Cost-benefit analysis of a one-server two-unit standby system subject to imperfect switching device,random inspection and k-failure modes

This paper deals with cost-analysis of a single-server two-unit cold standby system subject to random inspection and k-failure modes. A switch is used to operate the standby unit which works successfully with known probability p(=1 −q). The service facility plays the dual role of inspection and repair of both failed unit and failed switch. Identifying the system at suitable regenerative epochs, the integral equations are set up for the probabilities of system being in the “up” or “down” state. Laplace transform technique is adopted to solve these equations and various reliability characteristics of interest to system designers and operations managers have been obtained.     

Cost-benefit analysis of single server n-unit imperfect switch system with delayed repair

This paper deals with the cost-benefit analysis of a single-server n-unit system with an imperfect switch where failures of the items (units or the switch) are not detected unless either inspected by the server or when the system is down. Initially, one unit is put into operation (the switch is working at t = 0) and n − 1 units are kept as cold standbys. A failed unit is replaced by a standby if the switch and a standby are available. The server visits the system at random to check for the failed item and the check is instantaneous. When the system is down, either because of want of the standby or failure of the switch, the server is called for, and is assumed to arrive instantaneously. The revenue as well as the cost of repair are arbitrary functions of time. The expected net gain in (0, t) is evaluated assuming that all the life-time distributions are exponential and all the repair time distributions are arbitrary.     

Cost-benefit analysis of a two-server, two-unit, warm standby system with different types of failure

This paper deal with a two-server, two-unit redundant system in which one unit is operative and the other is a warm standby. The operative unit can fail completely, either directly from the normal state or via a partial failure, while the warm standby unit only fails due to minor faults within it. One repairman is “regular”, he always remains with the system, and the other is an “expert” who is called when needed. The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results and some graphs pertaining to a particular case are also included.     

Cost-benefit analysis of a system with inspection, replacement and two types of repair

This paper investigates a mathematical model of a system composed of two units—one operative and the other in cold standby. There is a single repair facility which serves the triple role of inspection, repair and replacement of a failed unit. After inspection, the unit goes to minor (major) repair with probability p(q = 1 − p). Whenever the failed unit goes to major repair, an order is immediately placed for a new unit to replace the unit under major repair. Failure, inspection and delivery time distributions are negative exponential, whereas repair time distribution is arbitrary. The system is analysed in detail using the regenerative point technique and several reliability characteristics of interest to system designers and operation managers are obtained. Earlier results are verified in particular cases.     

Higher moments in cost-benefit analysis

This paper deals with the cost-benefit analysis of one-server two-unit hot standby system with imperfect switch where the repair densities depend upon the type of items (unit/standby/switch) waiting for repair. Initially one unit is put to operation (switch is working at t = 0) and the other unit is kept as a hot standby. The revenue as well as the cost of repair are arbitrary functions of time. Explicit expressions are obtained for expected net gain in [0,t] from which other characteristics like expected busy period due to repair of unit/standby/switch, expected up-time, expected number of repairs completed of unit/standby/switch etc. can be obtained.     

Stochastic analysis of a multi-unit cold standby system working in orbit form

This paper considers the analysis of a single server n-similar unit system. Initially k(<n) units form an orbit which functions if one unit functions at a time and the remaining n − k units work as cold standbys. When a unit fails in the orbit it is instantaneously replaced by one of the standbys with the help of a perfect transfer switch. The system is said to fail when n − k + 1 units have failed. The distribution of time to failure and time to repair of a unit are negative exponential. Using the regenerative point technique several reliability characteristics are obtained to carry out the cost-benefit analysis.     

Switch failure in a two-unit standby system with better utilization of units

This paper analyses a two-unit cold standby system with three modes and a switching device to put the offline unit into operation. The cold standby starts operating only after it becomes active. When turned on, the transfer switch (TS) operates successfully with fixed probability p(≡1 ? q). A single service facility is available to (i) repair a partially or totally failed unit, (ii) repair the failed TS and (iii) activate the cold standby unit. The failure rates are constant, the activation and the repair rates are general.     

A recursive algorithm evaluating the exact reliability of a consecutive κ-within-m-out-of-n:F system

A consecutive κ-within-m-out-of-n:F system consists of n linearly ordered components e₁,3.e_n. The system fails if among any m subsequent components there are k or more failed ones. A recursive algorithm is presented evaluating the reliability of the system whose components are independent and have unequal failure probabilities. This algorithm is computer implementable for “not too large m” (e.g. m ≤ 15 for PC machines).     

Cost-benefit analysis of a single server three-unit redundant system with inspection, delayed replacement and two types of repair

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. The type of the failure of operative or warm standby unit is detected by inspection only. The service facility plays the triple role of replacement, inspection and repair of a unit. Failure time distributions of operative and warm standby units are negative exponential whereas the distributions of replacement time, inspection time and repair times are arbitrary. The system has been studied by using regenerative points.     

A two-unit cold standby system with imperfect repair and excessive availability period

A two-unit cold standby redundant system supported by a single repair facility is considered. The units after repair do not behave like new ones and a unit can be repaired, at most, k(k < ∞) times. The failure time distribution of either unit is different after each repair. Further, the system performance is maintained for a random time even after breakdown. The reliability characteristics are provided for the model.     

A multi-component standby system subject to inspection and truncated normal failure time distribution

This paper investigates a stochastic model of a single server, two identical unit cold standby system. Each unit consists of n separately maintained independent components arranged in series. After each failure, an inspection is required to detect which component of the unit has failed. The failure time distribution of a unit is truncated normal while all the other time distributions are negative exponential. Using the regenerative point technique, we obtained various measures of system effectiveness to carry out the profit function analysis.     

Analysis of a three-unit redundant system with two types of repair and inspection

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement of a failed operative unit and a cold standby which takes a random amount of time to become operative/warm. After each repair a unit is sent for inspection to decide whether the repaired unit is perfect or imperfect. If the repaired unit is found to be imperfect then it goes for post-repair. Using the regenerative point technique in the Markov renewal process several reliability characteristics of interest to system designers and operation managers are obtained.     

Cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair

This paper deals with the cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair where each unit of the system has two modes, normal and failed. It is assumed that the failure, repair, replacement and inspection times are stochastically independent random variables each having an arbitrary distribution. The cold standby unit replaces the failed operative unit after a random amount of time. An inspection is required to decide whether it needs type I (minor repair) or type 2 (major repair). In this system the repairman is not always available with the system, but is called whenever the operative unit fails. 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. Pointwise availability, steady-state availability, busy period by a server and the expected cost per unit time of the system are obtained. Certain important results have been derived as particular cases.     

Cost-benefit analysis of one-server two-unit system with imperfect switch

This paper deals with the cost-benefit analysis of a one-server two-unit system subject to imperfect switch. The repair times of a unit and the switch are assumed to be arbitrarily distributed while the failure rate of a unit and of the switch are constants. Initially, one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. The system breaks down when no unit is available or when the switch is not available although the unit is available for operation. The system is characterised by the probability of its being in the up or down state at an instant and integral equations have been set up for these probabilities by identifying the system at suitable regeneration epochs. These equations have been solved using Laplace Transform Technique. Explicit expressions for the expected durations the server is busy in (0, t) with the repair work of the unit and the switch have been obtained to carry out the analysis.     

Cost-benefit analysis of one-server two-unit replacement system with imperfect switch

This paper deals with the cost-benefit analysis of a one-server two-unit system with imperfect switch where the unit, if available, is preferred to the standby. The repair time of an item (unit/standby/switch is arbitrarily distributed while failure rate of an item is constant. Initially, the unit is switched on (switch is working at t = 0). The repair of the switch is given preference after the current repair of the unit or standby is over. Explicit expressions for the expected up-time due to the unit, expected up-time due to the standby; expected busy period of the server due to the unit, due to the standby and that due to the switch are obtained to carry out the cost-benefit analysis.     

Fixed-width confidence interval estimation of the inverse coefficient of variation in a normal population

A sequential procedure is developed in order to construct a confidence interval of “fixed-width and preassigned coverage probability” for the inverse of the coefficient of variation of a normal population. The proposed sequential procedure is proved to be “asymptotically efficient and consistent” in the sense of Chow and Robbins ([1]: Ann. Math. Statist. 36, 457–462 (1965)). Asymptotic distribution of the stopping time is derived.     

A recursive algorithm evaluating the exact reliability of a circular consecutive k-within-m-out-of-n:F system

A circular consecutive k-within-m-out-of-n:F system consists of n cyclically ordered components ε₁…ε_n, ie. ε_i+1 succeedes e_i, iε {1,…,n-1}, e₁ succeedes e_n. The system fails if any m consecutive components include k or more failed ones. A recursive algorithm is presented evaluating the reliability of a system with independent components whose failure probabilities may be unequal. This algorithm is computer implementable for “not too large m” (e.g. m 8 for PC machines).     

Frontier of transparent oxide semiconductors

Recent advancements of transparent oxide semiconductors (TOS) toward new frontiers of “oxide electronics” are reviewed based on our efforts, categorized as “novel functional materials”, “heteroepitaxial growth techniques”, and “device fabrications”. Topics focused in this paper are: (1) highly conductive ITO thin film with atomically flat surface, (2) p-type TOS material ZnRh₂O₄, (3) deep-ultraviolet (DUV) transparent conductive oxide β-Ga₂O₃ thin film, (4) electrochromic oxyfuolide NbO₂F, (5) single-crystalline films of InGaO₃(ZnO)_m grown by reactive solid-phase epitaxy, (6) p-type semiconductor LaCuOS/Se epitaxial films capable of emitting UV- and purple-light, (7) p–n homojunction based on bipolar CuInO₂, (8) transparent FET based on single-crystalline InGaO₃(ZnO)₅ films, and (9) UV-light emitting diode based on p–n heterojunction.