Reliability analysis of time-dependent cascade system with deterministic cycle times

Reliability analysis of time-dependent 2-cascade and 3-cascade systems is carried out using stress/strength models by considering each of the stress and strength variables as deterministic or random fixed or random independent. The number of cycles in any period of time t is assumed to be deterministic. The components are identical in the sense that the components have exactly the same strength if the strength variable is deterministic and have independent and identical distributions if the strength variable is random. Attenuation factors, K_i's, are constants. Expressions for system reliability are obtained and reliability values are computed for specific values of N, the number of cycles, when stress and strength distributions are exponential.     

An M θ/G/1/m system with two-threshold hysteresis strategy of service intensity switching

For an M ^??/G/1/m system, two??basic and post-threshold??service modes with distribution functions F(x) and $\tilde F(x)$ of the service time are applied. The post-threshold mode starts functioning if, at instant t of the beginning of the current customer service, number ??(t) of customers in the system satisfies the condition ??(t) > h ₂. The basic mode is restored at the instant when the customer such that ??(t) ?? h ₁, where h ₁ ?? h ₂, begins to be served. The Laplace transforms are found for the distribution of the number of customers in the system on the busy period and for the distribution function of the busy period, the mean duration of the busy period is determined, and formulas are derived for the stationary distribution of the number of customers in the system and stationary characteristics. The solution of the problem of optimal synthesis of a system with given characteristics is illustrated by an example. The obtained results are verified with the help of an simulation model developed with the use of the GPSS World software.     

Reliability calculation of redundant systems with non-identical units

The present paper develops mathematical models for evaluating the exact reliability and mean time to failure of k-out-of-m: G systems with different unit failure probabilities. The ith unit is assumed to be characterized by a general hazard rate h_i(t) = λ_it^b.The models are based on the concepts of tie sets; they are fairly simple and can be used for any values of m and k. The algorithm developed for these models is suitable for adoption for a computer code.     

An Mθ/G/1 system with hysteretic switching of the service intensity

For an M^θ/G/1 system, two—basic and post-threshold—service modes with distribution functions F(x) and $\tilde F$ (x) of the service time are applied. The post-threshold mode starts functioning if, at instant t of the beginning of the current customer service, number ξ(t) of customers in the system satisfies the condition ξ(t) > h ₂. The basic mode is restored at the instant when the customer such that ξ(t) ≤ h ₁, where h ₁ ≤ h ₂, begins to be served. The mean duration of the busy period is determined, formulas for the stationary distribution of the number of customers in the system and stationary characteristics are derived. The results are verified with the help of simulation models developed with the use of the GPSS World tools.     

Characterization of transient currents in HfO2 capacitors in the short timescale

We present a detailed experimental investigation of transient currents in HfO₂ capacitors in the short timescale. We show that the transient currents flowing through the capacitor plates when the gate voltage is reset to zero after a low voltage stress period follow a power-law time dependence t^−α (with α ? 1) over more than eight decades of time and down to the μs timescale. As transient currents in HfO₂ are largely increased with respect to the SiO₂ case, these results confirm that transient effects can be a severe issue for the successful integration of high-k dielectrics.     

Studies in Cascade Reliability?I

An n-Cascade system is defined as a special type of standby system with n components. A component fails if the stress on it is not less than its strength. When a component in cascade fails, the next in standby is activated and will take on the stress. However, the stress on this component will be a multiple k times the stress that acted on its predecessor. The system fails if due to an initial stress, each of the components in succession fails. The stress is random and the component strengths are independent and identically distributed variates, with specified probability functions; k is constant. Expressions for system reliability are obtained when the stress and strength distributions are exponential. Reliability values for a 2-cascade system with Gamma and Normal stress and strength distributions are computed, some of which are presented graphically.     

The linear stage of evolution of electron-hole avalanches in semiconductors

A complete analytical solution of the problem of the linear stage of evolution of electron-hole avalanches in the uniform time-independent electric field E _ext is derived. The theory accounts for the drift, diffusion, and impact ionization of electrons and holes, thus providing a means for calculating the space-time distributions of fields and charges as well as all the basic parameters of the avalanches up to the onset of nonlinear effects at the time t _a . Formulas for the group velocity of the avalanches and for the velocity of its leading fronts are derived. It is shown that the time t _a must be determined from the condition that the impact ionization coefficient α in the center of the avalanche be reduced by a specified small quantity η. A transcendent equation is derived, which allows the calculation of the time t _a as a function of the quantity η, the unperturbed coefficient α(E _ext), and other parameters of the semiconductor. It is found that, when α(E _ext) is increased by two orders of magnitude, the total number of electron-hole pairs generated up to the point t _a decreases by nearly three orders of magnitude.     

Prévision du cycle des taches solaires

Given the dates tand Tfor sunspot cycle minima and maxima and allowing for a probable secondary modulation with an approximate 16 cycles period, the author applies a forecasting method developed earlier to sunspot cycles n ^os 21 and 22. According to the resulting prediction these coming elementary cycles will be longer (about 14 years) than the 11 years average. Predicted values for the Zürich number Rare about 80 and 50, respectively.     

Peculiarities of finding characteristic functions of the generating process in the model of stationary linear AR(2) process with negative binomial distribution

The linear random AR(2) autoregressive process having the negative binomial distribution has been considered. It has the form ξ _t + a ₁ξ _t-1 + a ₂ξ _t-2 = ? _t , t ∈ Z, where {a ₁, a ₂ ≠ 0} are the autoregressive parameters; Z = {...,-1,0,1,...} is the sequence of integers; {ξ _t ,t ∈ Z} is the random process with discrete time and independent values having the infinitely divisible distribution law that is called generating process. The method of finding the characteristic function of the generating process for linear autoregressive process having negative binomial distribution is presented. This inverse problem is solved by using properties of the characteristic function of stationary linear autoregressive process that can be presented in the Kolmogorov canonical form and as a linear stationary autoregressive process. An example of finding the Poisson spectrum of jumps and the characteristic function for the linear second order autoregressive process (AR(2)) with negative binomial distribution has been also presented.     

Reliability characteristics of high-k dielectrics

In this paper, recent results of Weibull slopes, area scaling factors, and breakdown behaviors observed for both soft breakdown and hard breakdown are discussed. These results would help to shed light on the breakdown mechanism of HfO₂ gate dielectrics. The Weibull slope β of the hard breakdown for both the area dependence and the time-to-dielectric-breakdown distribution was found to be β=2, whereas that of the soft breakdown was about 1.4 (EOT=14 Å). We also integrated the time-to-breakdown characteristics of HfO₂ under unipolar AC voltage stress on MOS capacitors. The results show that longer lifetime of HfO₂ has been observed when compared to constant voltage stress. Higher frequency and lower duty cycle in the AC stress resulted in longer lifetime. As thickness decreases, the amount of lifetime enhancement decreases. The enhancement of unipolar t_BD is attributed to less charge trapping during the “on time”, t_on and charge detrapping during the off time, t_off. It is proposed that time (τ_in) for charge to be trapped in HfO₂ is longer than t_on of unipolar stress under high frequency. In addition to experimental results, possible solutions are discussed.     

Algebraic properties of BCH codes useful for decoding

In this paper theorems are presented which allow the simplified decoding of (n, k, δ) BCH codes in certain cases of practical interest. Such results are in a way implicit in the theory of BCH codes, but so far have not appeared explicitly in the literature. It is shown that any t₀ errors, 1 ? t₀ ? δ-1, can be detected by using any set of only t₀ consecutive coefficients of the syndrome polynomial. The correction of any t₀ errors, 1 ? t₀ ? [(δ-1)/2], can be performed by using any set of 2t₀ consecutive coefficients of the syndrome polynomial, where [x] means the integer part of x. Similar results are derived for punctured BCH codes. In this case sets of t₀ or 2t₀ consecutive coefficients, respectively, for detecting or correcting t₀ errors, are selected from the δ-1-p higher-order coefficients of the modified syndrome polynomial, where p is the number of digits punctured from a code word. These results hold true even when the punctured digits are not consecutive.     

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

This paper deals with the cost-benefit analysis of a one-server two-unit system with imperfect switch where the server is summoned upon failure of an item (i.e. unit or switch). The amount of time the server takes to arrive is a random variable, distributed arbitrarily. The server leaves when there is no item waiting for repair. The repair times are arbitrarily distributed whereas all failure rates are constant. Initially one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. Explicit expressions for the expected uptime in (0, t) of the system, busy period of the server due to repair of a unit and that of the switch are obtained to carry out the cost-benefit analysis.     

Reliability analysis of an intermittently used system

We consider a one unit system backed by a repair facility, the system itself being used intermittently with the use (need) and non-use (no need) period alternating in a Markov manner while the repair and life time of the unit are assumed to be independent random variables distributed quite generally. If a need arises in the time interval in which the unit is under repair or if the unit fails while it is in need, the need waits for a random period. If however the repair time is longer than the waiting time, a disappointment results and the need is taken care of by other means. The probabilistic analysis of the system is provided and suitable measures characteristic of the system are obtained. In particular explicit expressions are provided for the probability distribution of the time to the first disappointment as well as the expected value of the number of disappointments in an arbitrary time interval.Reliability Analysis of an Intermittently used System