On the interval reliability of systems modelled by finite semi-Markov processes

In this paper, semi-Markov models of repairable systems are considered whose finite state space is partitioned into two sets, the set of ‘up’ states, U, and the set of ‘down’ states, D. The focus of attention is the system's interval reliability which is defined as the probability of the system being in U throughout a given time interval [t, t + x] where t, x ε [0, +∞) are fixed. Two results in the Laplace transform domain are obtained for the interval reliability. The first one is a closed form expression for the double Laplace transform with respect to both variables t and x. The second result is concerned with a closed form expression of the (single) Laplace transform of the interval reliability with respect to the variable t under the additional assumption that the modelling semi-Markov process is Markovian on U. As an example, the semi-Markov model of a two-unit repairable system is considered. The steady-state behaviour of the system's interval reliability is examined by a Tauberian theorem.     

Second-order peak detection for multicomponent high-resolution LC/MS data

The first step when analyzing multicomponent LC/MS data from complex samples such as biofluid metabolic profiles is to separate the data into information and noise via, for example, peak detection. Due to the complex nature of this type of data, with problems such as alternating backgrounds and differing peak shapes, this can be a very complex task. This paper presents and evaluates a two-dimensional peak detection algorithm based on raw vector-represented LC/MS data. The algorithm exploits the fact that in high-resolution centroid data chromatographic peaks emerge flanked with data voids in the corresponding mass axis. According to the proposed method, only 4 per thousand of the total amount of data from a urine sample is defined as chromatographic peaks; however, 94% of the raw data variance is captured within these peaks. Compared to bucketed data, results show that essentially the same features that an experienced analyst would define as peaks can automatically be extracted with a minimum of noise and background. The method is simple and requires a priori knowledge of only the minimum chromatographic peak width-a system-dependent parameter that is easily assessed. Additional meta parameters are estimated from the data themselves. The result is well-defined chromatographic peaks that are consistently arranged in a matrix at their corresponding m/z values. In the context of automated analysis, the method thus provides an alternative to the traditional approach of bucketing the data followed by denoising and/or one-dimensional peak detection. The software implementation of the proposed algorithm is available at http://www.anchem.su.se/peakd as compiled code for Matlab.     

Bayes predictive analysis of a fundamental software reliabilitymodel

The concepts of Bayes prediction analysis are used to obtain predictive distributions of the next time to failure of software when its past failure behavior is known. The technique is applied to the Jelinski-Moranda software-reliability model, which in turn can show an improved predictive performance for some data sets even when compared with some more sophisticated software-reliability models. A Bayes software-reliability model is presented which can be applied to obtain the next time to failure PDF (probability distribution function) and CDF (cumulative distribution function) for all testing protocols. The number of initial faults and the per-fault failure rate are assumed to be s -independent and Poisson and gamma distributed respectively. For certain data sets, the technique yields better predictions than some alternative methods if the frequential likelihood and U-plot criteria are adopted     

Evaluation of the Multimycotoxin-Degrading Efficiency of Rhodococcus erythropolis NI1 Strain with the Three-Step Zebrafish Microinjection Method

The multimycotoxin-degrading efficiency of the Rhodococcus erythropolis NI1 strain was investigated with a previously developed three-step method. NI1 bacterial metabolites, single and combined mycotoxins and their NI1 degradation products, were injected into one cell stage zebrafish embryos in the same doses. Toxic and interaction effects were supplemented with UHPLC-MS/MS measurement of toxin concentrations. Results showed that the NI1 strain was able to degrade mycotoxins and their mixtures in different proportions, where a higher ratio of mycotoxins were reduced in combination than single ones. The NI1 strain reduced the toxic effects of mycotoxins and mixtures, except for the AFB1+T-2 mixture. Degradation products of the AFB1+T-2 mixture by the NI1 strain were more toxic than the initial AFB1+T-2 mixture, while the analytical results showed very high degradation, which means that the NI1 strain degraded this mixture to toxic degradation products. The NI1 strain was able to detoxify the AFB1, ZEN, T-2 toxins and mixtures (except for AFB1+T-2 mixture) during the degradation experiments, which means that the NI1 strain degraded these to non-toxic degradation products. The results demonstrate that single exposures of mycotoxins were very toxic. The combined exposure of mycotoxins had synergistic effects, except for ZEN+T-2 and AFB1+ZEN +T-2, whose mixtures had very strong antagonistic effects.     

Flowgraph Models in Reliability and Finite Automata

We discuss the interrelationship of two seemingly unrelated subjects: the theory of finite automata, and reliability theory, finite automata, more generally known as generalized transition graphs, are dasiaconvertedpsila to regular expressions by manipulating their pictorial representation, a directed graph, by elimination of its states one-by-one until two states are left, connected by an edge whose label is a regular expression equivalent to the initially given finite automata or generalized transition graph. Flowgraphs are used to represent semi-Markov reliability models. They are directed graphs with edges labeled with expressions of the form pG(s), where p is the probability of transition from node i to node j, say; and G(s) is the transform (Laplace transform, moment generating function, or characteristic function) of the waiting time in i given that the next transition is to j. Usually, transforms of waiting time distributions (e.g. time to first failure) are obtained from these graph representations by applying Mason's Rule (e.g. Huzurbazar, Mason, and Osaki), or, by the Cofactor Rule. In this paper we are concerned with obtaining transforms of waiting times by direct manipulation of the flowgraphs along the lines in finite automata. The goal of the paper is to observe that identical patterns of reasoning are applicable in both fields. This interconnects two apparently unrelated fields of knowledge, an interesting observation for its own sake but also important from a tool & technique point of view.     

Reliability analysis of recovery blocks with nested clusters offailure points

A Markov model is developed to obtain first and second moments of the number of successfully processed input-points for recovery blocks with a primary module and two alternate modules. A nested structure of clusters of failure points is assumed. When in a failure cluster of the primary module, the input sequence encounters clusters of failure points belonging to the first alternate module, in which case the second alternate is invoked. Some special cases are discussed in detail. A Markov chain model for one of the well-documented fault-tolerant software techniques, the recovery block, is analyzed. The model is intended to study recovery block reliability when the sequence of input values traverses nested clusters of failure points in the input domain. The method of solution exploited the specific structure of the state-transition diagram, which is two-dimensional. Moments of the number of successfully processed input points were obtained by recursively solving infinite systems of linear equations     

The number of working periods of a repairable Markov system duringa finite time interval

In reliability analysis, continuous parameter homogeneous irreducible finite Markov processes are used to model repairable systems with time-independent transition rates between individual states. The state space is then partitioned into the set of up states and the set of down states. The number of completed repair events during a finite time interval is an important (undiscounted) cost measure for such a system; it can be expressed in terms of the number of working periods during the same time interval. This paper derives a closed-form expression for the PMF of this latter quantity. The tool used is a recent result on the joint distribution of sojourn times in finite Markov processes. The MatLab implementation of the Markov model of a 2-unit parallel power transmission system is used to demonstrate the utility of the formula. The quantity examined is the number of completed repairs during a finite time interval. The method is viable in this case whereas the more usual randomization technique is not     

A new approach to the cumulative operational time for semi-Markov models of repairable systems

Semi-Markovian reliability models of repairable systems are considered here, whose state space is partitioned into the set of up-, and the set of down-states. The cdf of the cumulative operational time over a finite time interval [0,t] is represented in terms of the work-mission-availability and a system of integral equations is shown to hold for the latter. The equations are of the convolution type which then allows closed form expressions to be established for both the work-mission-availability and the cdf of the cumulative operational time. The semi-Markov model of a two-unit system is examined numerically by solving the resulting integral equations with the two-point trapezoidal rule. The results are compared with those from simulation and an earlier solution scheme based on (non-convolution) integral equations for the cdf of the cumulative operational time.     

Joint interval reliability for Markov systems with an application in transmission line reliability

We consider Markov reliability models whose finite state space is partitioned into the set of up states and the set of down states . Given a collection of k disjoint time intervals I_ℓ=[t_ℓ,t_ℓ+x_ℓ], ℓ=1,…,k, the joint interval reliability is defined as the probability of the system being in for all time instances in I₁I_k. A closed form expression is derived here for the joint interval reliability for this class of models. The result is applied to power transmission lines in a two-state fluctuating environment. We use the Linux versions of the free packages Maxima and Scilab in our implementation for symbolic and numerical work, respectively.