Poly methyl methacrylate PMMA polymer has been used continually in dental application during the recent years. Yet, it is commonly known for its poor strength properties for long periods under pressure. The aim of this research was to improve the performance of PMMA denture base through the addition of different nanoparticles selected from artificial and natural sources. For comparison, Nano -particles from Al2O3 and crushed pistachio shell were utilised. (1%, 2% and 3%) were the weight fraction used in this study for both reinforcement types. In this work, a study and evaluation in of Compression Strength (C.S.) as well as Young’s Modulus (Y) was done before and after exposure for special liquids. The new prepared composites were immersed in two type of liquids (vinegar and olive oil). Both physical values were determined periodically for three specific times (10, 20 and 30 min).All tests were carried out at room temperature. As a result a clear increase was obtained in the evaluated values of (C.S.) and Young’s Modulus for the composite samples after the addition of both type of particles compared to the pure case. As the weight fraction was increased, these values also increased. It was found that the pure polymer (PMMA) lost almost half of the value of C.S. after 30 min of exposure in both liquid used. When immersing the prepared composites inside both liquids While the obtained results for pistachio shells particles showed slight increase after 10 min of exposure then a slight decrease through the time. Overall, the prepared composites for both type particles showed a better behavior after immersion in these liquids than the pure PMMA polymer. Also, a significant enhancement was clear with the determined value of Young’s Modulus between the prepared composites compared to the non-reinforced PMMA in all situations.
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In this study, the stress-strength model R = P(Y < X < Z) is discussed as an important parts of reliability system by assuming that the random variables follow Invers Rayleigh Distribution. Some traditional estimation methods are used to estimate the parameters namely; Maximum Likelihood, Moment method, and Uniformly Minimum Variance Unbiased estimator and Shrinkage estimator using three types of shrinkage weight factors. As well as, Monte Carlo simulation are used to compare the estimation methods based on mean squared error criteria.
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In this paper, the reliability of the stress-strength model is derived for probability P(Y<X) of a component having its strength X exposed to one independent stress Y, when X and Y are following Gompertz Fréchet distribution with unknown shape parameters and known parameters . Different methods were used to estimate reliability R and Gompertz Fréchet distribution parameters, which are maximum likelihood, least square, weighted least square, regression, and ranked set sampling. Also, a comparison of these estimators was made by a simulation study based on mean square error (MSE) criteria. The comparison confirms that the performance of the maximum likelihood estimator is better than that of the other estimators.
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In this paper, a Bayesian analysis is made to estimate the Reliability of two stress-strength model systems. First: the reliability of a one component strengths X under stress Y. Second, reliability of one component strength under three stresses. Where X and Y are independent generalized exponential-Poison random variables with parameters (α,λ,θ) and (β,λ,θ) . The analysis is concerned with and based on doubly type II censored samples using gamma prior under four different loss functions, namely quadratic loss function, weighted loss functions, linear and non-linear exponential loss function. The estimators are compared by mean squared error criteria due to a simulation study. We also find that the mean square error is
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