Estimation of parameters of a model of a complex repairable system

This paper deals with estimation of parameters of a model of a complex repairable system with 3ne unit on operation and the remaining (N − 1) units as inactive standbys and having a repair facility. Various operating characteristics, namely, reliability, availability, mean time to failure of the system, s-expected numbers of repairs in (0, t], s-expected numbers of failures of the system in (0, t] are estimated under two censoring schemes namely, the type-I censoring and type-II censoring schemes.     

可靠性试验样本量和截尾时间的计算

可靠性寿命试验中，一般都因受到费用和时间的限制，因此要用截尾试验获得信息，再据此对其可靠性进行统计推断，用非参数估计的方法探讨了进行可靠性试验的样本量或截尾时间的估计方法。     

Stochastic degradation models with several accelerating variables

Many products & systems age, wear, or degrade over time before they fail or break down. Thus, in many engineering reliability experiments, measures of degradation or wear toward failure can often be observed over a period of time before failure occurs. Because the degradation values provide additional information beyond that provided by the failure observations, both sets of observations need to be considered when doing inference on the statistical parameters of the product or system lifetime distributions. For highly-reliable modern products, it often takes much more time to obtain lifetime & degradation data under usual use conditions, and this requires one to use accelerated tests. Accelerated tests expose the products to greater environmental stress levels so that we can obtain lifetime & degradation measurements in a more timely fashion. In addition, many products are exposed to several environmental variables in some manufacturing processes, or under some operating conditions. This motivates the need for developing general accelerated test models with several accelerating variables for inference based on both observed failure values, and degradation measurements. In this paper, new accelerated test models are developed based on a generalized cumulative damage approach with a stochastic process characterizing a degradation phenomenon.     

Nonparametric estimation of mean time to failure with unknown stochastic censoring

In this note we study a nonparametric estimator of the mean time to failure within the model of random censorship, provided only failures are recorded, and censoring times are not available. The s-bias of this estimator is of order O(1) and does not vanish with increasing sample size. We present bounds for the main term of the s-bias under additional assumptions such as the Koziol-Green model of random censoring and lifetime distributions belonging to the IFRA or DFRA classes. A corrected estimator s-bias is proposed for use in reliability practice, provided that the underlying lifetime distribution is IFRA or DFRA. This is a valuable tool if one is able to observe only failure times.     

Performance analysis of a random packet selection policy formulticast switching

This paper studies a random packet selection policy for multicast switching. An input packet generates a fixed number of primary copies plus a random number of secondary copies. Assuming a constant number of contending packets during a slot, the system is modeled as a discrete time birth process. A difference equation describing the dynamics of this process is derived, the solution of which gives a closed form expression for the distribution of the number of packets chosen. Then this result is extended to the steady state distribution through a Markov chain analysis. It is shown that the old packets have larger fanout than the fresh packets and the copy distribution of the mixed packets is determined. The packet and copy throughput taking into account the old packets have been obtained. We determined the mean packet delay as well as an upperbound for packet loss probabilities for finite buffer sizes. The asymptotic distribution of the number of packets is also given for large switch sizes under saturation by applying results from the renewal theory. Finally, simulations are done to determine the performance of the switch under mixed (unicast plus multicast) traffic     

Reliability evaluation of a first order standby system with module redundancy

By defining a module to be a coherent subsystem of independently operating components each with a constant failure rate, this article derives expressions for the reliability of a standby redundant system consisting of an operating module together with a cold or warm standby module. The closed form reliability expressions are dependent upon the minimal path sets of each module as well as the component failure rates. Expressions are also derived for the mean time to system failure as well as the variance of the system time to failure distribution.     

Some characteristics of a man-machine system operating subject to different weather conditions

This paper deals with some characteristics of a single unit of a man-machine system operating under different weather conditions. It is assumed that the failure, repair and change of weather conditions (normal-stormy) 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-Stieltjes 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. Several important results have been derived as particular cases.     

Analysis of a two-engine aeroplane model with two types of failure and preventive maintenance

This paper deals with an aeroplane model; namely, a two-unit (non-identical) parallel system with dual mode of failures—(1) failure due to change in operating characteristics and (2) failure due to common cause. The system goes for preventive maintenance at random epochs. We assume that the failure, repair and maintenance times are stochastically independent random variates each having an arbitrary distribution. Using the regenerative point technique several measures of reliability are obtained. Certain important results have been derived as particular cases.     

Access control in multicast packet switching

Access control and performance for multicast packet switching in a broadband network environment are studied. In terms of scheduling the transmission of the copies of the packet onto output ports, two basic service disciplines are defined: one-shot scheduling (all the copies transmitted in the same time slot) and call splitting (transmission over several time slots). As subcategories of call splitting, SS (strict-sense) specifies that each packet can send at most one copy to the destination per time slot, whereas WS (wide-sense) does not carry this restriction. A scheme called revision scheduling, which mitigates the head-of-line (HOL) blocking effect by sequentially combining the one-shot scheduling and the call splitting disciplines, is proposed. Output contention resolution implementations, in the form of combinational logic circuits designed to resolve output contentions arising in each of the call scheduling disciplines, are introduced. A neural-network-based contention resolution algorithm is proposed to demonstrate the improvement of the optimal scheduling     

Inference for a Multivariate Exponential Distribution with a Censored Sample

Maximum likelihood estimators for the parameters of a multivariate exponential Cdf are easily obtained from partial information about a random sample, censored or not. The partial information consists of the minimum from each multivariate observation and the counts of how often each r.v. was equal to the minimum in an observation. The censoring might cause only the smallest r out of n minima to be observed along with the counts. The estimators depend on the total time-on-test statistic familiar in univariate exponential life testing. A likelihood ratio test for s-independence is derived which has s-significance ? = 0 and easily calculated power function.     

Generalized Linear Mixed Models for Reliability Analysis of Multi-Copy Repairable Systems

The power law process (PLP) is usually applied to failure data from a single repairable system. When a system has a number of copies for analysis, the usual approach is to assume homogeneity among all system copies, and then to pool data from these copies. In the real world, however, it may be more reasonable to assume heterogeneity among the system copies. Therefore, this paper proposes a new generalized linear mixed model (GLMM), called PLP-GLMM, to analyse failure data from multi-copy repairable systems. In the PLP-GLMM, the underlying model for each system copy is assumed to be a PLP at Stage 1, and parameters vary among copies at Stage 2. The PLP-GLMM can make inferences about both the population, and each system copy when accounting for copy-to-copy variance. A modified Anderson-Darling test is adapted to the goodness-of-fit test of the PLP-GLMM. A numerical application is given to show the effectiveness of the model     

Initial Provisioning of a Standby System with Deteriorating and Repairable Spares

A technique is developed for finding the time dependent operating probabilities used by reliability systems designers for provisioning a system with N + k identical units, k of which are called spares and N called operating units, and s repair facilities. System failure occurs when less than N units are operational. Units fail with exponential interfailure times and are repaired with exponential service time. Idle spares fail due to deterioration at a rate possibly different from that of the operating units. Graphs are presented which show the minimum numbers of spares needed to achieve system reliabilities of 0.90 and 0.99 as a function of time. The technique is applicable for finding, numerically, the first passage time distribution for any system modeled by birth and death processes.     

Reliability analysis of a Markovian deteriorating system

The reliability of a complex system passes through a gradual deterioration until at some critical level, the system fails completely. The study of such a system failure requires the application of Markov processes to obtain reliability measures such as mean time of system failure. The Laplace transform of reliability of the system starting from each operating state is employed for solving such a complex system of differential equations. A four-state deteriorating system is considered and various particular cases of the arbitrary repair times distribution are discussed.     

Alternative time scales for systems with random usage

In various reliability applications, there can be different time scales in which to measure time to failure, or assess the performance of objects. For instance, for automobiles the chronological age & the total number of driving hours, as measures of usage, are good candidates for the time scale. An impact of a random usage on some properties of time to failure distribution functions is studied. It is shown that a random usage can change the shape of the failure rate of an object compared with the shape of the failure rate for the deterministic usage. Specifically, the sharply increasing failure rate can turn into a decreasing one, which is, in fact, surprising. The random usage can also change the aging properties of distributions under consideration, and this should be taken into account in applications. Several simple examples illustrate the developed concept.     

Performance study of ATM multicast switching systems

We evaluate the performance of an N × N ATM discrete time multicast switch model with input queueing operating under two input access disciplines. First we present the analysis for the case of a purely random access discipline and subsequently we concentrate on a cyclic priority access based on a circulating token ring. In both cases, we focus on two HOL (head-of-line) packet service disciplines. Under the first (one-shot transmission discipline), all the copies generated by each HOL packet seek simultaneous transmission during the same time slot. Under the second service discipline (call-splitting), all HOL copies that can be transmitted in the same time slot are released while blocked copies compete for transmission in subsequent slots. In our analysis the performance measures introduced are the average packet delay in the input buffers as well as the maximum throughput of the switch. A significant part of the analysis is based on matrix geometric techniques. Finally, numerical results are presented and compared with computer simulations.     

Using multi-stage and stratified sampling for inferringfault-coverage probabilities

Development of fault-tolerant computing systems requires accurate reliability modeling. Analytic, simulation, and hybrid models are commonly used for obtaining reliability measures. These measures are functions of component failure rates and fault-coverage (probabilities). Coverage provides information about the fault and error detection, isolation, and system recovery capabilities. This parameter can be derived by physical or simulated fault injection. Statistical inference has been used to extract meaningful information from sample observation. The problem of conducting fault injection experiments and statistically inferring the coverage from the information gathered in those experiments is addressed in this paper. We perform statistical experiments in a multi-dimensional space of events. In this way all major factors which influence the coverage (fault locations, timing characteristics of the fault, and the workload) are accounted for. Multi-stage, stratified, and combined multi-stage and stratified sampling are used in this paper for deriving the coverage. Equations of the mean, variance, and confidence interval of the coverage are provided. The statistical error produced by the injected faults which do not induce errors in the tested system (also known as the nonresponse problem) is considered, A program which emulates a typical fault environment was developed and four hypothetical systems are analyzed     

On improved confidence bounds for system reliability

In this paper, new bounding strategies are presented to improve confidence interval estimation for system reliability based on component level reliability, and associated uncertainty data. Research efforts have been focused on two interdependent areas: 1) development & improvement of analytical approaches for quantifying the uncertainty associated with the system reliability estimate when data regarding component reliability is available; and 2) based on these analytical approaches, generating statistical inference methods that can be used to make accurate estimations about the reliability of a system. The analytical approach presented relies on a recursive rationale that can be applied to obtain the variance associated with the system reliability estimate, provided the system can be decomposed into a series-parallel configuration. The bounding procedure is independent of parametric assumptions regarding component time to failure, and can be applied whenever component reliability data are available. To assess the validity of the proposed procedure, three test cases have been analyzed. For each case, Monte-Carlo simulation has been used to generate component failure data, based on nominal component reliability values. Based on these simulated data, lower bounds have been constructed, and then compared against nominal system reliability to generate an expected confidence level. The results obtained exhibit a significant improvement in the accuracy of the confidence intervals for the system reliability when compared with existing approximation methods. The procedure described is effective, relatively simple, and widely applicable.     

Efficient testing of SRAM with optimized march sequences and a novel DFT technique for emerging failures due to process variations

With increasing inter-die and intra-die parameter variations in sub-100-nm process technologies, new failure mechanisms are emerging in CMOS circuits. These failures lead to reduction in reliability of circuits, especially the area-constrained SRAM cells. In this paper, we have analyzed the emerging failure mechanisms in SRAM caches due to transistor V/sub t/ variations, which results from process variations. Also we have proposed solutions to detect those failures efficiently. In particular, in this work, SRAM failure mechanisms under transistor V/sub t/ variations are mapped to logic fault models. March test sequences have been optimized to address the emerging failure mechanisms with minimal overhead on test time. Moreover, we have proposed a design for test circuit to complement the March test sequence for at-speed testing of SRAMs. The proposed technique, referred as double sensing, can be used to test the stability of SRAM cells during read operations. Using the proposed March test sequence along with the double sensing technique, a test time reduction of 29% is achieved, compared to the existing test techniques with the same fault coverage. We have also demonstrated that double sensing can be used during SRAM normal operation for online detection and correction of any number of random read faults.     

A note on the statistical characteristics of a two-unit system

Expressions for the Laplace transforms of reliability and availability functions are obtained for a two-unit system, with different repair times for the units which have failed from online and standby states, and a dead time value for the repair facility by the use of regeneration point technique. The system consists of two-units with one repair facility. The repair facility is not available for a random time immediately after each repair completion. From the Laplace transforms of reliability and availability functions the steady state availability, reliability and mean time to system failure can be obtained.     

Failure Time for a Redundant Repairable System of Two Dissimilar Elements

The distribution of time to failure for a system consisting of two dissimilar elements or subsystems operating redundantly and susceptible to repair is discussed. It is assumed that the times to failure for the two system elements are independent random variables from possibly different exponential distributions, and that the repair times peculiar to each element are independently distributed in an arbitrary fashion. For this basic model a derivation is given of the Laplace-Stieltjes transform of the distribution function of time to system failure, i.e, the time until both elements are simultaneously down for repair, measured from an instant at which both are operating. An explicit formula is given for the mean or expected time to system failure, a natural approximation to the latter is exhibited, and numerical comparisons indicate the quality of this approximation for various repair time distributions. In a second model the possibility of system failures due to overloading the remaining element after a single element failure is explicitly recognized. The assumptions made for the basic model are augmented by a stochastic process describing the random occurrence of overloads. Numerical examples are given. Finally, it is shown how the above models may be easily modified to account for delays in initiating repairs resulting from only occasional system surveillance, and to account for random catastrophic failures.