Edmond J. Vanderperre

Overall availability of a robot with internal safety device

We introduce a robot-safety device system composed of a robot with internal (built-in) safety device. The system is characterized by a safety shut-down rule and by the natural feature of standby. In order to obtain the point availability of the twin-system, we introduce a stochastic process endowed with a time-dependent potential satisfying an integro-differential equation. The explicit solution procedure requires the (new) notion of ineffective lifetime - versus - effective lifetime of the robot. The analysis of the long-run availability requires the introduction of a signed measure. As an example, we display a computer-plotted graph of the point availability obtained by inversion of the corresponding Laplace-transform.

Long-run availability of a priority system: a numerical approach

We consider a two-unit cold standby system attended by two repairmen and subjected to a priority rule. In order to describe the random behavior of the twin system, we employ a stochastic process endowed with state probability functions satisfying coupled Hokstad-type differential equations. An explicit evaluation of the exact solution is in general quite intricate. Therefore, we propose a numerical solution of the equations. Finally, particular but important repair time distributions are involved to analyze the long-run availability of the T-system. Numerical results are illustrated by adequate computer-plotted graphs.

Reliability analysis of a renewable multiple cold standby system

We present a general reliability analysis of the basic multiple cold standby system attended by a single repair facility. The particular case of deterministic repair provides some explicit results for the survival function illustrated by computer-plotted graphs.

Point availability of a robot-safety device

We consider a robot-safety device system attended by two repairmen. In order to derive the point availability of the robot-safety device, we introduce a stochastic process endowed with time dependent probability measures. The point availability satisfies a generalized integral equation of the convolution-type. The solution procedure is based on the methodology of Laplace (Stieltjes) transformations. We also derive the long-run availability of the robot-safety device.

Reliability analysis of a repairable duplex system

We analyse the survival time of a repairable duplex system characterised by cold standby and by a pre-emptive priority rule. We allow general probability distributions for failure and repair. Moreover, an important realistic feature of the system is the general assumption that the non-priority unit has a memory. This combination of features has not been analysed in the previous literature. Our (new) methodology is based on a concatenation of a Cauchy-type integral representation of the modified Heaviside unit-step function and a two-sided stochastic inequality. Finally, we introduce a security interval related to a security level and a suitable risk-criterion based on the survival function of the system. As a practical application, we analyse some particular cases of the survival function jointly with the security interval corresponding to a security level of 90.

Risk analysis of a robot-safety device system subjected to a priority rule

We introduce a robot-safety device system characterized by cold stand-by and by an admissible risky state. The system is attended by a single repairman and the robot has overall (break-in) priority in repair with regard to the safety device. We obtain an explicit formula for the point availability of the robot via an integral equation of the renewal-type. The explicit solution requires the notion of effective repair-versus-virtual repair. In order to decide whether the risky state is admissible, we also introduce a risk criterion. The criterion is always satisfied in the case of fast repair. As an example, we consider the case of Weibull-Gnedenko repair and we display a computer-plotted graph of the point availability obtained by a direct numerical solution of a convolution-type integral equation.

On Gaver's parallel system sustained by a cold standby unit and attended by two repairmen

We consider Gavers parallel system sustained by a cold standby unit and attended by two identical repairmen. The system satisfies the usual conditions (i.i.d. random variables, perfect repair, instantaneous and perfect switch, queueing). Each operative unit has a constant failure rate and a deterministic repair time. We analyse the total joint idle time of both repairmen during the survival time of the system. The analysis requires the solution of a delay-differential equation. A numerical example illustrates the structure of the solution for some particular values of the underlying parameters.

Overall availability and risk analysis of a general robot–safety device system

We analyse the availability of a general robot–safety device system characterised by the feature of cold standby and by an admissible risky state. In contrast to the previous literature, we allow a general failure-free time distribution for the robot and, as an example, we present computational results for Coxian failure and repair time distributions. In order to decide whether the risky state is admissible, we introduce a risk criterion based on the notion of rare events. The criterion is always satisfied in the case of fast repair.

A Markov time related to a robot-safety device system

Abstract.We consider a robot-safety device system attended by two different repairmen. The twin-system is characterized by the natural feature of cold standby and an admissible risky state. Apart from tangible results obtained in the previous Literature, we introduce a Markov time called the recovery time of the system. In order to obtain the corresponding distribution, we employ a stochastic process endowed with time dependent state probabilities related to the point availability of a renewable robot without safety device. Finally, as an example, we consider the case of Weibull repair (for the robot) and deterministic repair (for the safety device). We provide several computer-plotted graphs obtained by advanced numerical methods.

A Markov time related to a priority system

We consider a basic renewable duplex system characterized by cold standby and subjected to a priority rule. Apart from a general stochastic analysis presented in the previous literature, we introduce a Markov time called the recovery time of the system. In order to obtain the corresponding Laplace-Stieltjes transform, we employ a stochastic process endowed with transition measures satisfying generalized coupled differential equations. The solution is provided by the theory of sectionally holomorphic functions.