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Frequency Distribution Charts
Published in Edward M. Schrock, Henry L. Lefevre, The Good and the Bad News About Quality, 2020
Edward M. Schrock, Henry L. Lefevre
Conclusions that might be drawn from this chart include: The data distribution is not normal; it is truncated. A truncated distribution has one or both ends cut off.The median of the data is in the middle of the specification; the manufacturer deserves credit for keeping the process on target.The specification was too tight for the process capability of the producer. The distribution may have been normal when the parts were made but it was changed.
Basic Reliability Mathematics
Published in Mohammad Modarres, Mark P. Kaminskiy, Vasiliy Krivtsov, Reliability Engineering and Risk Analysis, 2016
Mohammad Modarres, Mark P. Kaminskiy, Vasiliy Krivtsov
A truncated distribution is therefore a conditional distribution that restricts the domain of another probability distribution. The following general equation forms apply to the truncated distribution, where f0(x) and F0(x) are the pdf and cdf of the nontruncated distribution.
A proposed approach for approximating lower truncated normal cumulative distribution: application to reliability of used devices
Published in Cogent Engineering, 2022
Mohammad M. Hamasha, Haneen Ali, Faisal Aqlan, Abdulaziz Ahmed, Sa’d Hamasha
If a portion of the data with smaller, larger, or both values is cut off, the distribution of the rest data is known as the lower, upper, or two-sided truncated distribution, respectively. The reason for truncating the data is due to the lack of interest in the cut part and it is carried out on a population or a sample according to the situation. The truncated distributions are found in all applied sciences, but they are more important in economics, management and engineering. For example, hardware/devices distributions after being used for a certain period are lower truncated distribution. Furthermore. a fit products distribution after out-of-specification products have been removed is considered truncated. Specifically, if the product does not have an upper side specification, the distribution of fit products becomes lower truncated. Moreover, in Probit and Tobit models in statistics, the truncated distribution is the results.
Improving the conversion accuracy between bridge element conditions and NBI ratings using deep convolutional neural networks
Published in Structure and Infrastructure Engineering, 2020
Graziano Fiorillo, Hani Nassif
Machine learning algorithms can experience overfitting, which corresponds to obtaining high accuracy on the training dataset used to learn the model parameters due to excessive training iterations, while performing poorly on the validation dataset. This is particularly true when the number of samples is limited. To reduce this effect, several techniques are available depending on the problem analysed. A simple, yet powerful approach is to increase the dataset by adding some ‘noise’ to the original data. In this way the predicting algorithm learns about this disturbance and will be less sensitive to the variation of the predictors. This approach helps the model to be more robust (Chollet & Allaire, 2018). In this study, we apply an identically independent distributed random noise to each of the predictors in BE taken from a normal distribution such that the augmented dataset BEau is as follow: where NS is a matrix containing the noise values of size M × P, where M is the number of observations in input, P is the number of predictors, and ν is a propagation factor to increase the size of the augmented data as desired. According to Equation (5) the size of BEau is Given the nature of the health indexes, ranging between 0 and 100%, by using the normal distribution, the standard deviation should be contained to less than 5% to avoid an unrealistic instantiation of the predictors. As an alternative, a truncated distribution can also be employed. To further fight overfitting, neuron values can be randomly discarded as the learning of the network parameters propagates towards the end; this method is called dropout (Chollet & Allaire, 2018). However, some authors discourage this practice in deep neural network applications in favour of the batch normalisation technique, which consists of centering the data with zero mean and unit variance after each transformation. This approach also reduces the computational cost for training the network (Ioffe & Szegedy, 2015).