Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.

A parametric model for the interval censored survival times of Acacia mangium plantation in a spacing trial

Survival times for the Acacia mangium plantation in the Segaliud Lokan Project, Sabah, East Malaysia were analysed based on 20 permanent sample plots (PSPs) established in 1988 as a spacing experiment. The PSPs were established following a complete randomized block design with five levels of spacing randomly assigned to units within four blocks at different sites. The survival times of trees in years are of interest. Since the inventories were only conducted annually, the actual survival time for each tree was not observed. Hence, the data set comprises censored survival times. Initial analysis of the survival of the Acacia mangium plantation suggested there is block by spacing interaction; a Weibull model gives a reasonable fit to the replicate survival times within each PSP; but a standard Weibull regression model is inappropriate because the shape parameter differs between PSPs. In this paper we investigate the form of the non-constant Weibull shape parameter. Parsimonious models for the Weibull survival times have been derived using maximum likelihood methods. The factor selection for the parameters is based on a backward elimination procedure. The models are compared using likelihood ratio statistics. The results suggest that both Weibull parameters depend on spacing and block.

Infant mortality model for lifetime data

In this paper we introduce a parametric model for handling lifetime data where an early lifetime can be related to the infant-mortality failure or to the wear processes but we do not know which risk is responsible for the failure. The maximum likelihood approach and the sampling-based approach are used to get the inferences of interest. Some special cases of the proposed model are studied via Monte Carlo methods for size and power of hypothesis tests. To illustrate the proposed methodology, we introduce an example consisting of a real data set.

Testes em modelos weibull na forma estendida de Marshall-Olkin

In survival analysis, the response is usually the time until the occurrence of an event of interest, called failure time. The main characteristic of survival data is the presence of censoring which is a partial observation of response. Associated with this information, some models occupy an important position by properly fit several practical situations, among which we can mention the Weibull model. Marshall-Olkin extended form distributions other a basic generalization that enables greater exibility in adjusting lifetime data. This paper presents a simulation study that compares the gradient test and the likelihood ratio test using the Marshall-Olkin extended form Weibull distribution. As a result, there is only a small advantage for the likelihood ratio test

Cat's claw oxindole alkaloid isomerization induced by common extraction methods

Cat's claw oxindole alkaloids are prone to isomerization in aqueous solution. However, studies on their behavior in extraction processes are scarce. This paper addressed the issue by considering five commonly used extraction processes. Unlike dynamic maceration (DM) and ultrasound-assisted extraction, substantial isomerization was induced by static maceration, turbo-extraction and reflux extraction. After heating under reflux in DM, the kinetic order of isomerization was established and equations were fitted successfully using a four-parameter Weibull model (R² > 0.999). Different isomerization rates and equilibrium constants were verified, revealing a possible matrix effect on alkaloid isomerization.

Germination of Ocotea pulchella (Nees) Mez (Lauraceae) seeds in laboratory and natural restinga environment conditions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Ascorbic acid degradation kinetics in tomatoes at different drying conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Desenvolvimento e caracterização de sistemas nanoestruturados para potencial administração nasal de zidovudina

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Avaliação da longevidade de vacas da raça Nelore por diferentes critérios utilizando análise de sobrevivência

Pós-graduação em Genética e Melhoramento Animal - FCAV

The Effects of High Pressure Processing on Peanut Sauce Inoculated with Salmonella

Recent Salmonella outbreaks have prompted the need for new processing options for peanut products. Traditional heating kill-steps have shown to be ineffective in lipid-rich matrices such as peanut products. High pressure processing is one such option for peanut sauce because it has a high water activity, which has proved to be a large contributing factor in microbial lethality due to high pressure processing. Four different formulations of peanut sauce were inoculated with a five strain Salmonella cocktail and high pressure processed. Results indicate that increasing pressure or increasing hold time increases log10 reductions. The Weibull model was fitted to each kill curve, with b and n values significantly optimized for each curve (p-value < 0.05). Most curves had an n parameter value less than 1, indicating that the population had a dramatic initial reduction, but tailed off as time increased, leaving a small resistant population. ANOVA analysis of the b and n parameters show that there are more significant differences between b parameters than n parameters, meaning that most treatments showed similar tailing effect, but differed on the shape of the curve. Comparisons between peanut sauce formulations at the same pressure treatments indicate that increasing amount of organic peanut butter within the sauce formulation decreases log10 reductions. This could be due to a protective effect from the lipids in the peanut butter, or it may be due to other factors such as nutrient availability or water activity. Sauces pressurized at lower temperatures had decreased log10 reductions, indicating that cooler temperatures offered some protective effect. Log10 reductions exceeded 5 logs, indicating that high pressure processing may be a suitable option as a kill-step for Salmonella in industrial processing of peanut sauces. Future research should include high pressure processing on other peanut products with high water activities such as sauces and syrups as well as research to determine the effects of water activity and lipid composition with a food matrix such as peanut sauces.

Microencapsulation of Ketoprofen in Blends of Acrylic Resins by Spray Drying

Microparticles of ketoprofen entrapped in blends of acrylic resins (Eudragit RL 30D and RS 30D) were successfully produced by spray drying. The effects of the proportion ketoprofen : polymer (1: 1 and 1: 3) and of spray-drying parameters (drying gas inlet temperatures of 80 and 100 degrees C; microencapsulating composition feed flow rates of 4 and 6 g/min) on the microparticles properties (drug content, encapsulation efficiency, mean particle size, moisture content, and dissolution behavior) were evaluated. Differential scanning calorimetry (DSC) thermograms and X-ray diffractograms of the spray-dried product, the free drug, and the physical mixture between the free drug and spray-dried composition (blank) were carried out. Microparticles obtained at inlet temperature of 80 degrees C, feed flow rate of 4 g/min, and ketoprofen : acrylic resin ratio of 1: 3 presented an encapsulation efficiency of 88.1%, moisture content of 5.8%, production yield around 50%, and a higher reduction in dissolution rate of the entrapped ketoprofen. Sigmoidal shape dissolution profiles were presented by the spray-dried microparticles. The dissolution profiles were relatively well described by the Weibull model, a showing high coefficient of determination, R-2, and a mean absolute error between experimental and estimated values of between 4.6 and 10.1%.

The assumptions and effects of conservative procedures in low -dose risk assessment for setting safety standards

Conservative procedures in low-dose risk assessment are used to set safety standards for known or suspected carcinogens. However, the assumptions upon which the methods are based and the effects of these methods are not well understood.^ To minimize the number of false-negatives and to reduce the cost of bioassays, animals are given very high doses of potential carcinogens. Results must then be extrapolated to much smaller doses to set safety standards for risks such as one per million. There are a number of competing methods that add a conservative safety factor into these calculations.^ A method of quantifying the conservatism of these methods was described and tested on eight procedures used in setting low-dose safety standards. The results using these procedures were compared by computer simulation and by the use of data from a large scale animal study.^ The method consisted of determining a "true safe dose" (tsd) according to an assumed underlying model. If one assumed that Y = the probability of cancer = P(d), a known mathematical function of the dose, then by setting Y to some predetermined acceptable risk, one can solve for d, the model's "true safe dose".^ Simulations were generated, assuming a binomial distribution, for an artificial bioassay. The eight procedures were then used to determine a "virtual safe dose" (vsd) that estimates the tsd, assuming a risk of one per million. A ratio R = ((tsd-vsd)/vsd) was calculated for each "experiment" (simulation). The mean R of 500 simulations and the probability R $<$ 0 was used to measure the over and under conservatism of each procedure.^ The eight procedures included Weil's method, Hoel's method, the Mantel-Byran method, the improved Mantel-Byran, Gross's method, fitting a one-hit model, Crump's procedure, and applying Rai and Van Ryzin's method to a Weibull model.^ None of the procedures performed uniformly well for all types of dose-response curves. When the data were linear, the one-hit model, Hoel's method, or the Gross-Mantel method worked reasonably well. However, when the data were non-linear, these same methods were overly conservative. Crump's procedure and the Weibull model performed better in these situations. ^

Evaluation of the reliability of commercial concentrator triple-junction solar cells by means of accelerated life tests (ALT)

A temperature accelerated life test on commercial concentrator lattice-matched GaInP/GaInAs/Ge triple-junction solar cells has been carried out. The solar cells have been tested at three different temperatures: 119, 126 and 164 °C and the nominal photo-current condition (820 X) has been emulated by injecting current in darkness. All the solar cells have presented catastrophic failures. The failure distributions at the three tested temperatures have been fitted to an Arrhenius-Weibull model. An Arrhenius activation energy of 1.58 eV was determined from the fit. The main reliability functions and parameters (reliability function, instantaneous failure rate, mean time to failure, warranty time) of these solar cells at the nominal working temperature (80 °C) have been obtained. The warranty time obtained for a failure population of 5 % has been 69 years. Thus, a long-term warranty could be offered for these particular solar cells working at 820 X, 8 hours per day at 80 °C.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.