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This paper proposes a new time scaled Wiener process with random effects that has been specially designed to allow the description of non‐monotonic degradation phenomena with bathtub shaped degradation rate, here intended as derivative of the mean function. Two different parameterizations of the proposed Wiener process are suggested, and the main features of the process are illustrated and discussed. The maximum likelihood estimation of its parameters is addressed. A failure threshold model is adopted to formulate and estimate the probability distribution function of the remaining useful life, which constitutes the core prognostic tool in condition‐based maintenance. As a motivating example, the proposed model is applied to a set of real degradation data of metal‐oxide‐semiconductor field‐effect transistors, where, as a result of preliminary analyses, some of the process parameters are assumed to be random in order to describe the considerable heterogeneity observed between the degradation paths of different units. Obtained results demonstrate the affordability and utility of the proposed model, especially for the estimation of unit‐specific features performed on the basis of degradation data collected in the early phase of the life of a unit belonging to the considered heterogeneous population. [ABSTRACT FROM AUTHOR]

The article titled "Discussion of 'Specifying prior distributions in reliability applications'" provides a comprehensive review of Bayesian inferential procedures for analyzing censored data in reliability applications. It discusses different types of censoring and provides guidance on setting prior distributions for commonly used distributions. The article also explores noninformative and weakly informative prior distributions and their combinations for model selection using the Bayes factor. The text discusses the mathematical formula for calculating the probability of observed data under a specific model and the concept of marginal probability. It emphasizes the importance of proper prior distributions and provides guidance on their formulation. No datasets were generated or analyzed in this study. [Extracted from the article]

Most of the stochastic models adopted to describe the evolution over time of degradation phenomena of technological units assume that their degradation level can increase indeterminately. However, these degradation phenomena are typically subjected to obvious bounds, if only because technological units have finite size. In fact, very often, this inconsistency does not significantly affect the effectiveness of unbounded degradation models, since degrading units are usually assumed to fail when their degradation level exceeds a failure threshold that is much smaller than the obvious bounds. Nevertheless, in some cases, due to the very nature of the underlying degradation mechanism, less obvious bounds could exist, which are not necessarily far from the failure thresholds. The question that arises is whether the use of a bounded degradation model, in this latter type of experimental situations, could be beneficial. For this purpose, since a bounded degradation process should necessarily have dependent increments, in this paper we investigate the potential of a new bounded transformed gamma (TG) process to adequately describe bounded degradation phenomena and predict their future evolution. Differently from other existing gamma process based bounded degradation models, here the upper bound is treated as an unknown parameter that has to be estimated from the available degradation data. A numerical example is presented where the parameters of the proposed model are estimated from simulated data. Then the model is applied to a set of wear measures of cylinder liners that equip a diesel engine for marine propulsion, which have also stimulated this study. Model parameters are estimated by using the maximum likelihood (ML) method. The fitting ability of the proposed new bounded process is compared to that of an unbounded gamma process, which was previously adopted to analyze the same liner wear data. Obtained results are critically discussed in the paper. [ABSTRACT FROM AUTHOR]

An s-based methodology that can be used to carry out a condition-based estimate of liner reliability with respect to failure through excessive wear, and to plan condition-based maintenance activity, is presented. The proposed method facilitates reducing maintenance costs within noticeably affecting liner reliability, and gives probability of inspecting or replacing liners only when there is a high likelihood that their wear level will exceed the wear limit before the next inspection date.

A new model, called the 2-parameter Engelhardt-Bain process (2-EBP), is proposed to describe the failure pattern of complex repairable systems showing a bounded intensity function. The 2-EBP model can be viewed as a dynamic power law process (PLP) but caution has to be used when the presence of a bounded intensity function can be conjectured.

New repairable systems are generally subjected to development programs in order to improve system reliability before starting mass production. This paper proposes a Bayesian approach to analyze failure data from repairable systems undergoing a Test-Find-Test program. The system failure process in each testing stage is modeled using a Power-Law Process (PLP). Information on the effect of design modifications introduced into the system before starting a new testing stage is used, together with the posterior density of the PLP parameters at the current stage, to formalize the prior density at the beginning of the new stage. Contrary to the usual assumption, in this paper the PLP parameters are assumed to be dependent random variables. The system reliability is measured in terms of the number of failures that will occur in a batch of new units in a given time interval, for example the warranty period. A numerical example is presented to illustrate the proposed procedure., 1. Introduction Testing programs are often performed during the development phase of a repairable system in order to improve the equipment's reliability level so that a given reliability target can [...]

An exponential reliability-growth model is proposed as an alternative to other models commonly used to analyze failure processes of repairable equipment in development programs.

Reliability-growth models have become popular because of the need to ensure systems reliability even during the development stage of a system. In light of the inadequacies of existing models, a nonparametric reliability-growth model based on the Bayes-decision framework has been developed. The model tracks the number of failures at each testing stage and makes decisions about system reliability.

A Bayesian approach based on the Markov Chain Monte Carlo technique is proposed for the non-homogeneous gamma process with power-law shape function. Vague and informative priors, formalized on some quantities having a "physical" meaning, are provided. Point and interval estimation of process parameters and some functions thereof are developed, as well as prediction on some observable quantities that are useful in defining the maintenance strategy is proposed. Some useful approximations are derived for the conditional and unconditional mean and median of the residual life to reduce computational time. Finally, the proposed approach is applied to a real dataset. [ABSTRACT FROM AUTHOR]

This paper proposes and illustrates a new perturbed gamma degradation process where the measurement error is modeled as a non‐Gaussian random variable that depends stochastically on the actual degradation level. The expression of the likelihood function for a generic set of noisy degradation measurements is derived, and the expression of the remaining useful life distribution of a degrading unit that fails when its degradation level exceeds a given threshold limit is formulated. A particle filter method is suggested, which allows one to compute the likelihood function and to estimate the remaining useful life distribution in a quick yet efficient manner. In addition, a closed‐form approximation of the perturbed gamma process is proposed to use in the special, yet meaningful, case where the standard deviation of the measurement error depends linearly on the actual degradation level. Finally, an applicative example is discussed, where the parameters of the perturbed gamma process, the remaining useful life distribution, and the mean remaining useful life of the degrading units are estimated from a set of noisy real degradation data. [ABSTRACT FROM AUTHOR]