Lifetime Distribution and Associated Inference of Systems with Multiple Degradation Measurements Based on Gamma Processes

Pan, Zhengqiang; Feng, Jing; Sun, Quan

doi:10.17531/ein.2016.2.20

Cited by 10 publications

(9 citation statements)

References 19 publications

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“…In such cases, it is important to consider multivariate models to obtain robust reliability estimates. Some important applications of multivariate gamma processes in reliability analysis have been presented by Hao et al [9], Pan and Balakrishnan [18], Pan and Balakrishnan [19], Pan et al [20], Pan et al [21], Park and Padgett [23], Sari et al [26], Wang et al [31], and Zhou et al [36]. In most of the multivariate degradation models, it is considered that each of the multiple PC are governed by a univariate stochastic gamma process and then the joint model is obtained via copula functions.…”

Section: Science and Technologymentioning

confidence: 99%

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Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random eﬀects

Rodríguez‐Picón¹

2016

EiN

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Article citation info: IntroductionIn recent years, important developments have been presented in the area of reliability inference of products and systems based on degradation models. Such models are important tools to obtain reliability information when few failure data is available [11], and consists in analyzing the gradual deterioration in performance of a performance characteristic (PC), also known as degradation process, in terms of the accumulated damage over time [27]. For some products, a failure would be defined at a specified critical level of degradation, which means that the product may not stop working completely as in the case of hard failures, but be defined when the cumulative degradation path crosses the critical level of degradation; such failures are known as soft failures. In general, if a failure can be defined in terms of a specified critical level of degradation it is possible to obtain a reliability assessment based on degradation process models [12]. Based on this, a modeling approach for degradation processes may consist in relating the degradation over time with a continuous stochastic process such that it is possible to describe the failure generating mechanisms.For certain PC, the desirable properties that a model must have to describe its degradation process are that the degradation process should always be positive and strictly increasing. In this paper, the gamma process is considered as a model to govern the degradation process of certain PC, given the characteristics that its increments are independent and non-negative having a gamma distribution that results in an always positive, strictly increasing stochastic process. As performance can only decrease over time, this is why it is considered to be suitable to model wear, crack growth, corrosion, consumption, fatigue, erosion, or any PC [16]. Some important applications of the gamma process in the reliability assessment of products can be found in Bagdonavicius and Nikulin [2], Park and Padgett [22], and Bagdonavicius and Nikulin [3].RodRíguez-Picón LA. Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects. eksploatacja i niezawodnosc -Maintenance and Reliability 2017; 19 (1)

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Section: Science and Technologymentioning

confidence: 99%

“…Considering all the bivariate models B i , i=1,2,3,4,5, and the reliability functions described in (20)(21), the reliability plots for terminal 1 and 2 were obtained and are compared in Figure 6. The best fitting model is B 5 , which implies a RE model for terminal 1 and a RV model for terminal 2.…”

Section: Reliability Assessmentmentioning

confidence: 99%

Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random eﬀects

Rodríguez‐Picón¹

2016

EiN

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“…Although the use of gamma process may be complicated when dealing with the first‐time passage distributions, given that the obtained probability distribution function (PDF) has no explicit form. This implies the use of approximations to the Birnbaum‐Saunders distribution and the inverse Gaussian distribution, which consider a discrete version of the first passage times of the gamma process and the central limit theorem to approach the passage time of the normalized cumulative degradation increments with a critical level to the Birnbaum‐Saunders distribution …”

Section: Introductionmentioning

confidence: 99%

Degradation modeling of 2 fatigue‐crack growth characteristics based on inverse Gaussian processes: A case study

Rodríguez‐Picón

Alvarado‐Iniesta

2018

Appl Stoch Models Bus & Ind

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Most modern products that are highly reliable are complex in their inner and outer structures. This situation indicates quality characterization by the interaction of multiple performance characteristics, which motivates the utilization of robust reliability models to obtain robust estimates. It is paramount to obtaining substantial information about a product's life cycle; therefore, when multiple performance characteristics are dependent, it is important to find models that address the joint distribution of performance degradation of such. In this paper, a reliability model for products with 2 fatigue-crack growth characteristics related to 2 degradation processes is developed. The proposed model considers the dependence among degradation processes by using copula functions considering the marginal degradation processes as inverse Gaussian processes. The statistical inference is performed by using a Bayesian approach to estimate the parameters of the joint bivariate model. A time-scale transformation is considered to assure monotone paths of the degradation trajectories. The comparison results of the reliability analysis, under both dependent and independent assumptions, are reported with the implementation of the proposed modeling in a case study, which consists of the crack propagation data of 2 terminals of an electronic device. the characteristics that its increments are independent and nonnegative, having a gamma distribution with an identical scale parameter. 3-6 Moreover, considering its monotonicity property and that performance can only decrease over time, this is why it is considered to be suitable to model wear, crack growth, corrosion, consumption, fatigue, etc. 7-13 Although the use of gamma process may be complicated when dealing with the first-time passage distributions, given that the obtained probability distribution function (PDF) has no explicit form. This implies the use of approximations to the Birnbaum-Saunders distribution and the inverse Gaussian distribution, which consider a discrete version of the first passage times of the gamma process and the central limit theorem to approach the passage time of the normalized cumulative degradation increments with a critical level to the Birnbaum-Saunders distribution. 8,14,15 The geometric Brownian motion as a degradation process has been presented as another important alternative. The sample path of this process, as in the case of the gamma process, is also monotone. Different applications of this process in degradation analysis can be found in the works of Park and Padgett, 9 Elsayed and Liao, 16 Park and Padgett, 17 and Chiang et al. 18 The inverse Gaussian (IG) process is another important choice for degradation modeling; this process also provides monotone degradation paths, and it is closely related to the Wiener process with drift. Indeed, it can be treated as the first passage distribution of a Wiener process. An important practical advantage of the IG process over the gamma process is the closed form of its first-time passage distributio...

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“…Pan et al suggested using a multivariate Birnbaum-Saunders distribution and its marginal distributions for lifetime distribution analysis of systems that have multiple dependent performance characteristics. In the proposed models, the system degradation was assumed to follow the gamma processes [6]. Asgharzadeh et al presented a method for two-parameter bathtub-shaped lifetime distribution estimation based on upper record values by constructing exact confidence intervals and exact joint confidence regions of parameters [7].…”

Section: Introductionmentioning

confidence: 99%

Reliability-Based Analytic Models for Fatigue Lifetime Distribution Estimation of Series Mechanical Systems under Random Load considering Strength Degradation Path Dependence

Gao

Xie

2017

Mathematical Problems in Engineering

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Time-dependent statistical characteristics of load process and strength degradation process are critical to lifetime distribution of series mechanical systems. Conventional rain-flow counting method for lifetime distribution estimation has limited practical application due to its strict requirement for statistical properties of load process. Besides, dynamic interaction between load process and strength degradation process results in strength degradation path dependence (SDPD). SDPD and failure dependence of components jointly bring considerable difficulties in prediction of system lifetime distribution and system residual lifetime distribution. To address these problems, reliability-based analytic models for estimation of whole lifetime distribution and residual lifetime distribution of series mechanical systems under random load are developed in this paper, which take the time-dependent statistical parameters of load process and strength degradation process as the input of the models. Furthermore, SDPD and failure dependence of components are taken into account in the proposed models in an explicit mathematical expression. The results show that SDPD, failure dependence of components, and initial strength dispersion have significant influences on system lifetime distribution.

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Lifetime Distribution and Associated Inference of Systems with Multiple Degradation Measurements Based on Gamma Processes

Cited by 10 publications

References 19 publications

Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random eﬀects

Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random eﬀects

Degradation modeling of 2 fatigue‐crack growth characteristics based on inverse Gaussian processes: A case study

Reliability-Based Analytic Models for Fatigue Lifetime Distribution Estimation of Series Mechanical Systems under Random Load considering Strength Degradation Path Dependence

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