Abstract: Stochastic modeling concerns the use of probability
to model real-world situations in which uncertainty is present.
Therefore, the purpose of stochastic modeling is to estimate the
probability of outcomes within a forecast, i.e. to be able to predict
what conditions or decisions might happen under different situations.
In the present study, we present a model of a stochastic diffusion
process based on the bi-Weibull distribution function (its trend
is proportional to the bi-Weibull probability density function). In
general, the Weibull distribution has the ability to assume the
characteristics of many different types of distributions. This has
made it very popular among engineers and quality practitioners, who
have considered it the most commonly used distribution for studying
problems such as modeling reliability data, accelerated life testing,
and maintainability modeling and analysis. In this work, we start
by obtaining the probabilistic characteristics of this model, as the
explicit expression of the process, its trends, and its distribution by
transforming the diffusion process in a Wiener process as shown in
the Ricciaardi theorem. Then, we develop the statistical inference of
this model using the maximum likelihood methodology. Finally, we
analyse with simulated data the computational problems associated
with the parameters, an issue of great importance in its application to
real data with the use of the convergence analysis methods. Overall,
the use of a stochastic model reflects only a pragmatic decision on
the part of the modeler. According to the data that is available and
the universe of models known to the modeler, this model represents
the best currently available description of the phenomenon under
consideration.
Abstract: This paper discusses the effects of using progressive Type-I right censoring on the design of the Simple Step Accelerated Life testing using Bayesian approach for Weibull life products under the assumption of cumulative exposure model. The optimization criterion used in this paper is to minimize the expected pre-posterior variance of the Pth percentile time of failures. The model variables are the stress changing time and the stress value for the first step. A comparison between the conventional and the progressive Type-I right censoring is provided. The results have shown that the progressive Type-I right censoring reduces the cost of testing on the expense of the test precision when the sample size is small. Moreover, the results have shown that using strong priors or large sample size reduces the sensitivity of the test precision to the censoring proportion. Hence, the progressive Type-I right censoring is recommended in these cases as progressive Type-I right censoring reduces the cost of the test and doesn't affect the precision of the test a lot. Moreover, the results have shown that using direct or indirect priors affects the precision of the test.
Abstract: Sometimes the amount of time available for testing could be considerably less than the expected lifetime of the component. To overcome such a problem, there is the accelerated life-testing alternative aimed at forcing components to fail by testing them at much higher-than-intended application conditions. These models are known as acceleration models. One possible way to translate test results obtained under accelerated conditions to normal using conditions could be through the application of the “Maxwell Distribution Law.” In this paper we will apply a combined approach of a sequential life testing and an accelerated life testing to a low alloy high-strength steel component used in the construction of overpasses in Brazil. The underlying sampling distribution will be three-parameter Inverse Weibull model. To estimate the three parameters of the Inverse Weibull model we will use a maximum likelihood approach for censored failure data. We will be assuming a linear acceleration condition. To evaluate the accuracy (significance) of the parameter values obtained under normal conditions for the underlying Inverse Weibull model we will apply to the expected normal failure times a sequential life testing using a truncation mechanism. An example will illustrate the application of this procedure.
Abstract: In this paper, the test purpose will be to assess
whether or not the accelerated model proposed by Eyring will be able
to translate results for the shape and scale parameters of an
underlying Weibull model, obtained under two accelerating using
conditions, to expected normal using condition results for these
parameters. The product being analyzed is a new type of insulate
fluid, and the accelerating factor is the voltage stresses applied to the
fluid at two different levels (30KV and 40KV). The normal operating
voltage is 25KV. In this case, it was possible to test the insulate fluid
at normal voltage using condition. Both results for the two
parameters of the Weibull model, obtained under normal using
condition and translated from accelerated using conditions to normal
conditions, will be compared to each other to assess the accuracy of
the Eyring model when the accelerating factor is only the voltage
stress.