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Step‐stress accelerated degradation test (SSADT) has become a prevailing approach to lifetime assessment for highly reliable products. In practice, many products suffer from multiple degradation processes that significantly contribute to failures. In this paper, we investigate the optimal SSADT plans for products subject to two dependent degradation characteristics modeled by a bivariate inverse Gaussian process. The drift parameter of each process is assumed to be influenced by a common stress factor. A bivariate Birnbaum‐Saunders (BVBS)‐type distribution is employed to approximate the lifetime distribution and facilitate the derivation of the objective function. The optimal plans are prescribed under three common optimality criteria in the presence of constraints on test units and inspections. A revisited example of fatigue crack is then presented to demonstrate the proposed methods. Finally, the sensitivity of the SSADT plans is studied, and the results exhibit fair robustness of the optimal plans. [ABSTRACT FROM AUTHOR]

The accelerated Degradation testing (ADT) experiments are important technical methods in reliability studies. Different type of accelerating degradation models has developed with the time and can be used in different types of situations. However, it has become necessary for the manager to test how many numbers of unit should be tested at a particular stress level so that the cost of testing is less. Accelerated Degradation testing (ADT) is preferred to be used in mechanized industries to obtain the required information about the reliability of product components and materials in a short period of time. Accelerated test conditions involve higher than usual pressure, temperature, voltage, vibration or any other combination of them. Data collected at such accelerated conditions are extrapolated through a physically suitable statistical model to estimate the lifetime distribution at design condition stress the life data collected from the high stresses the need to be extrapolated to estimate the life distribution under the normal-use condition. A special class of the ADT is the step-stress testing which regularly increases the stress levels at some pre-fixed time points until the test unit fails. Such experiments allow the experimenter to run the test units at higher-than-usual stress conditions in order to secure failures more quickly. The Inverse Gaussian process is flexible in incorporating random effects and explanatory variables. The different types of models based on IG process are random drift model, random volatility model and random drift-volatility model. In this paper we have considered random drift model for the study on stochastic degradation models for simple step-stress model using inverse Gaussian process observed in degradation problems. [ABSTRACT FROM AUTHOR]

Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results.

In view of the disadvantage that traditional evaluation method of accelerated degradation testing (ADT) complex statistical analysis, in this paper, the randomness and monotonicity of the degradation path for products with high reliability and long lifetime are taken into consideration based on Inverse Gaussian (IG) process. The evaluation method of step-down-stress ADT as well as its reliability function are established based on IG process. At same time, both the simple IG process and IG process with random effects are considered, respectively. The maximum likelihood estimation method and Markov Chain Monte Carlo (MCMC) estimation method are presented to estimate the unknown parameters in the proposed degradation models, respectively. Finally, the proposed evaluation methods are demonstrated by the step-down-stress ADT data of a certain type of missile tank. The results show that the proposed evaluation method is reasonable and valid in this paper. In addition, compared with simple IG process model, IG process with random effects model has many superb properties when dealing with random effects of products in ADT.

Condition-based maintenance has been widely used in the maintenance strategy of equipment or systems. Aiming at the maintenance decision-making of the equipment with dynamic degradation characteristics, a dynamic condition-based maintenance model is proposed based on Inverse Gaussian process in this paper. Firstly, an Inverse Gaussian process with stochastic parameter is proposed to describe the change of the equipment degradation characteristics during operation, and the important stochastic properties related to condition-based maintenance is deduced. Secondly, the dynamic maintenance threshold function is proposed, and its different values at different degradation stages can reduce the early failure risk of the equipment while ensuring a lower expected cost ratio. On this basis, a dynamic maintenance decision-making model with multi-objectives is established. A numerical example is illustrated to verify the correctness and practicability of the proposed method, and the sensitivity analysis results of the related parameters prove the necessity of considering the dynamic degradation characteristics of equipment. The comparison result proves that the method proposed in this paper can obtain better safety and economy of maintenance than the method with fixed thresholds.

Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Javed et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Accelerated degradation testing (ADT) is commonly used to obtain degradation data of products by exerting loads over usage conditions. Such data can be used for estimating component lifetime and reliability under usage conditions. The design of ADT entails to establish a model of the degradation process and define the test plan to satisfy given criteria under the constraint of limited test resources. Bayesian optimal design is a method of decision theory under uncertainty, which uses historical data and expert information to find the optimal test plan. Different expected utility functions can be selected as objectives. This paper presents a method for Bayesian optimal design of ADT, based on the inverse Gaussian process and considering three objectives for the optimization: relative entropy, quadratic loss function, and Bayesian D-optimality. The Markov chain Monte Carlo and the surface fitting methods are used to obtain the optimal plan. By sensitivity analysis and a proposed efficiency factor, the Bayesian D-optimality is identified as the most robust and appropriate objective for Bayesian optimization of ADT.

In manufacturing, cutting tools gradually wear out during the cutting process and decrease in cutting precision. A cutting tool has to be replaced if its degradation exceeds a certain threshold, which is determined by the required cutting precision. To effectively schedule production and maintenance actions, it is vital to model the wear process of cutting tools and predict their remaining useful life (RUL). However, it is difficult to determine the RUL of cutting tools with cutting precision as a failure criterion, as cutting precision is not directly measurable. This paper proposed a RUL prediction method for a cutting tool, developed based on a degradation model, with the roughness of the cutting surface as a failure criterion. The surface roughness was linked to the wearing process of a cutting tool through a random threshold, and accounts for the impact of the dynamic working environment and variable materials of working pieces. The wear process is modeled using a random-effects inverse Gaussian (IG) process. The degradation rate is assumed to be unit-specific, considering the dynamic wear mechanism and a heterogeneous population. To adaptively update the model parameters for online RUL prediction, an expectation–maximization (EM) algorithm has been developed. The proposed method is illustrated using an example study. The experiments were performed on specimens of 7109 aluminum alloy by milling in the normalized state. The results reveal that the proposed method effectively evaluates the RUL of cutting tools according to the specified surface roughness, therefore improving cutting quality and efficiency.

A multi-objective optimization method for constant stress accelerated degradation test is proposed in order to solve the problem of different or even conflicted test configuration under different optimization objectives. The inverse Gaussian process is used as a degradation model, and the unknown parameters are solved by maximum likelihood estimation. The two optimization criteria of the maximum determinant of the information matrix and the minimum asymptotic variance of P-quantile are considered. The improved multi-objective particle swarm optimization algorithm is proposed to search test optimal configuration, and the Pareto solution set for dual-objectives is obtained. Finally, the effectiveness of the method is illustrated by a group of examples of electrical connectors. Compared with the single-objective optimization design, the proposed method is more reasonable and convenient for test configuration. The performance index of the test function indicates that the optimal algorithm we proposed has some obvious advantages over the NSGA-II in diversity and convergence of the Pareto solutions and it is significant in guiding engineering practice.