has a different (increased) failure rate from that of a new one. Upon major repair the unit works as good as new (normal unit). Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique the system characteristics of interest to system designers and operations managers have been obtained.     

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.     

Profit analysis of a cold standby system with two repair distributions

A single server two-identical unit cold standby system is analysed. Each unit has two operative modes—normal and quasi-normal. When a normal unit fails, it undergoes minor repair with probability p₁ and p₂ respectively. Upon minor repair unit works with reduced efficiency and is known as quasi-normal unit while upon major repair unit works as good as new (normal unit). When a quasi-normal unit fails, it undergoes minor or major repair with probability q₁ and q₂ respectively. Failure rates of normal and quasi-normal units are different. Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique in MRP the system characteristics of interest to system designers and operations managers have been obtained.     

Stochastic behaviour of a two-unit redundant system with switchover time

There is a two-unit standby redundant system. Standby is kept in cold state. Whenever one unit is operating and the other is in the waiting standby state, switching is initiated on the latter after a random time. If the operative unit fails before the time to initiate switching action on the waiting standby unit, the system fails and the failed unit immediately undergoes repair type 2 along with the switching. However, if the operative unit fails when the other unit is as standby (after switchover), the failed unit undergoes repair type 1 and the unit as standby takes over the operation. All the distributions are arbitrary except failure-time, which is exponential.The system is defined with the help of states which generate a pseudo semi-Markov process. Abundant use of results from the theory of SMP has been made to obtain a large number of parameters which measure reliability characteristics of the system viz. MTSF, steady-state availability, expected number of visits to a state, conditional transition probabilities, first passage time distributions, expected profit rate, etc. Numerical examples are included to illustrate the results.     

Availability analysis of a two-unit (dissimilar) parallel system with inspection and bivariate exponential life times

This paper investigates a two-units (non-identical) parallel system. Inspection is required to detect a failed unit but not the system with both failed units. The life time distribution of each unit is bivariate exponential (BVE) while the other distributions (i.e. repair, inspection and interinspection time) are arbitrary. Various state probabilities along with steady-state characteristics of the system are investigated.     

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 of Special Redundant Systems Considering Exchange Time and Repair Time

The reliability of a 2-out-of-3 parallel redundant system having a limited number of standby spare units is derived when the exchange of the failed unit for a spare unit is not instantaneous. The reliability can be represented in the form of a failure state diagram. When the number of standby spares and the repair rate are both small, the influence of the exchange rate is small. When the number of standby spares and the repair rate are both large, the influence of the exchange rate is large. The number of standby spares and the repair rate influence the probability that system failure occurs after all spare units have failed. The exchange rate strongly influences the probability of system failure during the exchange time.     

Reliability Considerations for a 2-Unit Redundant System with Erlang-Failure and General Repair Distributions

This paper considers the case of a 2-identical-unit redundant system with Erlang-failure and general repair distributions. Two cases are considered: 1) the failure of each unit is independent of the other; 2) when one unit fails, the failure distribution in the other unit changes. The Laplace transforms of the distribution of time to system failure and the explicit formula for the mean time to system failure are derived.     

Analysis of a two-unit hot standby system with three modes

This paper discusses the stochastic behaviour of a two-unit hot standby redundant system having exponential failure and a single repair facility with general repair time distribution. Each unit of the system has three possible states—normal, partial failure and total failure. Breakdown of the system occurs when both the units are in total failure mode. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.