Computing steady-state mean time to failure for non-coherent repairable systems

Mean time to failure (MTTF) is an important reliability measure. Previous research is mainly concerned with the MTTF computation of coherent systems. In this paper, we derive equations to calculate the steady-state MTTF for noncoherent systems. Based on the equations, we extend the BDD by adding an intersection edge in each BDD node to efficiently store additional information for MTTF computation of noncoherent systems. A recursive algorithm is developed for MTTF computation using the extended BDD. To accelerate building the extended BDD, a method is proposed to avoid calculating the intersection edge for some nodes by keeping node monotonicity during the BDD construction. We show the efficiency of our algorithm by applying it to some example fault trees, real-life applications, and large fault tree benchmarks.     

On estimating the mean time to failure with unknown censoring

Sometimes, in reliability studies, neither the life of all failed units nor the number of units still functioning is known at any specific time due to problems such as administrative delays. Consequently, one might consider an estimate of the mean time to failure (MTTF) based only on known failure times of part of the units. An investigation is conducted into the bias and efficiency of such an estimator for either an exponential or a Weibull distribution. In the exponential case, exact expressions are obtained, and, for the Weibull case, a Monte Carlo simulation was used. The estimate of MTTF based on known lifetimes of failed units alone underestimates with smaller variance and higher mean squared error than does the estimate based on the total accumulated lifetime of both failed and surviving units     

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.     

Mean time to first failure of repairable systems with one coldspare

A general (nonMarkov) 1-out-of-2:G system with statistically-identical components, repair, and cold standby is reviewed. Coverage is considered, viz, failures of the switching mechanism for activating the spare. The explicit derivation of the mean time-to-first-failure and its in-depth discussion appear to be new. The state transition graph and the Petri net both show the way to general (n-1)-out-of-n:G systems of this category. However, for n>2, results are given only for statistically-identical components which are all as good as new, when a repaired component is put to use. This limits applicability of results to electronic systems     

Approximation of mean time between failure when a system hasperiodic maintenance

This paper describes a simple technique for estimating the mean time between failure (MTBF) of a system that has periodic maintenance at regular intervals. This type of maintenance is typically found in high reliability, mission-oriented applications where it is convenient to perform maintenance after the completion of the mission. This approximation technique can greatly simplify the MTBF analysis for large systems. The motivation for this analysis was to understand the nature of the error in the approximation and to develop a means for quantifying that error. This paper provides the derivation of the equations that bound the error that can result when using this approximation method. It shows that, for most applications, the MTBF calculations can be greatly simplified with only a very small sacrifice in accuracy     

On the influence of coding on the mean time to failure fordegrading memories with defects

The application of a combined test-error-correcting procedure is studied to improve the mean time to failure (MTTF) for degrading memory systems with defects. The degradation is characterized by the probability p that within a unit of time a memory cell changes from the operational state to the permanent defect state. Bounds are given on the MTTF and it is shown that, for memories with N words of k information bits, coding gives an improvement in MTTF proportional to (k/n) N(d_min^-2)/(d_min ^-1), where d_min and (k/n) are the minimum distance and the efficiency of the code used, respectively. Thus the time gain for a simple minimum-distance-3 is proportional to N^-1. A memory word test is combined with a simple defect-matching code. This yields reliable operation with one defect in a word of length k+2 at a code efficiency k/(k+2)     

Comparisons of block diagram and Markov method system reliability and mean time to failure results for constant and non-constant unit failure rates

This paper presents a comparison of system reliability and mean time to failure results obtained using two different methods (i.e. block diagram and Markov) for the same system with constant and non-constant unit failures rates. The device of stages approach is used to obtain the non-constant unit failure rate when using the Markov method.     

Look first to failure

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On the first failure time of two-unit systems in two environments

Using semi-Markov processes and PH distribution, we study the first failure time of two-unit systems in two environments, and show that the first failure time distribution is a PH distribution if the repair time distribution is a PH distribution.     

The maximum mean time to blocking routing in circuit-switchednetworks

The Maximum Mean Time to Blocking (MTB) Routing is a state- and time-dependent adaptive routing scheme. In this scheme, overflowed calls are routed to an alternate path having the longest mean time to blocking. The mean time to blocking of a link is a function of the trunk group size, the traffic rate, and the instantaneous trunk group occupancy and is a particularly suitable measure of the busy status of links in networks with nonuniform trunk group sizes and asymmetric traffic rates. The computation of the mean time to blocking of a path is very demanding and two approximations are proposed. A comparative performance evaluation through a call-by-call computer simulation shows that the MTB routing can give a superior throughput-blocking performance     

Third-order delay-locked loop: mean time to lose lock and optimalparameters

A systematic approximation for the mean time to lose lock (MTLL) of a coherent third-order PN-code tracking loop has been derived. Such loops are essential in various spread spectrum systems (Global Positioning System, for example). The computation of the MTLL is based on the singular perturbation method. The application of this method to the coherent delay-locked loop (DLL) yields an approximate expression for the MTLL. Therefore, with the proposed loop model the authors are able to analyze this third-order system at a level that gives a well understanding of the nonlinear loop behavior and the exit phenomenon. The influence of a loop offset due to an acceleration rate (jerk) between transmitter and receiver on the optimal filter parameters is described by comparing MTLL and tracking error performance. As intuitively might be expected it turns out that acceleration rate and code rate are exchangeable in the sense that a lower code rate allows a higher acceleration rate (and vice versa) for the same signal-to-noise ratio in order to maintain the same performance. In a case study, GPS code tracking for objects with high jerk is briefly discussed     

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Bathtub failure rate and upside-down bathtub mean residual life

This paper shows that: (1) the mean residual life (MRL) of a component has an upside-down bathtub-shape if the component has a bathtub-shape failure-rate function, but the converse does not hold; and (2) there is an optimal burn-in policy to maximize the MRL when the underlying lifetime distribution has a bathtub-shape failure rate     

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在我们行业中时常会出现一种十分尴尬的现象，就是在整机厂对印制电路板的产品招标会上常会出现标书中的价格高低相差极大的情况，结果不仅混乱了公正的价格，也使很多印制电路板企业进退两难。     

Exact calculation of mean CCSNo7 link alignment time

Two methods of mean CCSNo7 link alignment time calculation are suggested. One of these methods is also applicable for mean CCSNo7 link changeover time calculation. The results obtained are compared to results of known methods and simulation results     

ARIMA models used to predict the time to degradation failure of TTL ICs

ARIMA models are employed to predict the time to degradation failure from life-test data on high-reliability TTL ICs. The circuits investigated are the 134LB1, 106LB1, 133LR3, and 11LA8. The test lengths are 110 000–150 000 h. The interval forecasts for the 106LB1 and 134LB1 indicate a lifetime shorter than the warranty value 150 000 h. Those for the 133LR3 and 133LA8 are consistent with their warranty lifetime 200 000 h under low-duty conditions [1].     

Mean time to failure formulas for standard reliability networks with erlangian distributed component failure times

This paper presents newly developed mean time to failure formulas for reliability networks such as series, parallel, k-out-of-n, series-parallel, parallel-series and a bridge with special case Erlangian distributed component failure times.     

Correction for apparent prolongation of mean transit time resultingfrom response time in a thermodilution system

A method of correcting an apparent prolongation in the measured transit time (MTT) resulting from the response time of the thermodilution system was investigated. The mean response times (MRTs) were measured for five commercially available thermistor-tipped catheters by recording their step function response curves. Using a flow loop model filled with saline through a mixing chamber, pairs of thermodilution curves were recorded simultaneously with pairs of catheters, and the influence of MRT on MTT was studied for the constant flow rates of 1-6 L/min. The difference in MRTs between a pair of thermodilution systems correlated with the difference in MTTs between a corresponding pair of thermodilution curves, yielding an equation. It was concluded that the apparent prolongation of MTT due to response time can be eliminated by subtracting the MRT from the measured MTT