Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure

Consider a J-component series system which is put on Accelerated Life Test (ALT) involving K stress variables. First, a general formulation of ALT is provided for log-location-scale family of distributions. A general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, log-linear model, etc., as special cases. Later, the component lives are assumed to be independent Weibull random variables with a common shape parameter. A full Bayesian methodology is then developed by letting only the scale parameters of the Weibull component lives depend on the stress variables through the general stress translation function. Priors on all the parameters, namely the stress coefficients and the Weibull shape parameter, are assumed to be log-concave and independent of each other. This assumption is to facilitate Gibbs sampling from the joint posterior. The samples thus generated from the joint posterior is then used to obtain the Bayesian point and interval estimates of the system reliability at usage condition.

Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure

Consider a J-component series system which is put on Accelerated Life Test (ALT) involving K stress variables. First, a general formulation of ALT is provided for log-location-scale family of distributions. A general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, log-linear model, etc., as special cases. Later, the component lives are assumed to be independent Weibull random variables with a common shape parameter. A full Bayesian methodology is then developed by letting only the scale parameters of the Weibull component lives depend on the stress variables through the general stress translation function. Priors on all the parameters, namely the stress coefficients and the Weibull shape parameter, are assumed to be log-concave and independent of each other. This assumption is to facilitate Gibbs sampling from the joint posterior. The samples thus generated from the joint posterior is then used to obtain the Bayesian point and interval estimates of the system reliability at usage condition.

Weibull modulus for diverse strength due to sample-specificity

By sample specificity it is meant that specimens with the same nominal material parameters and tested under the same environmental conditions may exhibit different behavior with diversified strength. Such an effect has been widely observed in the testing of material failure and is usually attributed to the heterogeneity of material at the mesoscopic level. The degree with which mesoscopic heterogeneity affects macroscopic failure is still not clear. Recently, the problem has been examined by making use of statistical ensemble evolution of dynamical system and the mesoscopic stress re-distribution model (SRD). Sample specificity was observed for non-global mean stress field models, such as the duster mean field model, stress concentration at tip of microdamage, etc. Certain heterogeneity of microdamage could be sensitive to particular SRD leading to domino type of coalescence. Such an effect could start from the microdamage heterogeneity and then be magnified to other scale levels. This trans-scale sensitivity is the origin of sample specificity. The sample specificity leads to a failure probability Phi (N) with a transitional region 0 < (N) < 1, so that globally stable and catastrophic modes could co-exist. It is found that the scatter in strength can fit the Weibull distribution very well. Hence, the Weibull modulus is indicative of sample specificity. Numerical results obtained from the SRD for different non-global mean stress fields show that Weibull modulus increases with increasing sample span and influence region of microdamage.

Estudio de fallas en dieléctricos aplicando la distribución estadística de Weibull con datos truncados

Resumen: En el siguiente trabajo se presentan resultados preliminares en la implementación de análisis de fallas aplicando una distribución de Weibull a partir del truncamiento de la población considerada. Se muestra adicionalmente cuáles son los esfuerzos orientados tanto experimentalmente como computacionalmente.

Fracture statistics of brittle materials: Weibull or normal distribution

The fit of fracture strength data of brittle materials (Si3N4, SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For Si3N4, the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.

Influence of threshold stress on the estimation of the Weibull statistics

The influence of threshold stress on the estimation of the Weibull statistics is discussed in terms of the Akaike information criterion. Numerical simulations show that, if sample data are limited in number and threshold stress is not too large, the two-parameter Weibull distribution is still a preferred choice. For example, the fit of strength data of glass and ceramics to the two- and three-parameter Weibull distributions is compared.

Warranty Prediction Using Weibull Simulation

The main objective of this master’s thesis is to examine if Weibull analysis is suitable method for warranty forecasting in the Case Company. The Case Company has used Reliasoft’s Weibull++ software, which is basing on the Weibull method, but the Company has noticed that the analysis has not given right results. This study was conducted making Weibull simulations in different profit centers of the Case Company and then comparing actual cost and forecasted cost. Simula-tions were made using different time frames and two methods for determining future deliveries. The first sub objective is to examine, which parameters of simulations will give the best result to each profit center. The second sub objective of this study is to create a simple control model for following forecasted costs and actual realized costs. The third sub objective is to document all Qlikview-parameters of profit centers. This study is a constructive research, and solutions for company’s problems are figured out in this master’s thesis. In the theory parts were introduced quality issues, for example; what is quality, quality costing and cost of poor quality. Quality is one of the major aspects in the Case Company, so understand-ing the link between quality and warranty forecasting is important. Warranty management was also introduced and other different tools for warranty forecasting. The Weibull method and its mathematical properties and reliability engineering were introduced. The main results of this master’s thesis are that the Weibull analysis forecasted too high costs, when calculating provision. Although, some forecasted values of profit centers were lower than actual values, the method works better for planning purposes. One of the reasons is that quality improving or alternatively quality decreasing is not showing in the results of the analysis in the short run. The other reason for too high values is that the products of the Case Company are com-plex and analyses were made in the profit center-level. The Weibull method was developed for standard products, but products of the Case Company consists of many complex components. According to the theory, this method was developed for homogeneous-data. So the most im-portant notification is that the analysis should be made in the product level, not the profit center level, when the data is more homogeneous.