Wagner Borges

A simple test for new better than used in expectation

We present a statistical procedure to test that a life distribution is exponential against the al ternative that it is continuous new better than used in expectation. The test is shown to be consistent and asymptotic relative efficiency resul ts are obtained against the competitor developed earlier by Hollander and Proschan [2], for certain families of alternatives.

An Axiomatic Characterization of Multistate Coherent Structures

Mathematical models for multistate reliability systems of multistate components have been proposed by Barlow and Wu (Barlow, R. E., A. S. Wu. 1978. Coherent systems with multistate components. Math. Oper. Res. 3 275–281.), El-Neweihi et al. (El-Neweihi, E., F. Proschan, J. Sethuraman. 1978. Multistate coherent systems. J. Appl. Probab. 15 675–688.) and Griffith (Griffith, W. S. 1980. Multistate reliability models. J. Appl. Probab. 17 735–744.). Unlike the approach used by Barlow and Wu, the other authors preferred to establish their classes of models through sets of axioms extending the early binary notions and containing as special cases the class of models suggested by Barlow and Wu. Since the Barlow and Wu approach is set theoretic and the model definition is essentially qualitative, a question of interest concerns its axiomatic characterization among larger classes of models. In this paper such a characterization is established that relates the Barlow and Wu models to the other classes of models intro...

A Statistical Model for Shelf Life Estimation Using Sensory Evaluations Scores

Abstract This article focuses on the problem of estimating the shelf life of food products by modeling the results coming from sensory evaluations. In such studies, trained panelists are asked to judge food attributes by reference to a scale of numbers (scores varying often from 0 to 6). The usual statistical approach for data analysis is to fit a regression line relating the scores and the time of evaluation. The estimate of the shelf life is obtained by solving the regression equation and replacing the score by a cut-off point (which indicates product “failure”) previously chosen by the food company. The procedure used in these sensory evaluations is such that one never knows the exact “time to failure”. Consequently, data arising from these studies are either right or left censored. We propose a model which incorporates these informations and assumes a Weibull for the underlying distribution of the failure time. Simulation studies were implemented. The approach was used in a real data set coming from sensory evaluations of a dehydrated food product.

On the sampling distribution of clement's capability index

Most of the research effort concerning the development and statistical study of capability indices has been devoted to normal processes. In this paper a statistical study of a capability index for non-normal processes proposed by Clements (1989) is developed. An approximate distribution for the natural estimator of the index is obtained from a distribution free point of view and a simulation study is used to compare it with its empirical distribution. An approximate conservative lower confidence limit for the index is also constructed.

Sample plans comparisons for shelf life estimation using sensory evaluation scores

Sensory evaluations to determine the shelf life of food products are routinely conducted in food experimentation as a part of each product development program, whether it includes a new product, product improvement or a change in type or specification of an ingredient. In such experiments, trained panelists are asked to judge food attributes by reference to a scale of numbers. The “failure time” associated with a product unit under test is usually defined as the time required to reach a cut‐off point previously defined by the food company. Important issues associated with the planning and execution of this kind of testing are total sampling size, frequency of sample withdrawals, panel design, and statistical analysis of the panel data, to list a few. Different approaches have been proposed for the analysis of this kind of data. In particular, Freitas et al. proposed an alternative model based on a dichotomization of the score data and a Weibull as the underlying distribution for the time to failure. Also, through a simulation study, the bias and mean square error of the estimates obtained for percentiles and fraction defectives were evaluated. These quantities were used to estimate the shelf life. The simulation study used only the same sample plan implemented in the real situation. This paper focuses on the planning issues associated with these experiments. Sample plans are contrasted and compared in a simulation study, through the use of the approach proposed by Freitas et al.. The simulation results showed that, in general, one can get results much more precise and with smaller bias with a shorter follow‐up time, allocating more panelists to each evaluation time.

On the limiting distribution of the failure time of fibrous materials

A large deviation theorem of the Cramer–Petrov type and a ranking limit theorem of Loeve are used to derive an approximation for the statistical distribution of the failure time of fibrous materials. For that, fibrous materials are modeled as a series of independent and identical bundles of parallel filaments and the asymptotic distribution of their failure time is determined in terms of statistical characteristics of the individual filaments, as both the number of filaments in each bundle and the number of bundles in the chain grow large simultaneously. While keeping the number n of filaments in each bundle fixed and increasing only the chain length k leads to a Weibull limiting distribution for the failure time, letting both increase in such a way that log k ( n ) = o ( n ), we show that the limit distribution is for . Since fibrous materials which are both long and have many filaments prevail, the result is of importance in the materials science area since refined approximations to failure-time distributions can be achieved.