A. J. van der Merwe

Bayesian Control Chart for Nonconformities

The c-chart or the control chart for nonconformities is designed for the case where one deals with the number of defects or nonconformities observed. A control chart can be developed for the total or average number of nonconformities per unit, which is well modeled by the Poisson distribution. In this paper the c-chart will be studied, where the usual operation of the c-chart will be extended by introducing a Bayesian approach for the c-chart. Control chart limits, average run lengths, and false alarm rates will be determined by using a Bayesian method. These results will be compared with the results obtained when using the classical (frequentist) method. Copyright

Bayesian calibration in the estimation of the age of rhinoceros

In this paper the Bayesian approach for nonlinear multivariate calibration will be illustrated. This goal will be achieved by applying the Gibbs sampler to the rhinoceros data given by Clarke (1992, Biometrics, 48(4), 1081–1094). It will be shown that the point estimates obtained from the profile likelihoods and those calculated from the marginal posterior densities using improper priors will in most cases be similar.

Bayesian process monitoring schemes for the two-parameter exponential distribution

ABSTRACTIn this paper a Bayesian procedure is applied to obtain control limits for the location and scale parameters, as well as for a one-sided upper tolerance limit in the case of the two-parameter exponential distribution. An advantage of the upper tolerance limit is that it monitors the location and scale parameter at the same time. By using Jeffreys’ non-informative prior, the predictive distributions of future maximum likelihood estimators of the location and scale parameters are derived analytically. The predictive distributions are used to determine the distribution of the “run-length” and expected “run-length”. A dataset given in Krishnamoorthy and Mathew (2009) are used for illustrative purposes. The data are the mileages for some military personnel carriers that failed in service. The paper illustrates the flexibility and unique features of the Bayesian simulation method.ABSTRACT In this paper a Bayesian procedure is applied to obtain control limits for the location and scale parameters, as well as for a one-sided upper tolerance limit in the case of the two-parameter exponential distribution. An advantage of the upper tolerance limit is that it monitors the location and scale parameter at the same time. By using Jeffreys’ non-informative prior, the predictive distributions of future maximum likelihood estimators of the location and scale parameters are derived analytically. The predictive distributions are used to determine the distribution of the “run-length” and expected “run-length”. A dataset given in Krishnamoorthy and Mathew (2009) are used for illustrative purposes. The data are the mileages for some military personnel carriers that failed in service. The paper illustrates the flexibility and unique features of the Bayesian simulation method.

A Bayesian control chart for a common coefficient of variation

ABSTRACT By using the medical data analyzed by Kang et al. (2007), a Bayesian procedure is applied to obtain control limits for the coefficient of variation. Reference and probability matching priors are derived for a common coefficient of variation across the range of sample values. By simulating the posterior predictive density function of a future coefficient of variation, it is shown that the control limits are effectively identical to those obtained by Kang et al. (2007) for the specific dataset they used. This article illustrates the flexibility and unique features of the Bayesian simulation method for obtaining posterior distributions, predictive intervals, and run-lengths in the case of the coefficient of variation. A simulation study shows that the 95% Bayesian confidence intervals for the coefficient of variation have the correct frequentist coverage.

The development of a physiotherapy intervention programme for mandibular condyle fracture patients : research

Resin-bonded fixed dental prostheses had variable popularity since the technique for splinting mandibular anterior teeth with a perforated metal casting was described by Rochette. His work was then suggested as an alternative to conventional metal-ceramic fixed FDPs and its substantial removal of tooth structure needed to create strong, anatomically contoured, and esthetic restorations. The most accepted design for resin bonded bridge is covering the maximum area of palatal or lingual surface of the abutment which give moderate fracture strength in low stress area like lateral incisor, in this research we tried to compare that conventional design for restoring upper lateral incisor with other more conservative one (by reducing the retainer size) that was proposed to enhance esthetic and fracture strength. Finite element analysis (using solid work software) was used to compare fracture strength of three different restorative material used (PFM, IPS Empress &Vita In-Ceram zirconium) simulation of occlusal load on the pontic portion of the restoration (solid work was fed by all the individual properties to predict the behavior of the actual object). This study proved that the fracture strength of the proposed conservative design may exceed that of the conventional design. Research Article Citation: Amr Touny Abbas, Enas Fateh Elbab, Manal Rafie, et al. Finite Element Study of Fracture Strength of Two Different Resin Bonded Bridge Designs. Oral Health Dental Sci. 2017; 1(1): 1-6.Introduction: The need for physiotherapy in the treatment of mandibular condyle fractures has been highlighted, but there has been no agreement regarding an exercise programme for these patients Aims and objectives: The study aimed to develop proposals for an appropriate program for patients who had sustained mandibular condyle fractures. Design: Quantitative, non-experimental study, by means of a Delphi questionnaire. Methods: Data obtained from the literature and a previously conducted needs analysis was used in compiling a Delphi questionnaire dealing with the type and dosage of a suitable physiotherapeutic treatment protocol. The questionnaire was distributed amongst 20 experts (national and international) in the fields of physiotherapy, maxillo-facial surgery and dental surgery. A convenience sampling method was used to select appropriately trained participants for the Delphi review panel. Results: The Delphi technique was used in the development of a suitable physiotherapy intervention program for mandibular condyle fracture patients. Inter-reviewer consensus was reached regarding the commencement and dosage of various jaw exercises, as well as what would constitute in-hospital physiotherapy visits. Conclusions: The proposed post-surgical intervention program could serve as a baseline for clinical implementation and in further research studies. The advantages of referring these patients to physiotherapy are also highlighted.

Bayesian inferences on nonlinear functions of the parameters in linear regression

A variety of statistical problems (e.g. the x-intercept in linear regression, the abscissa of the point of intersection of two simple linear regression lines or the point of extremum in quadratic regression) can be viewed as questions of inference on nonlinear functions of the parameters in the general linear regression model. In this paper inferences on the threshold temperatures and summation constants in crop development will be made. A Bayesian approach for the general formulation of this problem will be developed. By using numerical integration, credibility intervals for individual functions as well as for linear combinations of the functions of the parameters can be obtained. The implementation of an odds ratio procedure is facilitated by placing a proper prior on the ratio of the relevant parameters.

Exact-and approximate bayes credibility intervals for the one-way analysis of variance model

In most hierarchical Bayes cases the posterior distributions are difficult to derive and cannot be obtained in closed form. In some special cases, however, it is possible to obtain the exact moments of the posterior distributions. By applying these moments and Pearson curves or Cornish-Fisher expansions to real problems, good approximations of the exact posterior distributions of individual parameter values as well as linear combinations of parameter values could easily be obtained.