Asymmetric Loss Research Articles

An aircraft engine remaining useful life prediction method based on predictive vector angle minimization and feature fusion gate improved transformer model

Remaining useful life (RUL) prediction is crucial for achieving intelligent and predictive maintenance of aircraft engines. In practical applications, advance prediction values smaller than the true values can prevent serious deferred maintenance accidents. Using asymmetric loss functions directly leads to noticeable accuracy degradation, and existing methods often fail to satisfy accuracy and advance prediction requirements. To address this problem, this paper proposes a novel RUL prediction method based on the Prediction Vector Angle (PVA) minimization and Feature Fusion Gate (FFG) improved Transformer network. Specifically, the FFG is proposed to enhance Transformer prediction accuracy by dynamically fusing global and local features. The concept of PVA is first introduced based on the tilting properties of the RUL descent process. The target of the prediction model is cleverly transformed from error minimization to PVA minimization through the cosine similarity loss function. Various experiments on the CMAPSS dataset demonstrate the effectiveness of the proposed method in achieving high accuracy and advanced prediction. Compared to the state-of-the-art method, RMSE is reduced by at least 2.94 % and Score by 7.00 %. Finally, the PVA minimization mechanism significantly improves long short-term memory and convolutional neural network performance. The proposed method is noteworthy for its superiority and applicability.

Asymmetric Osteopenia in Adolescent Idiopathic Scoliosis Based on Hounsfield Unit of Computed Tomography.

To characterize the asymmetrical loss of bone mass and identify the association between scoliosis and osteopenia in patients with adolescent idiopathic scoliosis (AIS). Demographic information, Cobb angle, and Hounsfield unit (HU) of the neutral vertebra (NV) and apical vertebra (apex) of the major curve were collected retrospectively in 54 AIS patients. For 84 control subjects, HU values were measured at T12 and L5. Propensity score matching was performed to balance the interference of age and BMI. In the AIS group, the concave and convex lateral HU of the NV and the convex lateral HU of the apex were negatively correlated with the Cobb angle. The AIS patients had lower bilateral HU. The mean HU and the apex-convex HU were also lower in the AIS group, while the apex-concave HU was slightly higher. After matching, the apex-convex HU of the AIS group remained lower, while the apex-concave HU was higher. Patients with AIS exhibit osteopenia, particularly on the convex side. The severity of scoliosis was found to be directly proportional to the severity of bone loss and the degree of bilateral osteopenia asymmetry. Appropriate intervention for bone loss may be able to curb the progression of scoliosis.

Benefits of Cochlear Implantation for Older Adults With Asymmetric Hearing Loss.

FDA-approved indications for cochlear implantation include patients with severe-to-profound unilateral hearing loss (UHL) or asymmetric hearing loss (AHL); however, these indications are not covered for Medicare beneficiaries. We assessed the outcomes of cochlear implant (CI) use for older adults with UHL or AHL. Eighteen older adults (≥65 years of age at surgery) with UHL/AHL participated in a prospective, longitudinal investigation evaluating outcomes of CI use. Speech recognition for the affected ear was evaluated with consonant-nucleus-consonant (CNC) words. Spatial hearing was assessed with measures of sound source localization and sentence recognition in noise. The target sentence was presented from the front and the masker was either co-located with the target (SoNo), presented toward the affected ear (SoNci) or contralateral ear (SoNcontra). Perceived benefit was assessed with the Speech, Spatial, and Qualities of Hearing scale (SSQ) and the Tinnitus Handicap Inventory (THI). Participants experienced significant improvements with CI use for CNC words (mean [SD]; preop: 8% [10%], 1 yr: 51% [22%], 5 yr: 50% [19%]), masked sentence recognition (SoNcontra preop: 5% [6%], 1 yr: 22% [15%], 5 yr: 41% [14%]), and localization (preop: 76° [18°], 1 yr: 40° [11°], 5 yr: 41° [14°]),and reported significant improvements in hearing abilities (SSQ Spatial Hearing preop: 3 [1], 1 yr: 6 [2], 5 yr: 6 [2]) and tinnitus severity (THI preop: 16 [18], 1 yr: 4 [14], 5 yr: 6 [12]). Older adults with UHL/AHL experience significant improvements in speech recognition, spatial hearing, and subjective perceptions (e.g., hearing abilities and tinnitus severity) with a CI as compared to pre-operative abilities. IV Laryngoscope, 2024.

Audiological outcome of bimodal CI users over time and depending on different influencing factors

Hearing-impaired persons with asymmetric hearing loss and aunilateral indication for acochlear implant (CI) generally benefit from abimodal hearing solution. The influence of bimodal fitting on speech comprehension (SC) over time has not yet been sufficiently investigated. The present study examines the influence of bimodal fitting on SC in bimodally fitted CI users with postlingual deafness at least 36months after implantation and analyzes possible influencing factors. Included in this retrospective longitudinal study were 54bimodally fitted speech-competent CI users with at least 36months of CI experience. Audiometric data of these CI users at predefined timepoints were compared. The change in the results of the Freiburg monosyllabic test (FT) over 36months was significant (p < 5%) for the deafness group at <10years for both the 65 dB sound pressure level (SPL) and at 80 dB SPL and also significant for the deafness group ≥10years for 65 dB SPL. In the Oldenburg sentence test (OlSa) there was ahighly significant change (p < 0.1%) for S0, S0N0, and S0NCI configurations and avery significant change (p < 1%) for S0NHA (HA: hearing aid). Age at implantation as apossible influencing factor could not be confirmed in the FT. In contrast, the duration of deafness was anegative influencing factor for SC with CI in the FT, whereas alonger duration of deafness was associated with worse results in the FT. The degree of hearing loss in the ear fitted with an HA did not influence SC. The median bimodal benefit (here: difference in SC with bimodal fitting compared to unilateral HA fitting for FT at 65 dB SPL) was 10% over the total study period. For amedian of 79% of the test subjects, the bimodal benefit was found over the entire period of 36months. Over time, SC improves significantly with aCI for the bimodal test subjects. The investigated influencing factors (age, duration of deafness, and degree of hearing loss in the contralateral ear) support the indication for bimodal provision in accordance with the guideline in Germany for cochlear implantation-regardless of age, duration of deafness, and hearing ability of the contralateral ear.

Unilateral Hearing Loss and Auditory Asymmetry in Mitochondrial Disease: A Scoping Review.

Background/Objectives: Mitochondrial transfer RNA mutations are one of the most important causes of hereditary hearing loss in humans. In most cases, its presentation is bilateral and symmetrical; however, there are numerous cases of single-sided presentation or asymmetrical onset described in the literature that may represent a diagnostic challenge. The aim of this review is to present the evidence of auditory asymmetry in mitochondrial diseases, highlighting the possible presence of cases with atypical presentation. Methods: A review of the English literature to date on hearing loss and mitochondrial diseases was performed using PubMed, Scopus, and Google Scholar databases. The literature review was performed using the Preferred Reporting Items for Systematic Reviews and Meta-analysis (PRISMA) guidelines for scoping review. Results: A total of 10 full-text articles were included in this review, comprising 25 patients with single-sided or asymmetrical hearing loss associated with mitochondrial disease. Conclusions: Sensorineural hearing loss due to mitochondrial disease can represent a complex diagnostic challenge in cases of asymmetric or unilateral presentation. It is critical to recognize this clinical variant and to diagnose it in daily clinical practice.

Estimation of the Reliability Function of the Generalized Rayleigh Distribution under Progressive First-Failure Censoring Model

This study investigates the statistical inference of the parameters, reliability function, and hazard function of the generalized Rayleigh distribution under progressive first-failure censoring samples, considering factors such as long product lifetime and challenging experimental conditions. Firstly, the progressive first-failure model is introduced, and the maximum likelihood estimation for the parameters, reliability function, and hazard function under this model are discussed. For interval estimation, confidence intervals have been constructed for the parameters, reliability function, and hazard function using the bootstrap method. Next, in Bayesian estimation, considering informative priors and non-information priors, the Bayesian estimation of the parameters, reliability function, and hazard function under symmetric and asymmetric loss functions is obtained using the MCMC method. Finally, Monte Carlo simulation is conducted to compare mean square errors, evaluating the superiority of the maximum likelihood estimation and Bayesian estimation under different loss functions. The performance of the estimation methods used in the study is illustrated through illustrative examples. The results indicate that Bayesian estimation outperforms maximum likelihood estimation.

Sound-seeking before and after hearing loss in mice

How we move our bodies affects how we perceive sound. For instance, head movements help us to better localize the source of a sound and to compensate for asymmetric hearing loss. However, many auditory experiments are designed to restrict head and body movements. To study the role of movement in hearing, we developed a behavioral task called sound-seeking that rewarded freely moving mice for tracking down an ongoing sound source. Over the course of learning, mice more efficiently navigated to the sound. Next, we asked how sound-seeking was affected by hearing loss induced by surgical removal of the malleus from the middle ear. After bilateral hearing loss sound-seeking performance drastically declined and did not recover. In striking contrast, after unilateral hearing loss mice were only transiently impaired and then recovered their sound-seek ability over about a week. Throughout recovery, unilateral mice increasingly relied on a movement strategy of sequentially checking potential locations for the sound source. In contrast, the startle reflex (an innate auditory behavior) was preserved after unilateral hearing loss and abolished by bilateral hearing loss without recovery over time. In sum, mice compensate with body movement for permanent unilateral damage to the peripheral auditory system. Looking forward, this paradigm provides an opportunity to examine how movement enhances perception and enables resilient adaptation to sensory disorders.

Leveraging a Hybrid Machine Learning Approach for Compressive Strength Estimation of Roller-Compacted Concrete with Recycled Aggregates

In recent years, the use of recycled aggregate (RA) in roller-compacted concrete (RCC) for pavement construction has been increasingly attractive due to various environmental and economic benefits. Early determination of the compressive strength (CS) is crucial for the construction and maintenance of pavement. This paper presents the idea of combining metaheuristics and an advanced gradient boosting regressor for estimating the compressive strength of roller-compacted concrete containing RA. A dataset, including 270 samples, has been collected from previous experimental works. Recycled aggregates of construction demolition waste, reclaimed asphalt pavement, and industrial slag waste are considered in this dataset. The extreme gradient boosting machine (XGBoost) is employed to generalize a functional mapping between the CS and its influencing factors. A recently proposed gradient-based optimizer (GBO) is used to fine-tune the training phase of XGBoost in a data-driven manner. Experimental results show that the hybrid GBO-XGBoost model achieves outstanding prediction accuracy with a root mean square error of 2.64 and a mean absolute percentage error less than 8%. The proposed method is capable of explaining up to 94% of the variation in the CS. Additionally, an asymmetric loss function is implemented with GBO-XGBoost to mitigate the overestimation of CS values. It was found that the proposed model trained with the asymmetric loss function helped reduce overestimated cases by 17%. Hence, the newly developed GBO-XGBoost can be a robust and reliable approach for predicting the CS of RCC using RA.

A novel asymmetric loss function for deep clustering-based health monitoring and anomaly detection for spacecraft telemetry

A novel asymmetric loss function for deep clustering-based health monitoring and anomaly detection for spacecraft telemetry

The fork protection complex promotes parental histone recycling and epigenetic memory

The inheritance of parental histones across the replication fork is thought to mediate epigenetic memory. Here, we reveal that fission yeast Mrc1 (CLASPIN in humans) binds H3-H4 tetramers and operates as a central coordinator of symmetric parental histone inheritance. Mrc1 mutants in a key connector domain disrupted segregation of parental histones to the lagging strand comparable to Mcm2 histone-binding mutants. Both mutants showed clonal and asymmetric loss of H3K9me-mediated gene silencing. AlphaFold predicted co-chaperoning of H3-H4 tetramers by Mrc1 and Mcm2, with the Mrc1 connector domain bridging histone and Mcm2 binding. Biochemical and functional analysis validated this model and revealed a duality in Mrc1 function: disabling histone binding in the connector domain disrupted lagging-strand recycling while another histone-binding mutation impaired leading strand recycling. We propose that Mrc1 toggles histones between the lagging and leading strand recycling pathways, in part by intra-replisome co-chaperoning, to ensure epigenetic transmission to both daughter cells.

A novel transformer-based few-shot learning method for intelligent fault diagnosis with noisy labels under varying working conditions

Recent years have witnessed the success of Few-shot Learning (FSL) methods in equipment reliability enhancement and fault diagnosis, by virtue of learning from limited data and adapting to new operating conditions. However, due to sensor bias, manual collection, and mislabeling, label noise is inevitably introduced into the dataset, which further reduces the quality of supervised information contained in the few-shot dataset, posing significant challenges for accurate fault diagnosis. In this paper, the problem of Few-shot Fault Diagnosis with Noisy Labels (FFDNL) is studied for the first time, and a novel method named Enhanced Transformer with Asymmetric Loss Function (ETALF) is proposed. ETALF leverages the self-attention mechanism of the transformer to dynamically measure the similarity between fault samples in the support set to enhance the model's robustness against label noise, then naturally aggregates the similar samples into corresponding correct prototypes. Furthermore, an asymmetric loss function is designed, which adaptively assigns the model with larger penalties for incorrect category predictions and smaller penalties for correct category predictions, thereby enhancing fault diagnostic performance through inherent asymmetry. Comprehensive experiments are conducted on two benchmark datasets, and the compared results with representative approaches validate the effectiveness of our proposed ETALF in performing intelligent fault diagnosis using limited and noise-labeled data under varying working conditions, which achieves accuracies of 97.77% and 95.78% with 0.2 noisy-level labels during meta-training and meta-testing on the CWRU and KAIST datasets, respectively.

On bayesian bonus-malus premium under linex loss function with applications

The majority of bonus-malus systems (BMS) determine the premium for each policyholder solely based on their claim frequency. Adopting this method would be unjust. A driver who files a claim for small damage cannot be subjected to the same penalties as a driver responsible for a claim involving significant damage. To achieve a balance in the portfolio between good and bad drivers, a new portion of the premium is computed as a compromise. To do this, the claim severity is created and assessed to provide a fair premium. The consideration was determined by taking into account both the quantity and magnitude of the claims. This work assumes that the frequency of claims follows a Poisson-Akash distribution, but the severity of claims follows a newly proposed distribution known as the Inverse-Gamma Lindley distribution. The bonus-malus premiums were computed using the Bayesian approach for both the frequency and severity of claims. The premium is computed using the asymmetric Linex loss function for both the frequency and severity of claims in the bonus-malus system. Illustrative instances utilizing an actual dataset for the application of BMS are presented, showcasing the use of claim frequency alone and the combination of claim frequency and claim severity. The R software is employed for these demonstrations. We concluded this paper with a discussion comparing the premiums obtained in each case.

Cochlear Implantation in Single-Sided Deafness and Asymmetric Hearing Loss: 12 Months Follow-up Results of a European Multicenter Evaluation.

People with single-sided deafness (SSD) or asymmetric hearing loss (AHL) have particular difficulty understanding speech in noisy listening situations and in sound localization. The objective of this multicenter study is to evaluate the effect of a cochlear implant (CI) in adults with single-sided deafness (SSD) or asymmetric hearing loss (AHL), particularly regarding sound localization and speech intelligibility with additional interest in electric-acoustic pitch matching. A prospective longitudinal study at 7 European tertiary referral centers was conducted including 19 SSD and 16 AHL subjects undergoing cochlear implantation. Sound localization accuracy was investigated in terms of root mean square error and signed bias before and after implantation. Speech recognition in quiet and speech reception thresholds in noise for several spatial configurations were assessed preoperatively and at several post-activation time points. Pitch perception with CI was tracked using pitch matching. Data up to 12 months post activation were collected. In both SSD and AHL subjects, CI significantly improved sound localization for sound sources on the implant side, and thus overall sound localization. Speech recognition in quiet with the implant ear improved significantly. In noise, a significant head shadow effect was found for SSD subjects only. However, the evaluation of AHL subjects was limited by the small sample size. No uniform development of pitch perception with the implant ear was observed. The benefits shown in this study confirm and expand the existing body of evidence for the effectiveness of CI in SSD and AHL. Particularly, improved localization was shown to result from increased localization accuracy on the implant side.

On the suitability of a convolutional neural network based RCM-emulator for fine spatio-temporal precipitation

High resolution regional climate models (RCM) are necessary to capture local precipitation but are too expensive to fully explore the uncertainties associated with future projections. To resolve the large cost of RCMs, Doury et al. (2023) proposed a neural network based RCM-emulator for the near-surface temperature, at a daily and 12 km-resolution. It uses existing RCM simulations to learn the relationship between low-resolution predictors and high resolution surface variables. When trained the emulator can be applied to any low resolution simulation to produce ensembles of high resolution emulated simulations. This study assesses the suitability of applying the RCM-emulator for precipitation thanks to a novel asymmetric loss function to reproduce the entire precipitation distribution over any grid point. Under a perfect conditions framework, the resulting emulator shows striking ability to reproduce the RCM original series with an excellent spatio-temporal correlation. In particular, a very good behaviour is obtained for the two tails of the distribution, measured by the number of dry days and the 99th quantile. Moreover, it creates consistent precipitation objects even if the highest frequency details are missed. The emulator quality holds for all simulations of the same RCM, with any driving GCM, ensuring transferability of the tool to GCMs never downscaled by the RCM. A first showcase of downscaling GCM simulations showed that the RCM-emulator brings significant added-value with respect to the GCM as it produces the correct high resolution spatial structure and heavy precipitation intensity. Nevertheless, further work is needed to establish a relevant evaluation framework for GCM applications.

K-Nearest Neighbors Estimator for Functional Asymmetry Shortfall Regression

This paper deals with the problem of financial risk management using a new expected shortfall regression. The latter is based on the expectile model for financial risk-threshold. Unlike the VaR model, the expectile threshold is constructed by an asymmetric least square loss function. We construct an estimator of this new model using the k-nearest neighbors (kNN) smoothing approach. The mathematical properties of the constructed estimator are stated through the establishment of the pointwise complete convergence. Additionally, we prove that the constructed estimator is uniformly consistent over the nearest neighbors (UCNN). Such asymptotic results constitute a good mathematical support of the proposed financial risk process. Thus, we examine the easy implantation of this process through an artificial and real data. Our empirical analysis confirms the superiority of the kNN-approach over the kernel method as well as the superiority of the expectile over the quantile in financial risk analysis.

The Influence of Asymmetric Hearing Loss on Peripheral and Central Auditory Processing Abilities in Patients With Vestibular Schwannoma.

Asymmetric or unilateral hearing loss (AHL) may cause irreversible changes in the processing of acoustic signals in the auditory system. We aim to provide a comprehensive view of the auditory processing abilities for subjects with acquired AHL, and to examine the influence of AHL on speech perception under difficult conditions, and on auditory temporal and intensity processing. We examined peripheral and central auditory functions for 25 subjects with AHL resulting from vestibular schwannoma, and compared them to those from 24 normal-hearing controls that were matched with the AHL subjects in mean age and hearing thresholds in the healthy ear. Besides the basic hearing threshold assessment, the tests comprised the detection of tones and gaps in a continuous noise, comprehension of speech in babble noise, binaural interactions, difference limen of intensity, and detection of frequency modulation. For the AHL subjects, the selected tests were performed separately for the healthy and diseased ear. We observed that binaural speech comprehension, gap detection, and frequency modulation detection abilities were dominated by the healthy ear and were comparable for both groups. The AHL subjects were less sensitive to interaural delays, however, they exhibited a higher sensitivity to sound level, as indicated by lower difference limen of intensity and a higher sensitivity to interaural intensity difference. Correlations between the individual test scores indicated that speech comprehension by the AHL subjects was associated with different auditory processing mechanisms than for the control subjects. The data suggest that AHL influences both peripheral and central auditory processing abilities and that speech comprehension under difficult conditions relies on different mechanisms for the AHL subjects than for normal-hearing controls.

Adaptive Strategies of Single-Sided Deaf Cochlear-Implant Users Revealed Through Resting State Activity: an Auditory PET Brain Imaging Study

Brain plasticity refers to the brain's ability to reorganize its structure or function in response to experiences, learning, and environmental influences. This phenomenon is particularly significant in individuals with deafness, as the brain adapts to compensate for the lack of auditory stimulation. The aim of this study is to investigate whether cochlear implantation can restore a normal pattern of brain activation following auditory stimulation in cases of asymmetric hearing loss. We used a PET-scan technique to assess brain activity after cochlear implantation, specifically during an auditory voice/non-voice discrimination task. The results indicated a nearly normal pattern of brain activity during the auditory discrimination task, except for increased activation in areas related to attentional processes compared to controls. Additionally, brain activity at rest showed significant changes in implanted participants, including cross modal visuo-auditory processing. Therefore, cochlear implants can restore the brain's activation pattern through long-term adaptive adjustments in intrinsic brain activity.

A Consensus to Revise the Minimum Speech Test Battery-Version 3.

The Minimum Speech Test Battery (MSTB) for adults was introduced in 1996 (Nilsson et al., 1996) and subsequently updated in 2011 (Advanced-Bionics et al., 2011). The MSTB has been widely used by clinicians as a guide for cochlear implant (CI) candidacy evaluations and to document post-operative speech recognition performance. Due to changes in candidacy over the past 10 years, a revision to the MSTB was needed. In 2022, the Institute for Cochlear Implant Training (ICIT) recruited a panel of expert CI audiologists to update and revise the MSTB. This panel utilized a modified Delphi consensus process to revise the test battery and to improve its applicability considering recent changes in CI care. This resulted in the MTSB-Version 3 (MSTB-3), which includes test protocols for identifying not only traditional CI candidates but also possible candidates for electric-acoustic stimulation and patients with single-sided deafness and asymmetric hearing loss. The MSTB-3 provides information that supplements the earlier versions of the MSTB, such as recommendations of when to refer patients for a CI, recommended patient-reported outcome measures, considerations regarding the use of cognitive screeners, and sample report templates for clinical documentation of pre- and post-operative care. Electronic versions of test stimuli, along with all the materials described above, will be available to clinicians via the ICIT website (https://www.cochlearimplanttraining.com). The goal of the MSTB-3 is to be an evidence-based test battery that will facilitate a streamlined standard of care for adult CI candidates and recipients that will be widely used by CI clinicians.

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Inference on Weibull inverted exponential distribution under progressive first-failure censoring with constant-stress partially accelerated life test

Accelerated life tests (ALTs) play a pivotal role in life testing experiments as they significantly reduce costs and testing time. Hence, this paper investigates the statistical inference issue for the Weibull inverted exponential distribution (WIED) under the progressive first-failure censoring (PFFC) data with the constant-stress partially ALT (CSPALT) under progressive first-failure censoring (PFFC) data for Weibull inverted exponential distribution (WIED). For classical inference, maximum likelihood (ML) estimates for both the parameters and the acceleration factor are derived. Making use of the Fisher information matrix (FIM), asymptotic confidence intervals (ACIs) are constructed for all parameters. Besides, two parametric bootstrap techniques are implemented. For Bayesian inference based on a proposed technique for eliciting the hyperparameters, the Markov chain Monte Carlo (MCMC) technique is provided to acquire Bayesian estimates. In this context, the Bayesian estimates are obtained under symmetric and asymmetric loss functions, and the corresponding credible intervals (CRIs) are constructed. A simulation study is carried out to assay the performance of the ML, bootstrap, and Bayesian estimates, as well as to compare the performance of the corresponding confidence intervals (CIs). Finally, real-life engineering data is analyzed for illustrative purposes.