Angelo Zanella

Testing the Hypotheses on the Fixed Effects in the Taguchi Approach with Combined Arrays

The paper examines a particular aspect of robustness related to the Taguchi approach to off-line quality control. In particular, the ‘combined array’ approach to experimental design is considered, which requires the noise factors to be reproduced as controllable factors in a laboratory or on a pilot plant level. We propose a statistical method for assessing the existence of controllable factor effects on the mean, in signifying that they are clearly distinguishable from the error random fluctuations even if there are noise factors typically affecting a response of interest in the real production or utilization of some goods. The method has recourse to a statistical test, whose percentage point, defining the acceptance/rejection regions of the hypothesis under study, is the appropriate percentile of a doubly non-central F distribution. The study of the power function of the test suggested the simplification of the latter, which is dealt with in the paper also with regard to an example of application of the proposed method. Copyright

A Simplified Latent Variable Structural Equation Model with Observable Variables Assessed on Ordinal Scales

The communication is related to a wide empirical research promoted by the Universita Cattolica del Sacro Cuore of Milan (UCSC) aimed at acquiring an insight into the real work possibilities of its graduates in the last seven years, as well as the appreciation and satisfaction of the firms which offered them a job position. The group of 1,264 firms which have a special connection with UCSC, regarding new job appointments, was considered and they were given a questionnaire, using web for sending and answering. The analysis of the 203 complete answers was conducted by having recourse to a structural equation model with latent variables.

Extending Taguchi's approach to adaptive stochastic control: A simplified model for feedback adjustments of both mean and variance

In Taguchi’s approach with regard to a quality characteristic Y one has to envisage the optimization of both the mean level, which has to be as near as possible to a target value s , and the variance, which has to be as small as possible. A typical criterion for doing so is that of trying to minimize the mean square error of Y with respect to s (see, for example, Box (1988) and Box and Jones (1992) for a more general approach). Process control based on a dynamic linear model already seems to be in line with the above criterion. Typically, feedback adjustments are de® ned so that the residual errorÐ given by the diVerence between the spontaneous output level Y and the dynamic adjustment based on the system transfer functionÐ has minimum mean square error. Now with regard to a discrete parameter process, for simplicity’s sake, consider the case when the pure delay in response to adjustment corresponds exactly to one unit of time. Then the `optimum’ residual error coincides over time with the noise At, say, which drives the system dynamics and whose components are assumed to have zero mean and to be at least uncorrelated. Thus, the adjustments compensate the random ̄ uctuations of the output level Y that can be forecast through the linear ® lter which transmits the noise to the system, but they do not aVect the probability distribution of At, which expresses the true noise factors at the root of the system’s random variability. A complete extension of the Taguchi approach leads one to consider whether it is also possible to de® ne some control actions related to noise factors. The contribution deals with the problem sketched above. More precisely, it is assumed that the noise At follows an autoregressive conditionally heteroscedastic (ARCH) process. This allows one to de® ne a dynamic control on the At s, which represent noise variance estimators, and correspondingly to obtain a kurtosis reduction in the probability distribution of the noise At. Related estimation problems are also considered.

Artistic and cultural heritage and statistics

We have to be very thankful to the speakers for pointing out so many diverse applications of statistics in the area of preservation of works of art. First of all as professional statisticians we feel pleased for not being cut off in a sector like this, which helps so much to make mans life richer and more spiritual. As far as I know, the topic to which this meeting is devoted is essentially new. When I first read the excellent papers that have just been presented, I was surprised by the large scope of the problems for whose solution statistics can play a key role and also by the extensive use of statistics already made, in connection with studies focusing on works of art preservation, which moreover were carried out in the framework of highest sophisticated technological approaches. The presentations we have been listening to are, in essence, rather specialized. However , if we consider them together, they enable us to find out a first tentative general pattern of possible uses of statistics in the sector under consideration, which appears not only new but very complex too. The following scheme helps in this direction (see Table 1). In the first place we have obviously to distinguish between works of art that have large and complicated structures, like churches, places, castles, etc. and those which in general are of limited size and simple shape, like paintings, frescos, sculptures, etc. In view of a systematic preservation programme the first step is to set up a data base, where for the works of special interest all the necessary information required to evaluate their preservation state and future deter iorat ion danger is recorded. This information should be possibly condensed in some numerical indicators that can help point out priorities. The paper by Baldi and Coppi, Models and methods for the construction of risk maps for cultural heritage, outlines the problems related to such a data base construction for macro-structures together with the statistical techniques of multivariate data analysis type which can be helpful for a classification in terms of ~de-

Some remarks on the physical models concerning two different approaches to inference in statistical process control

For technological applications it can be useful to identify some simple physical mechanisms, which, on the basis of the available knowledge of the production process, may suggest the most appropriate approach to statistical control of the random quantities of interest. For this purpose the notion of rupture point is introduced firstly. A rupture point is characterized bym randomly arising out of control states, assumed to be mutually exclusive and stochastically independent. Shewharts control charts seem to represent the natural statistical tool for controlling a rupture point; however it is shown that they are fully justified only when the hazard rates attached to the causes of failure are constant. Otherwise, typically in the presence of time increasing hazard rates, Shewharts control charts should be completed by a preventive intervention rule (preventive maintenance). In the second place, the notion of dynamic instability point is introduced, which is specifically characterized by assuming that the random quantity of interest is ruled by a stochastic differential equation with constant coefficients. By discretization, developed according to a possibly new approach, it is shown that the former model reduces to an equation error model, which is among the simplest used in adaptive control, and thus particularly easy to deal with in regard to parameter estimation and the definition of the optimum control rule.