CNR IAMI
Istituto per le Applicazioni
della Matematica e dell'Informatica
| via A. M. Ampère 56 - 20131 Milano (Italy) |
Giornata sull'affidabilità
Marzio MARSEGUERRA
References
1. F. A. Tillman, C. L. Hwang, W. Kuo, Optimization of System Reliability,
1980; Marcel Dekker.
Impiego di algoritmi genetici per la progettazione ottimale di impianto
When designing a system, several choices must be made concerning the type
of components to be used and their assembly configuration. The choice is
driven by the interaction of reliability/availability objectives with the
economic costs associated to the design implementation, system construction
and future operation. Optimization approaches to determine optimal
solutions to design problems have included dynamic programming, integer
programming, mixed integer and nonlinear programming, and heuristics. A
review of the work in this field can be found in Ref. 1 and 2. In
particular, the redundancy allocation problem has been studied extensively
[Ref. 3-6] but generally the configurations considered did not include
k-out-of-n: G redundancies, whereas this is the case in many practical
systems.
In this work we investigate an approach based on the use of genetic
algorithms, to determining the optimal system configuration, where the
choices can include also k-out-of-n: G schemes. Genetic algorithms are
computational tools founded on a direct analogy with the physical evolution
of species. An initial population of potential solutions, in the form of
coded bit strings, is created and allowed to evolve over successive
generations, through mating and mutation. These operations allow the
algorithm to explore the state space in an efficient manner.
Genetic algorithms have been used to solve several engineering problems and
are particularly effective for combinatorial optimization problems with
large, complex search spaces. Within the reliability field, however, there
have been very few examples of their use. In our work, the objective
function used to measure the fitness of a proposed solution is the net
profit of system operation for a given mission time. The net profit is
obtained by subtracting from the service revenue all the costs associated
to the system implementation and operation, i.e. component acquisition and
repair costs, system downtime costs, accident costs to restore external
environmental conditions and refund from losses in case of an accident. The
objective function so designed accounts implicitly for any availability and
reliability constraints through the system downtime and accident costs,
respectively. Mathematically, then, the problem becomes a search in the
system configuration space of that configuration which maximises the
objective function.
The optimization algorithm described above is applied to a simple system,
for validation purposes. The system is composed of three macro-components
A, B and C in series. For each macro-component a choice is to be made among
four different redundant configurations, including k-out-of-n: G schemes.
The validation is performed under the assumptions that the components
cannot be repaired and that failure of macro-component C leads to an
accident with external consequences. This last feature extends the
application to hazardous production plants such as those in the nuclear or
chemical fields. Under these assumptions, the objective function can be
computed analytically and the configuration which maximises it can be found
by inspection: the results thereby obtained are compared to those obtained
by the genetic algorithm and confirm the good performance of the
methodology implemented.
2. F. A. Tillman, C. L. Hwang, W. Kuo, Optimization Techniques for System
Reliability with Redundancy: A Review, IEEE Trans. Reliability, vol. R-26,
1977 Aug., pp. 148-155.
3. M.S. Chern, On the Computational Complexity of Reliability Redundancy
Allocation in a Series System, Operations Research Letters, Vol. 11, 1992
Jun., pp. 309 - 315.
4. R.E. Bellman, E. Dreyfus, Dynamic Programming and Reliability of
Multicomponent Devices, Operations Research, Vol. 6, 1958 Mar - Apr, pp.
200 - 206.
5. D.E. Fyffe, W.W. Hines, N.K. Lee, System Reliability Allocation and a
Computational Algorithm, IEEE Trans. Reliability, Vol. R-17, 1968 Jun., pp.
64 - 69.
6. Y. Nakagawa, S. Miyazaki, Surrogate Constraints Algorithm for
Reliability Optimization Problems with Two Constraints, IEEE Trans.
Reliability, Vol R-30, 1981 Jun, pp. 175 - 180.
Enrico ZIO
Analisi affidabilistica di sistema con metodo Monte Carlo in presenza di
invecchiamento, manutenzioni e obsolescenza tecnologica
This work stems from the consideration that a realistic analysis of the
safety and reliability of a system should include the influential aspects
of aging, maintenance and technological obsolescence. When doing so,
however, one should also take into account the economical constraints
relating to the plant operation and management which are typically in
contrast with the above issues of safety. Modeling all the above
safety/economical issues is quite a difficult, if not impossible, task from
an analytical viewpoint. Instead, the Monte Carlo approach seems well
suited for the task, thanks to its flexibility which allows one to
explicitly include, in quite a straightforward way, many of the
phenomenological aspects of the problem. Here we present a Monte Carlo
simulation scheme for modeling the unavailability of a system, taking into
account aging, maintenance and technological obsolescence.
Andrea SALTELLI
Analisi di sensitività: un ingrediente essenziale per la costruzione di
modelli matematici e computazionali
The modelling process following Rosen
Sensitivity Analysis (SA) as tool versus SA as an end (Rabitz versus
Oreskes)
The dry-cleaner bill model
About partitioning uncertainty among different sources
Setting and strategies
- Fixing unimportant factors
- Testing the relevance of models
- To falsify - corroborate a model or to select among different models
- As a pre-calibration tool
- To optimise R&D
- To partition epistemic from stochastic uncertainties
- For quality assurance and model reliability
Links of SA with Monte Carlo filtering and "Generalised SA" (Young)
Five properties for an ideal global SA method
- Model independence
- Influence of scale and shape
- Multidimensional averaging
- Capture of interaction effects
- Capacity to treat "sets" of factors as one
The new quasi-ideal methods
- Sobol'
- Extended FAST
Examples
- Level E
- KIM
- ARIMA models
Fabrizio RUGGERI
Analisi bayesiana dell'affidabilità di sistemi riparabili
We will review current research on the Bayesian analysis of the reliability
of repairable systems, i.e. systems that can be repaired after a failure
(possibly of a small component of it), keeping the same reliability level as
before the failure. Such a condition is often called `bad-as-old', even if
some authors call it `same-as-old'. Repair time is considered negligible, at
least with respect to the operating time of the system.
Data from repairable systems can be available in different forms. We could
have a unique system, recording its failures up to a given time T
(`time-truncated' data) or until a given number of failures occur
(`failure-truncated' data). Besides, we could consider k identical systems
for which just (random) operating time and number of failures in it are
available. Covariates can be introduced either in the parameters or in their
distributions when a hierarchical model is considered. In all these cases,
failures of repairable systems are often described by means of a non
homogeneous Poisson process, namely the Power Law Process.
Franco CARON, Enrico CAGNO e Mauro MANCINI
Un approccio bayesiano robusto per la valutazione della probabilità
di rottura di tubazioni per la distribuzione del gas in ambito metropolitano
We propose a robust Bayesian methodology to assess the
probability of failure in different kinds of low-pressure cast-iron
pipeline used in metropolitan gas distribution networks. In this
respect, after the identification of the factors leading to failure, the
main problem is the historical data on failures, which is generally
limited and incomplete, and often collected for other purposes.
Consequently, effective evaluation of the probability of failure must be
based on the integration of historical data and knowledge of company
experts. A real world case study is presented in which the company
expertise has been elicited by an ad hoc questionnaire and combined with
the historical data by means of Bayesian inference. The robustness of
the methodology has also been tested.
Antonio PIEVATOLO
Un modello per la descrizione dei guasti in sistemi riparabili complessi
This work originates from a consultancy project in a non-standard
context: modelling the failure process in a gas distribution network
whose size is increasing with time. The available data consist in
the failure times, the total length of the network at the beginning of each
year since the network started operating, and the laying dates
of the failed pipes. The network is divided into subnetworks according
to the laying date.
Each failure is then assigned to a subnetwork according to the
laying date of the failed pipe, and the failure process in each
subnetwork is modelled as a power law process independently of
the other subnetworks. The failure process of the whole network is
obtained by superimposing the power law processes of all the subnetworks.
The failure-to-subnetwork assignment is made because the network is
believed to be a system with increasing failure rate, so the laying
date of a pipe is relevant.
The problem also requires the treatment of missing
information, that is, some of the installation dates, so that
all the failures can then be assigned.
Parameter estimation and the treatment of missing data are
performed via standard Bayesian methods, where the necessary
computation is carried out with MCMC methods.
Two alternative models are proposed: one where all the information on the
laying dates is ignored, and another one where all the available information
is incorporated in the model. The two models are proved to coincide
when all the dates are missing and are uniformly distributed.