Stochastic analysis of a man-machine system with critical human error

This paper studies various economic reliability measures of a repairable man-machine system. The physical condition (good/poor) of the operator may affect the performance of the system. Repair time distributions of the system are general while all other transition time distributions are negative exponential. The system can be in one of the three modes—normal, partial failure and total failure. Regenerative technique in MRP is applied to obtain several reliability characteristics of interest to system designers.     

Stochastic models for predicting human reliability

This paper presents two mathematical Markov models to predict human reliability of time continuous operation tasks. Laplace transforms of the state probability equations are developed.     

最佳接收机误码率的两种估算观点

很多教材都是从统计的观点讨论分析了最佳接收机的误码率问题,统计的观点认为信道的噪声是非带限的高斯白噪声,分析的过程也假设接收机非带限。但是从实际和滤波的观点来看,任何形式的接收机都是频带受限的,进入到接收机检测器的噪声频带也会受限。文中基于统计和滤波的观点,讨论了最佳接收机的误码率问题,得出的结论相同,但是分析的过程体现了两者的不同之处,有助于更好的了解数字信号的最佳接收。     

Stochastic analysis of a general standby system with constant human error and arbitrary system repair rates

This paper presents a mathematical model for performing reliability and availability analyses of a general standby system with constant human error and common-cause failure rates. In addition, system repair times are assumed arbitrarily distributed. Markov and supplementary variable techniques were used to develop equations for the model. The method of linear ordinary differential equation is developed to obtain the general expressions of the steady state availability. The Laplace transform technique was used to obtain the system time-dependent availability, reliability and mean time to failure expressions.     

Worst-case error probability of a spread-spectrum system inenergy-limited interference

We consider a communication channel corrupted by thermal noise and by an unknown and arbitrary interference of bounded energy. For this channel, we derive a simple upper bound to the worst-case error probability suffered by a direct sequence (DS) communication system with error-correction coding, pseudorandom interleaving, and a correlation receiver. This bound is exponentially tight as the block length of the error correcting code becomes large. Numerical examples are given that illustrate the dependence of the bound on the choice of error correcting code, the type of interleaving used, and the relative energy of the Gaussian noise and arbitrary interference     

Stochastic analysis of a two-unit warm standby system with slow switch subject to hardware and human error failures

In this paper several important measures of reliability for a two-unit warm standby system with slow switch subject to hardware and human error failures are obtained using regenerative points technique in Markov renewal processes. All times distributions are exponential except the repair times distributions are general.     

PREHEP: human error probability based process unit selection

The paper describes a methodology to use human error probabilities (HEPs) as a basis for selecting functional process units in the design phase. The method helps us to understand the influence of human error (HE) on functional robustness of the units in earlier design phases, e.g., at the functional analysis level. This methodology can be used to detect the need for human operator support. The method consists of several steps. First alternative configurations of functional process units with different complexities are developed. For each configuration, a fault tree is developed to find the initiating events (failures of equipment) which lead to a chosen top event. This top event is an undesired event such as an overflowing tank. The initiating events are used to create event trees (ET) with special emphasis on operator actions, such as monitoring the process and fault diagnosis. A diagnosis diagram is used to simulate the fault diagnosis process and to identify the initiating failures. The probability of a top event due to human error can then be found by using existing HEP-data and by normalizing the failure probabilities of the equipment. The methodology is demonstrated for two examples of functional process units, each with two levels of complexity     

Average symbol error probability for M-ary DDPSK

A unified and exact analysis of the symbol error probability (SEP) for M-ary doubly-differential phase-shift keying (M-DDPSK) is presented. The SEP is expressed in terms of Fourier coefficients of the probability density function of the composite phase at the receiver input which are available for several channel scenarios including the additive white Gaussian noise, the fading, the fading-shadowing and the cochannel interference type of channel. Useful numerical results, obtained through the analytical expressions derived, are presented to compare the performance of 8-DDPSK and 8-DPSK over a channel in which, in addition to additive noise, a constant carrier frequency shift and Nakagami fading affect the transmission.     

Bounds on the error probability of FSK and PSK receivers due to non-Gaussian noise in fading channels

This paper derives upper and lower bounds on binary error probability as a function of signal-to-noise ratio for several digital data systems operating over a complex Gaussian fading channel. Bounds of varying degrees of tightness are obtained by placing certain physically meaningful constraints on the allowable detected noise probability distributions. Detailed derivations are given for bounds corresponding to constraints on the "crest-factor" of the detected noise and on the ratio of peak noise power to average signal power. The calculations include the effects of diversity corn-billing and are applicable to frequency-shift keying (FSK), binary and quaternary phase-shift keying (PSK) using a pilot tone as reference, and binary and quaternary PSK using the previous signaling element as a phase reference. It is an interesting result of this paper that for moderate noise crest factors the upper and lower bounds can be rather close. In the particular case of nondiversity operation, for example, the lower bound actually becomes approximately equal to the upper bound at SNR's of30dB or greater for noises with a crest factor as high as20dB.     

Evaluation of error probability for partial response systems

A computation algorithm has been developed to evaluate the exact probability of error for partial response (p.r.) signals in the presence of intersymbol interference and additive Gaussian noise in a digital communication system for a wide range of signal/noise ratio and sampling time error. This can readily be used to study the performance of already familiar p.r. signals or any new p.r. format which can be composed from a general p.r. polynomial.     

A simulation algorithm for computing failure probability of aconsecutive-k-out-of-r-from-n:F system

An efficient simulation algorithm for computing failure probability of a consecutive-k-out-of-r-from-n:F system (linear or circular) with any component reliability, is presented. The algorithm estimates both the failure probability of the system and the associated uncertainty (error). A complete interpretation of the algorithm results is given through a detailed error analysis     

Stochastic models for random-request availability

The system receives a stream of tasks which arrive according to some random processes. A new availability measure, random-request availability, is proposed. This stochastic model provides closed-form mathematical expressions which incorporate the 3 basic elements: random task arrivals; system state; and operational requirements of the system. An analytic model is derived and illustrated by numerical examples     

Computing upper bounds to error probability of coded modulationschemes

To evaluate an upper bound on error probabilities of signal constellations used for transmission over the additive white Gaussian noise (AWGN) channel, enumeration of all the constellation intradistances is required. These may be infinite in number, for example, when convolutional codes are used and the constellations are lattices. Truncation of the series does not necessarily provide a bound anymore, and must be done with care. Yet the union bound is very simple, as it does not require any further knowledge about the signal constellation than the distance enumerator. In this paper, we describe some methods that can be used to evaluate error probabilities of infinite signal constellations, and that require only a finite number of terms. These methods are applicable, for example, to convolutional codes decoded with a finite-depth Viterbi algorithm and to signal constellations carved from lattices. Coded modulations based on lattices and convolutional or block codes can also be dealt with. As an example of application, we analyze a variable-rate 3-stage coded modulation encoder/decoder, which has been built and is based on a combination of convolutional codes with a single-parity-check block code     

Upper bounds to the error probability of decision feedbackequalization

The exact computation of the symbol error probability of systems using decision feedback equalization is difficult due to the propagation of errors. New upper bounds to the error probability of decision feedback equalization, which take error propagation into account, are developed. The derivations of the bounds assume a causal channel response, independent data symbols, and independent noise samples. The bounds are valid for any noise process that has a symmetric and unimodal probability density function. In some cases, the new bounds are significantly tighter than a well-known upper bound of D.L. Duttweiler et al. (1974)     

Stochastic models for mission effectiveness

A stochastic model of mission effectiveness for a system which is required to perform a random number of tasks during its mission is developed. Mission effectiveness is defined as a combined measure of availability and reliability at each task-arrival time. An analytic model is derived under a general set of assumptions. Other models are outlined to show the wide applicability of this model for mission effectiveness     

On the undetected error probability for binary codes

In this paper, the undetected error probability for binary codes is studied. First complementary codes are studied. Next, a new proof of Abdel-Ghaffar's (1997) lower bound on the undetected error probability is presented and some generalizations are given. Further, upper and lower bounds on the undetected error probability for binary constant weight codes are given, and asymptotic versions are studied.     

Bit error probability for coherent M-ary PSK systems

A simple technique for evaluating the bit-error probability of coherent M-ary phase-shift keying (PSK) with any bit-mapping is proposed. Closed-form expressions are given in terms of error functions for half- and quadrant-plane probabilities in the decision space, avoiding the numerical evaluation of complicated integrals that occurs in the direct method. Bit error probability expressions for M-ary PSK with Gray, natural binary, and folded binary bit-mappings are derived     

A new formula for MDPSK symbol error probability

This article presents an extremely compact new formula for the symbol error probability in M-ary differential phase shift keying (MDPSK) that is extraordinarily similar to its counterpart for M-ary phase shift keying (MPSK). This result follows from a new form for a generic error probability associated with the phase angle between two vectors perturbed by Gaussian noise. The new form also leads to a new expression for the Marcum Q-function. As special cases, the generic error probability is noted to also contain MPSK, CPFSK, and digital FM. Finally, it is pointed out that the generic error probability simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum-likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK     

On symbol error probability bounds for ISI-like channels

Some issues with Forney's upper and lower bounds (1972) for the symbol error probability in systems with memory (e.g., intersymbol interference channels) have been pointed out in the literature. We expound on these issues. For the upper bound, we show that, although the most commonly cited proofs are not logically consistent, the bound is true for more general conditions. The reasoning leading to the lower bound is shown to be flawed and, in general,to lead to invalid lower bounds. We suggest a lower bound based on Mazo's bound (1975) as an alternative