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.     

Reliability of a reparable system with preventive maintenance and imperfect switch

A two-unit cold standby redundant system with repair, post-repair, preventive maintenance (PM) and imperfect switchover is considered using three types of PM [types (a), (b) and (c)]. The Laplace transform (LT) of the survivor function (sf) of time to the first system failure (TFSF) and the mean TFSF are derived. A theorem about the effect of PM [type (a)] is proved. Finally numerical calculations are presented to illustrate the results.     

A note on 3-state systems

D.M. Malon (ibid., vol. 38, p.275-6, Aug. 1989) points out a pitfall of certain reliability problems pertaining to systems of three-state devices. The inference to be drawn from his observation is that special care should be used in describing such systems and in specifying exactly what constitutes success and failure. The present authors (ibid., vol.37, p.388-94, Oct. 1988) have modeled systems that can be represented by a network with designated source and sink; the reliability problem they treated is described by the following two system failures: (1) the system fails (short) if there is a path of short-failed components joining the source and the sink; (2) the system fails (open) if every path joining the source and sink includes an open-failed component. The systems they modeled are therefore somewhat more general then the array structures treated by B.W. Jenney and D.J. Sherwin (ibid., vol.R-35, p.532-8, Dec. 1986). But since the two failure-modes are mutually exclusive, the pitfall that Malon describes does not affect the former. Jenney and Sherwin's difficulties do not arise because of the generality of the systems; rather, they appear in some of the more general reliability measures (such as j-out-of-m requirements) used on the sp-arrays and ps-arrays     

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.     

Optimal `series-parallel' networks of 3-state devices

A 3-state component is one which can fall in two different modes: an open mode and a shorted mode. Systems built from such components can also experience either of these two failure modes. For a given number of s-identical s-independent components, a pure `series' or pure `parallel' configuration would be most reliable if only one of the two failure modes were possible. This paper treats the problem of designing the most reliable configuration of a given number of s-identical components that can experience both failure modes. Two simple algorithms for designing an optimal configuration are presented, and by analysis of 6, 8, and 20-component systems they illustrate the extent to which other configurations can be more reliable than `series-parallel' or `parallel-series' arrays     

3-state BTL closed-loop PWM Class D amplifiers

One of the shortcomings of a number of Class D amplifiers (CDAs) designs is their susceptibility to supply noise, quantified by Power Supply Rejection Ratio (PSRR). Reported investigations thereto to-date remain incomplete/over-simplified, particularly the assumption that the AC ground is noise-less and a simplified fully-differential integrator model. In this paper, the effect of supply noise in the AC ground to PSRR is analytically investigated, and the associated analytical expressions derived. Of specific interest, the analysis is applied to the ubiquitous 3-state Bridge-tied-load (BTL) closed-loop PWM CDA, taking into consideration not only the effect of the non-ideal AC ground, but also the effect of the resistor and capacitor mismatch based on a realistic fully-differential integrator model. Further, the PSRR analysis of 3-state BTL closed-loop CDAs has to date been limited to the single-feedback topology and in this paper, extended to the double-feedback topology. These analyses and derived equations herein are useful as they provide valuable insights to CDA designers into the PSRR mechanisms—for example, the counter-intuitive observation that the CDA with 1st-order integrators provides similar or better PSRR than the CDA with 2nd-order integrators if both CDAs are designed to the same carrier attenuation—including the effect of various circuit parameters, and ensuing trade-offs. The derived analytical expressions are verified by means of HSPICE simulations and on the basis of practical measurements on discretely-realized CDAs.     

Cost analysis of a man-machine system operating under changing operator conditions

This paper deals with the stochastics behaviour of a man-machine system which is affected by the operator physical conditions. Operator physical condition is subject to a Markov process with two states - good and poor and is independent of the system state. Operating unit fails either due to operator error or system fault. Using Markov reneval process several characteristics such as mean time to system failure (MTSF), pointwise availability in (0,t], expected busy period of the repairman in (0,t] and expected profit earned by the system in (0,t] have been obtained.     

Cost analysis of a multi-component screening system in the paper industry

The paper discusses the screening system in the Paper Industry with three states—good, reduced and failed. The failure rates are constant while the repair rates are general. Formulation of the problem is carried out using simple probability consideration. Various probabilities are obtained along with steady state probabilities of the system. Availability and MTTF tables and graphs for various parameters are given which are useful to the designer and the management for improvement in design.     

Reliability of 3-state device systems with simultaneous failures

This work is concerned with computing the reliability of redundant systems of three-state (e.g., good, failed-open or failed-short) devices. Allowing for multiple failures, formulas are presented for calculating the reliability of a parallel-series system or a series-parallel system which is formed from three-state, non-DFM (dual failure-mode) devices, and which might require multiple paths to function. The words series and parallel are used in the layout-diagram sense. The formulation encompasses cases which have been analyzed by complex methods in numerous papers on the reliability of three-state DFM device systems. The effects of dominant failure-modes on the relationship between reliability of a series system and that of a parallel system, and on the relationship between the reliability of a parallel-series system and that of series-parallel system are presented     

Cost analysis of a two-unit standby system with two types of repairmen

This paper is concerned with a two-unit cold standby system with two types of repairmen. One “regular” repairman is kept for repairing the units as soon as they fail. It is assumed that sometimes he might not be able to do the repairs within some tolerable time (patience time). Another “expert” repairman, assumed to be perfect, is called on to do the repairs on the completion of this patience time or on the failure of the system, whichever is later.Various measures of system effectiveness are calculated using semi-Markov processes and regenerative processes. Based on these measures, a rule is developed whether the expert repairman should be called after the system failure. Further numerical results for a case, in which repair time and patience time both have non-Markovian property, are also investigated. Then the upper bound of the cost K₃, below which the expert repairman should be called immediately after the system failure and the corresponding increase in profit are calculated.     

Cost analysis of a two-unit standby system under the influence of earthquakes

This paper deals with two models. In model 1, which is cold standby, when an earthquake comes the operation of the unit is stopped. In model 2, which is warm standby, a medium intensity earthquake will cause a short circuit failure mode. The repair is available immediately upon calling. In model 1, the failure rate is taken to be constant whereas the repair time distribution is arbitrary. In model 2, the failure and repair time distributions are considered to be arbitrarily distributed. Applying the regenerative theory in Markov renewal processes, various reliability characteristics of interest have been explicitly obtained.     

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.     

Cost benefit analysis of a complex system with correlated failures and repairs

This paper studies the cost benefit analysis of a complex system consisting of two subsystems, say A and B, connected in series. Subsystem A consists of two identical units, whereas subsystem B has only one unit. The system operates if one of the two units of subsystem A and the subsystem B are operative. Assuming a bivariate exponential density for the joint distribution of failure and repair times of the units, some reliability characteristics useful to system managers have been obtained. Explicit results have also been obtained for the case when failure and repair times are uncorrelated.     

Cost analysis of a system with partial failure mode and abnormal weather conditions

This paper deals with the cost analysis of a system having three modes (normal, partial failure and total failure) in two weather conditions—normal and stormy. Failure rates of the system and rates of change of weather conditions are constant while the repair rates are general. The repair time distribution depends upon the starting state of the repair and it does not alter with the change in weather. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Earlier results are verified as particular cases.     

Cost analysis of a two unit cold standby system under different weather conditions

This paper deals with the cost analysis of a two unit cold standby system under two different weather conditions—normal and abnormal. Failure rates of units and rates of change of weather conditions are constant, whereas repair rates are general. The system is analysed in detail using regenerative point technique and results are obtained for mean time to system failure, steady state availability, busy period analysis, expected number of visits by repairman and expected profit earned by the system.     

Cost analysis in a two-unit standby system with a regular repairman and patience time

This paper develops a model for standby redundant system consisting of two identical units and a regular repairman. In an effort to increase the working time of the system, we put some “patience time” as the upper limit to repair time of the regular repairman. If the regular repairman is not able to do the repair within this patience time, we call an “expert” repairman for doing the repairs. Then the various measures of system effectiveness are calculated using semi-Markov processes and regenerative processes. Based on these measures, a rule is developed whether the services of the expert repairman should be utilized profitably or not. Further using numerical methods, we discuss the optimum patience time for various costs, maximizing the profit.     

基于DSP实现的8状态turbo码译码器

国际电信联合会在UMTS/3GPP规范中推荐8状态turbo码作为数据纠错的方案。本文回顾了turbo码的MAX-LOG-MAP译码算法,并分析了输入量化方式对译码性能的影响。在100MHz的定点DSP芯片上实现该算法时,译码速度达到110kbps～300kbps。     

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.     

Golay3稀疏孔径光学系统调制传递函数分析和成像研究

给出Golay3稀疏孔径光学系统的光瞳结构,分析其调制传递函数（MTF）特点。对不同填充因子的Golay3稀疏孔径光学系统模拟成像,并用几何均值滤波进行图像复原,以相关系数评价模拟成像质量和图像复原效果。结果表明：模拟成像和图像复原结果与调制传递函数分析结果一致;经几何均值滤波后,图像质量得到改善：图像复原效果随填充因子增大而提高。     

Cost analysis of a two unit cold standby system with preparation time for repair

This paper deals with a model of a two unit cold standby system with imperfect switch in which the repair man appears and disappears from the system randomly. The standby unit takes random switchover time for operation when the operative unit fails. Failure time of a unit, appearance and disappearance time of the repair man and switchover time of the standby unit are negative exponential, whereas repair time is arbitrary. The system is analysed by using regenerative point technique and several parameters of interest are obtained.