  Anomalies refer to the departure of systems and devices from their normal
behaviour in standard operating conditions. An anomaly in an industrial device
can indicate an upcoming failure, often in the temporal direction. In this
paper, we make two contributions: 1) we estimate conditional quantiles and
consider three different ways to define anomalies based on the estimated
quantiles. 2) we use a new learnable activation function in the popular Long
Short Term Memory networks (LSTM) architecture to model temporal long-range
dependency. In particular, we propose Parametric Elliot Function (PEF) as an
activation function (AF) inside LSTM, which saturates lately compared to
sigmoid and tanh. The proposed algorithms are compared with other well-known
anomaly detection algorithms, such as Isolation Forest (iForest), Elliptic
Envelope, Autoencoder, and modern Deep Learning models such as Deep
Autoencoding Gaussian Mixture Model (DAGMM), Generative Adversarial Networks
(GAN). The algorithms are evaluated in terms of various performance metrics,
such as Precision and Recall. The algorithms have been tested on multiple
industrial time-series datasets such as Yahoo, AWS, GE, and machine sensors. We
have found that the LSTM-based quantile algorithms are very effective and
outperformed the existing algorithms in identifying anomalies.
