A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

Reliability studies of the skew normal distribution

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability function of a skew normal random variable. We also compare it with the normal distribution with respect to certain stochastic orderings. Appropriate machinery is developed to obtain the reliability of a component when the strength and stress follow the skew normal distribution. Finally, IQ score data from Roberts (1988) is analyzed to illustrate the procedure.

Statistical Calculation of the Main Reliability Functions of GaAs Concentrator III-V Solar Cells

This paper presents some of the results of a method to determine the main reliability functions of concentrator solar cells. High concentrator GaAs single junction solar cells have been tested in an Accelerated Life Test. The method can be directly applied to multi-junction solar cells. The main conclusions of this test carried out show that these solar cells are robust devices with a very low probability of failure caused by degradation during their operation life (more than 30 years). The evaluation of the probability operation function (i.e. the reliability function R(t)) is obtained for two nominal operation conditions of these cells, namely simulated concentration ratios of 700 and 1050 suns. Preliminary determination of the Mean Time to Failure indicates a value much higher than the intended operation life time of the concentrator cells.

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.

Evaluation of the reliability of high concentrator GaAs solar cells by means of temperature accelerated aging tests

ABSTRACT Evaluating the reliability, warranty period, and power degradation of high concentration solar cells is crucial to introducing this new technology to the market. The reliability of high concentration GaAs solar cells, as measured in temperature accelerated life tests, is described in this paper. GaAs cells were tested under high thermal accelerated conditions that emulated operation under 700 or 1050 suns over a period exceeding 10 000 h. Progressive power degradation was observed, although no catastrophic failures occurred. An Arrhenius activation energy of 1.02 eV was determined from these tests. The solar cell reliability [R(t)] under working conditions of 65°C was evaluated for different failure limits (1–10% power loss). From this reliability function, the mean time to failure and the warranty time were evaluated. Solar cell temperature appeared to be the primary determinant of reliability and warranty period, with concentration being the secondary determinant. A 30-year warranty for these 1 mm2-sized GaAs cells (manufactured according to a light emitting diode-like approach) may be offered for both cell concentrations (700 and 1050 suns) if the solar cell is operated at a working temperature of 65°C.

Reliability management of machine tool technology: a case study of current practice

Considerable attention has been given in the literature to identifying and describing the effective elements which positively affect the improvement of product reliability. These have been perceived by many as the 'state of the art' in the manufacturing industry. The applicability, diffusion and effectiveness of such methods and philosophies, as a means of systematically improving the reliability of a product, come in the main from case studies and single and infra-industry empirical studies. These studies have both been carried out within the wider context of quality assurance and management, and taking reliability as a discipline in its own right. However, it is somewhat of a surprise that there are no recently published findings or research studies on the adoption of these methods by the machine tool industry. This may lead one to construct several hypothesised paradigms: (a) that machine tool manufacturers compared to other industries, are slow to respond to propositions given in the literature by theorists or (b) this may indicate that a large proportion of the manufacturers make little use of the reliability improvement techniques as described in the literature, with the overall perception that they will not lead to any significant improvements? On the other hand, it is evident that hypothetical verification of the operational and engineering methods of reliability achievement and improvement adopted in the machine tool industry is less widely researched. Therefore, research into this area is needed in order to explore the 'state of the art' practice in the machine tool industry. This is in terms of the status, structure and activities of the operation of the reliability function. This paper outlines a research programme being conducted with the co-operation of a leading machine tool manufacturer, whose UK manufacturing plant produces in the main Vertical Machining Centres (VMCs) and is continuously undergoing incremental transitions in product reliability improvement.

Inferência bayesiana não-paramétrica para elicitação da função de contabilidade

Pós-graduação em Matematica Aplicada e Computacional - FCT

Estimadores bayesianos de la fiabilidad con muestreo censurado

El estudio de la fiabilidad de componentes y sistemas tiene gran importancia en diversos campos de la ingenieria, y muy concretamente en el de la informatica. Al analizar la duracion de los elementos de la muestra hay que tener en cuenta los elementos que no fallan en el tiempo que dure el experimento, o bien los que fallen por causas distintas a la que es objeto de estudio. Por ello surgen nuevos tipos de muestreo que contemplan estos casos. El mas general de ellos, el muestreo censurado, es el que consideramos en nuestro trabajo. En este muestreo tanto el tiempo hasta que falla el componente como el tiempo de censura son variables aleatorias. Con la hipotesis de que ambos tiempos se distribuyen exponencialmente, el profesor Hurt estudio el comportamiento asintotico del estimador de maxima verosimilitud de la funcion de fiabilidad. En principio parece interesante utilizar metodos Bayesianos en el estudio de la fiabilidad porque incorporan al analisis la informacion a priori de la que se dispone normalmente en problemas reales. Por ello hemos considerado dos estimadores Bayesianos de la fiabilidad de una distribucion exponencial que son la media y la moda de la distribucion a posteriori. Hemos calculado la expansion asint6tica de la media, varianza y error cuadratico medio de ambos estimadores cuando la distribuci6n de censura es exponencial. Hemos obtenido tambien la distribucion asintotica de los estimadores para el caso m3s general de que la distribucion de censura sea de Weibull. Dos tipos de intervalos de confianza para muestras grandes se han propuesto para cada estimador. Los resultados se han comparado con los del estimador de maxima verosimilitud, y con los de dos estimadores no parametricos: limite producto y Bayesiano, resultando un comportamiento superior por parte de uno de nuestros estimadores. Finalmente nemos comprobado mediante simulacion que nuestros estimadores son robustos frente a la supuesta distribuci6n de censura, y que uno de los intervalos de confianza propuestos es valido con muestras pequenas. Este estudio ha servido tambien para confirmar el mejor comportamiento de uno de nuestros estimadores. SETTING OUT AND SUMMARY OF THE THESIS When we study the lifetime of components it's necessary to take into account the elements that don't fail during the experiment, or those that fail by reasons which are desirable to exclude from consideration. The model of random censorship is very usefull for analysing these data. In this model the time to failure and the time censor are random variables. We obtain two Bayes estimators of the reliability function of an exponential distribution based on randomly censored data. We have calculated the asymptotic expansion of the mean, variance and mean square error of both estimators, when the censor's distribution is exponential. We have obtained also the asymptotic distribution of the estimators for the more general case of censor's Weibull distribution. Two large-sample confidence bands have been proposed for each estimator. The results have been compared with those of the maximum likelihood estimator, and with those of two non parametric estimators: Product-limit and Bayesian. One of our estimators has the best behaviour. Finally we have shown by simulation, that our estimators are robust against the assumed censor's distribution, and that one of our intervals does well in small sample situation.

AN ENTROPIC THEORY OF DAMAGE WITH APPLICATIONS TO CORROSION-FATIGUE STRUCTURAL INTEGRITY ASSESSMENT

This dissertation demonstrates an explanation of damage and reliability of critical components and structures within the second law of thermodynamics. The approach relies on the fundamentals of irreversible thermodynamics, specifically the concept of entropy generation due to materials degradation as an index of damage. All failure mechanisms that cause degradation, damage accumulation and ultimate failure share a common feature, namely energy dissipation. Energy dissipation, as a fundamental measure for irreversibility in a thermodynamic treatment of non-equilibrium processes, leads to and can be expressed in terms of entropy generation. The dissertation proposes a theory of damage by relating entropy generation to energy dissipation via generalized thermodynamic forces and thermodynamic fluxes that formally describes the resulting damage. Following the proposed theory of entropic damage, an approach to reliability and integrity characterization based on thermodynamic entropy is discussed. It is shown that the variability in the amount of the thermodynamic-based damage and uncertainties about the parameters of a distribution model describing the variability, leads to a more consistent and broader definition of the well know time-to-failure distribution in reliability engineering. As such it has been shown that the reliability function can be derived from the thermodynamic laws rather than estimated from the observed failure histories. Furthermore, using the superior advantages of the use of entropy generation and accumulation as a damage index in comparison to common observable markers of damage such as crack size, a method is proposed to explain the prognostics and health management (PHM) in terms of the entropic damage. The proposed entropic-based damage theory to reliability and integrity is then demonstrated through experimental validation. Using this theorem, the corrosion-fatigue entropy generation function is derived, evaluated and employed for structural integrity, reliability assessment and remaining useful life (RUL) prediction of Aluminum 7075-T651 specimens tested.

Cross-cultural adaptation, reliability, internal consistency and validation of the Spinal Function Sort (SFS) for French- and German-speaking patients with back complaints.

Introduction Functional subjective evaluation through questionnaire is fundamental, but not often realized in patients with back complaints, lacking validated tools. The Spinal Function Sort (SFS) was only validated in English. We aimed to translate, adapt and validate the French (SFS-F) and German (SFS-G) versions of the SFS. Methods Three hundred and forty-four patients, experiencing various back complaints, were recruited in a French (n = 87) and a German-speaking (n = 257) center. Construct validity was estimated via correlations with SF-36 physical and mental scales, pain intensity and hospital anxiety and depression scales (HADS). Scale homogeneities were assessed by Cronbach's α. Test-retest reliability was assessed on 65 additional patients using intraclass correlation (IC). Results For the French and German translations, respectively, α were 0.98 and 0.98; IC 0.98 (95% CI: [0.97; 1.00]) and 0.94 (0.90; 0.98). Correlations with physical functioning were 0.63 (0.48; 0.74) and 0.67 (0.59; 0.73); with physical summary 0.60 (0.44; 0.72) and 0.52 (0.43; 0.61); with pain -0.33 (-0.51; -0.13) and -0.51 (-0.60; -0.42); with mental health -0.08 (-0.29; 0.14) and 0.25 (0.13; 0.36); with mental summary 0.01 (-0.21; 0.23) and 0.28 (0.16; 0.39); with depression -0.26 (-0.45; -0.05) and -0.42 (-0.52; -0.32); with anxiety -0.17 (-0.37; -0.04) and -0.45 (-0.54; -0.35). Conclusions Reliability was excellent for both languages. Convergent validity was good with SF-36 physical scales, moderate with VAS pain. Divergent validity was low with SF-36 mental scales in both translated versions and with HADS for the SFS-F (moderate in SFS-G). Both versions seem to be valid and reliable for evaluating perceived functional capacity in patients with back complaints.

Validity and reliability of the Portuguese version of Mandibular Function Impairment Questionnaire

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

Validity and reliability of using MVP 4 Function Walk4Life digital pedometers to assess physical activity levels among preschool-aged Head Start children

The Surgeon General recommends preschoolers 3-5 years old accumulate 60 minutes of moderate-to-vigorous physical activity (MVPA) per day. However, there is limited data measuring physical activity (PA) and MVPA amongst this population. The purpose of this cross-sectional study is to determine the validity, reliability, and feasibility of using MVP 4 Function Walk4Life digital pedometers (MVP-4) in measuring MVPA among preschoolers using the newly modified direct observational technique, System for Observing Fitness Instruction Time-Preschool Version (SOFIT-P) as the gold standard. An ethnically diverse population of 3-5 year old underserved children were recruited from two Harris County Department of Education (HCDE) Head Start centers. For 2 days at baseline and 2 days at post-test, 75 children enrolled wore MVP-4 pedometers for approximately 6-hours per observation day and were observed using SOFIT-P during predominantly active times. Statistical analyses used Pearson "r" correlation coefficients to determine mean minutes of PA and MVPA, convergent and criterion validity, and reliability. Significance was set at p = <0.05. Feasibility was determined through process evaluation information collected during this study via observations from data collectors and teacher input. Results show mean minutes of PA and MVPA ranged between 30-42 and 11-14 minutes, respectively. Convergent validity comparing BMI percentiles with MVP-4 PA outcomes show no significance at pre-test; however, each measurement at post-test showed significance for MVPA (p = 0.0247, p = 0.0056), respectively. Criterion validity comparing percent MVPA time between SOFIT-P and MVP-4 pedometers was determined; however, results deemed insufficient due to inconsistency in observation times while using the newly developed SOFIT-P. Reliability measures show no significance at pre-test, yet show significant results for all PA outcomes at post-test (p = 0.001, p = 0.001, p = 0.0010, p = 0.003), respectively. Finally, MVP-4 pedometers lacked feasibility due to logistical barriers in design. Researchers feel the significant results at post-test are secondary to increased familiarity and more accurate placement of pedometers across time. Researchers suggest manufacturers of MVP-4 pedometers further modify the instrument for ease of use with this population, following which future studies ought to determine validity using objective measures or all-day direct observation techniques.^

Analysis of pelvic floor musculature function during pregnancy and postpartum: a cohort study

Aim. To compare the measurements of women`s pelvic floor musculature strength (PFMS) during pregnancy and postpartum period. Background. Pregnancy and childbirth can have an influence on the muscles and pelvic floor and can cause morbidities of women`s genito-urinary tract. Design. A prospective cohort study. Methods. There were included 226 primigravidae women, attended by community health services in the city of Itapecerica da Serra, Sao Paulo, Brazil. The participants were followed in four stages: (1) within 12 weeks of pregnancy; (2) between 36-40 weeks of pregnancy; (3) within 48 hours after childbirth; (4) 42-60 days after childbirth. Data were collected from February 2007-August 2008. The pelvic floor musculature strength was evaluated by perineometry and digital vaginal palpation in stages 1, 2 and 4. The final sample included 110 women who completed all four stages of the study. Results. The pelvic floor musculature strength of the women did not change significantly during pregnancy or after delivery (anova: p = 0 center dot 78). In all three examined stages, a low-intensity pelvic floor musculature strength was prevalent (in mmHg: stage 1 = 15 center dot 9; stage 2 = 15 center dot 2, stage 4 = 14 center dot 7), with scores from 0-3 on the Oxford scale. The pelvic floor musculature strength did not differ in relation to maternal age, skin colour, conjugal status, dyspareunia, stool characteristics, type of delivery, or conditions of the perineum. An interaction between maternal nutritional state and newborn`s weight may affect the pelvic floor musculature strength (manova: p = 0 center dot 04). Conclusion. Pregnancy and childbirth did not reduce significantly pelvic floor musculature strength. The perineometry and digital vaginal palpation used to assess the pelvic floor musculature strength were well accepted by the women. Relevance to clinical practice. In clinical practice, digital vaginal palpation is effective for supporting the diagnosis of urinary, intestinal and sexual dysfunctions. Perineometry use is particularly important together with the performance of perineal exercises with biofeedback in the treatment these disorders.

Reliability and validity of physical fitness field tests for adults aged 55 to 70 years

The aim of this study was to examine the reliability and validity of field tests for assessing physical function in mid-aged and young-old people (55–70 y). Tests were selected that required minimal space and equipment and could be implemented in multiple field settings such as a general practitioner's office. Nineteen participants completed 2 field and 1 laboratory testing sessions. Intra-class correlations showed good reliability for the tests of upper body strength (lift and reach, R= .66), lower body strength (sit to stand, R= .80) and functional capacity (Canadian Step Test, R= .92), but not for leg power (single timed chair rise, R= .28). There was also good reliability for the balance test during 3 stances: parallel (94.7% agreement), semi-tandem (73.7%), and tandem (52.6%). Comparison of field test results with objective laboratory measures found good validity for the sit to stand (cf 1RM leg press, Pearson r= .68, p< .05), and for the step test (cf PWC140, r= −.60, p< .001), but not for the lift and reach (cf 1RM bench press, r= .43, p> .05), balance (r= −.13, −.18, .23) and rate of force development tests (r= −.28). It was concluded that the lower body strength and cardiovascular function tests were appropriate for use in field settings with mid-aged and young-old adults.