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Computational Modeling of Nanoparticles
Published in Sarhan M. Musa, ®, 2018
Elastic properties are not deterministic in the thin film that contains a small number of grains because the orientation of each grain is stochastic. In this case, multiple simulations should be performed to obtain the elastic properties. However, the number of simulations should be determined before the simulations. Without assuming normality, we need more than 30 simulations (samples) to construct an approximate 95% confidence interval (CI) for the mean elastic properties of a specific size polysilicon thin film (population). The CI is a formula that tells us how to use sample data to determine an interval that estimates a population parameter [44]. The confidence level (i.e., 95%) is the probability that an interval estimator encloses the population parameter. To determine the actual number of simulations, the following equation is used: () n=[(Za/2s0de)2]
Statistics for Quality
Published in K. S. Krishnamoorthi, V. Ram Krishnamoorthi, Arunkumar Pennathur, A First Course in Quality Engineering, 2018
K. S. Krishnamoorthi, V. Ram Krishnamoorthi, Arunkumar Pennathur
The value of an estimator computed from a single sample is called a point estimate. The point estimate, especially from a small sample, is of no value because it is just one observation of a random variable. Its value will vary from sample to sample and cannot be trusted as the true value of the parameter. Therefore, we resort to interval estimation, in which we create an interval in such a way that there is certain level of confidence—say, 95% or 99%—that the parameter we are seeking lies in the interval. Such an interval is called a confidence interval. We will see how these confidence intervals are created for the two parameters μ and σ2.
Estimation Using Confidence Intervals
Published in William M. Mendenhall, Terry L. Sincich, Statistics for Engineering and the Sciences, 2016
William M. Mendenhall, Terry L. Sincich
Another way to estimate the value of a population parameter θ is to use an interval estimator. An interval estimator is a rule, usually expressed as a formula, for calculating two points from the sample data. The objective is to form an interval that contains θ with a high degree of confidence. For example, if we estimate the mean time μ for a robot to complete a task to be between 2.7 and 3.1 minutes, then the interval 2.7 to 3.1 is an interval estimate of μ.
Fuzzy judgement model for assessment of improvement effectiveness to performance of processing characteristics
Published in International Journal of Production Research, 2023
Kuen-Suan Chen, Yuan-Lung Lai, Ming-Chieh Huang, Tsang-Chuan Chang
The samples obtained using statistical sampling are in fact only a small portion of the population. For this reason, a difference exists between the and derived from the observed values of the samples and the true population parameters; this difference is called the sampling error. To reduce sampling error, many researchers use large samples to increase the accuracy of their inferences. However, this approach still does not eliminate sampling error. Interval estimation provides a possible range for estimation of the population parameters, and this range captures the true population parameters with a certain degree of confidence (i.e. level of confidence). Therefore, interval estimation can provide more information about population parameters than point estimation can.
Artificial Intelligence Aided Agricultural Sensors for Plant Frostbite Protection
Published in Applied Artificial Intelligence, 2022
Shiva Hassanjani Roshan, Javad Kazemitabar, Ghorban Kheradmandian
In inferential statistics, statistical hypothesis testing is one of the most important and conventional methods. This test has been used in this study to guarantee the quality of the experiment results. Tor this purpose, the values for p-value and T-value are calculated. Null-hypothesis is usually an opinion about the parameter or the statistical population which had already existed and our goal is to reject the null hypothesis. Rejecting null-hypothesis means that our findings were statistically meaningful. The accuracy or error rate of voting for the rejection of null-hypothesis is called significance level which was assigned to 95% in this study. The significance level shows how much the maximum error was while rejecting the null-hypothesis. In addition to the parameters above, confidence interval, degree of freedom, and the mean are also obtained for the target variable. The confidence interval is a kind of interval estimation and shows the amount of confidence in the existence of a parameter in an interval or boundary of the studied population. The degree of freedom shows how much power of choice exists.
Interval estimation for Wiener processes based on accelerated degradation test data
Published in IISE Transactions, 2018
Lanqing Hong, Zhi-Sheng Ye, Josephine Kartika Sari
Compared with point estimation, interval estimation is usually of more interest, as it is able to quantify uncertainties in the estimators. Confidence intervals for parameters in the Wiener process, as well as reliability characteristics, such as product reliability and lifetime quantiles, are often obtained based on the asymptotic normal approximation or the bootstrap. For example, Whitmore and Schenkelberg (1997), Padgett and Tomlinson (2004), and Paroissin (2015) used the large-sample normal approximation to construct confidence intervals for model parameters, mean-time-to-failure and lifetime quantiles. Wang (2010) used both the bootstrap-percentile and the bootstrap-t methods to construct confidence intervals for parameters of a mixed-effects Wiener process. The interval estimation procedures based on the large sample normal approximation and the bootstrap are panaceas for most statistical problems. Their performance is usually asymptotically efficient. According to our simulation studies and application experiences, however, coverage probabilities of the confidence intervals so constructed are often not satisfactory for the Wiener degradation process, especially when the sizes of data are limited (see Section 4 for evidence). In addition, the bootstrap method is usually time-consuming.