*CNR IAMI
Istituto per le Applicazioni
della Matematica e dell'Informatica *

via A. M. Ampère 56 - 20131 Milano (Italy) |

**Giornata sull'affidabilità**

1. F. A. Tillman, C. L. Hwang, W. Kuo, Optimization of System Reliability,
1980; Marcel Dekker.

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.