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.

n-fold Weibull multiplicative model

In this paper we study the n-fold multiplicative model involving Weibull distributions and examine some properties of the model. These include the shapes for the density and failure rate functions and the WPP plot. These allow one to decide if a given data set can be adequately modelled by the model. We also discuss the estimation of model parameters based on the WPP plot. (C) 2001 Elsevier Science Ltd. All rights reserved.

Study of n-fold Weibull competing risk model

This paper deals with an n-fold Weibull competing risk model. A characterisation of the WPP plot is given along with estimation of model parameters when modelling a given data set. These are illustrated through two examples. A study of the different possible shapes for the density and failure rate functions is also presented. (C) 2003 Elsevier Ltd. All rights reserved.

Effect of prolonged inactivity on skeletal motor nerve terminals during aestivation in the burrowing frog, Cyclorana alboguttata

This study examined the effect of prolonged inactivity, associated with aestivation, on neuromuscular transmission in the green-striped burrowing frog, Cyclorana alboguttata. We compared the structure and function of the neuromuscular junctions on the iliofibularis muscle from active C. alboguttata and from C. alboguttata that had been aestivating for 6 months. Despite the prolonged period of immobility, there was no significant difference in the shape of the terminals (primary, secondary or tertiary branches) or the length of primary terminal branches between aestivators and non-aestivators. Furthermore, there was no significant difference in the membrane potentials of muscle fibres or in miniature end plate potential (EPP) frequency and amplitude. However, there was a significant decrease in evoked transmitter release characterised by a 56% decrease in mean EPP amplitude, and a 29% increase in the failure rate of nerve terminal action potentials to evoke transmitter release. The impact of this suite of neuromuscular characteristics on the locomotor performance of emergent frogs is discussed.

Magnetic resonance imaging and diseases of the liver and biliary tract. Part 2. Magnetic resonance cholangiography and angiography and conclusions

Magnetic resonance cholangiography (MRC) relies on the strong T-2 signal from stationary liquids, in this case bile, to generate images. No contrast agents are required, and the failure rate and risk of serious complications is lower than with endoscopic retrograde cholangiopancreatography (ERCP). Data from MRC can be summated to produce an image much like the cholangiogram obtained by using ERCP. In addition, MRC and conventional MRI can provide information about the biliary and other anatomy above and below a biliary obstruction. This provides information for therapeutic intervention that is probably most useful for hilar and intrahepatic biliary obstruction. Magnetic resonance cholangiography appears to be similar to ERCP with respect to sensitivity and specificity in detecting lesions causing biliary obstruction, and in the diagnosis of choledocholithiasis. It is also suited to the assessment of biliary anatomy (including the assessment of surgical bile-duct injuries) and intrahepatic biliary pathology. However, ERCP can be therapeutic as well as diagnostic, and MRC should be limited to situations where intervention is unlikely, where intrahepatic or hilar pathology is suspected, to delineate the biliary anatomy prior to other interventions, or after failed or inadequate ERCP. Magnetic resonance angiography (MRA) relies on the properties of flowing liquids to generate images. It is particularly suited to assessment of the hepatic vasculature and appears as good as conventional angiography. It has been shown to be useful in delineating vascular anatomy prior to liver transplantation or insertion of a transjugular intrahepatic portasystemic shunt. Magnetic resonance angiography may also be useful in predicting subsequent variceal haemorrhage in patients with oesophageal varices. (C) 2000 Blackwell Science Asia Pty Ltd.

Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.

Outcomes of transient evoked otoacoustic emission testing in 6-year-old school children: A comparison with pure tone screening and tympanometry

Objectives: (1) To establish test performance measures for Transient Evoked Otoacoustic Emission testing of 6-year-old children in a school setting; (2) To investigate whether Transient Evoked Otoacoustic Emission testing provides a more accurate and effective alternative to a pure tone screening plus tympanometry protocol. Methods: Pure tone screening, tympanometry and transient evoked otoacoustic emission data were collected from 940 subjects (1880 ears), with a mean age of 6.2 years. Subjects were tested in non-sound-treated rooms within 22 schools. Receiver operating characteristics curves along with specificity, sensitivity, accuracy and efficiency values were determined for a variety of transient evoked otoacoustic emission/pure tone screening/tympanometry comparisons. Results: The Transient Evoked Otoacoustic Emission failure rate for the group was 20.3%. The failure rate for pure tone screening was found to be 8.9%, whilst 18.6% of subjects failed a protocol consisting of combined pure tone screening and tympanometry results. In essence, findings from the comparison of overall Transient Evoked Otoacoustic Emission pass/fail with overall pure tone screening pass/fail suggested that use of a modified Rhode Island Hearing Assessment Project criterion would result in a very high probability that a child with a pass result has normal hearing (true negative). However, the hit rate was only moderate. Selection of a signal-to-noise ratio (SNR) criterion set at greater than or equal to 1 dB appeared to provide the best test performance measures for the range of SNR values investigated. Test performance measures generally declined when tympanometry results were included, with the exception of lower false alarm rates and higher positive predictive values. The exclusion of low frequency data from the Transient Evoked Otoacoustic Emission SNR versus pure tone screening analysis resulted in improved performance measures. Conclusions: The present study poses several implications for the clinical implementation of Transient Evoked Otoacoustic Emission screening for entry level school children. Transient Evoked Otoacoustic Emission pass/fail criteria will require revision. The findings of the current investigation offer support to the possible replacement of pure tone screening with Transient Evoked Otoacoustic Emission testing for 6-year-old children. However, they do not suggest the replacement of the pure tone screening plus tympanometry battery. (C) 2001 Elsevier Science Ireland Ltd. All rights reserved.

Development and survival of the diamondback moth (Lepidoptera : Plutellidae) at constant and alternating temperatures

Survival and development time from egg to adult emergence of the diamondback moth, Plutella xylostella (L.), were determined at 19 constant and 14 alternating temperature regimes from 4 to 40degreesC. Plutella xylostella developed successfully front egg to adult emergence at constant temperatures from 8 to 32degreesC. At temperatures from 4 to 6degreesC or from 34 to 40degreesC, partial or complete development of individual stages or instars was possible, with third and fourth instars having the widest temperature limits. The insect developed successfully from egg to adult emergence under alternating regimes including temperatures as low as 4degreesC or as high as 38degreesC. The degree-day model, the logistic equation, and the Wang model were used to describe the relationships between temperature and development rate at both constant and alternating temperatures. The degree-day model described the relationships well from 10 to 30degreesC. The logistic equation and the Wang model fit the data well at temperatures 32degreesC. Under alternating regimes, all three models gave good simulations of development in the mid-temperature range, but only the logistic equation gave close simulations in the low temperature range, and none gave close or consistent simulations in the high temperature range. The distribution of development time was described satisfactorily by a Weibull function. These rate and time distribution functions provide tools for simulating population development of P. xylostella over a wide range of temperature conditions.

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Tympanometry and TEOAE testing of children with Down Syndrome in Special Schools

Despite widespread awareness that children with Down syndrome are particularly susceptible to hearing pathologies, the audiological status of students with Down syndrome in special schools is all too often unknown. Unfortunately, hearing screening for this population is unable to rely on standard, behavioural test batteries. To facilitate future improvements in screening protocols, this study investigated the results of tympanometry and transient evoked otoacoustic emission (TEOAE) testing for a group of children with Down syndrome. Assessments were not conducted in the artificial context of a clinic or laboratory, but within the school environment. Outcomes are reported for 27 subjects with a mean age of 10 years 5 months (SD = 4;11). Tympanometry testing was failed in at least one ear by 41.7% of subjects, while a failure rate of 81.5% of subjects was observed for TEOAE testing. Therefore, it is concluded that immediate review of hearing screening programs for students with Down syndrome is highly advisable.

Three horizontal muscle squint surgery for large angle infantile esotropia

Background: To report the long-term outcome of a series of 49 patients who underwent three horizontal muscle squint surgery for large angle infantile esotropia. Methods: The patient records were retrospectively reviewed of 49 (24 girls [49%], 25 boys) consecutive patients with infantile esotropia of angle greater than or equal to60 Delta, who had undergone three horizontal muscle surgery performed by one surgeon (author GG). Surgery consisted of bilateral medial rectus recession combined with graded unilateral lateral rectus resection. Surgeries were carried out over a 6-year period with a mean follow-up period of 32.9 months (3.7-71.8 months). Results: Using Kaplan-Meier life-table analysis, cumulative surgical success (orthotropia +/-10 Delta) was 93.9% at 1 week, 91.8% at 2 and 6 months, 87.7% at 12 and 18 months, 79.9% at 2 years, 77.1% at 3, 4 and 5 years, and 70.6% at 6 years. The mean preoperative deviation was 68.7 Delta. The mean age at surgery was 12.9 months. The failure rate was independent of preoperative deviation. Prevalence of residual esotropia (>10 Delta) varied from 2.0% at 1 week to 17.0% at 6 years. Similarly the prevalence of consecutive exotropia (>10 Delta) varied from 4.0% at 1 week to 12.4% at 6 years. Conclusion: Operating in a graded fashion on three horizontal muscles in children with large angle infantile esotropia has a high success rate, even over long-term follow up. Based on the study's results, amounts of surgery for a given angle of strabismus are proposed.

Mathematical modelling

The development of a new process model of cement grinding in two-stage mills is discussed. The new model has been used to simulate cement grinding and predicting mill performance in open and closed circuit configuration. The new model considered the two-compartment mill as perfectly mixed slices in series. The breakage rate function uses the back calculation technique to determine offline using drop weight and abrasion tests.