A Bayesian Approach to Competing Risks Model with Masked Causes of Failure and Incomplete Failure Times

Yousif, Yosra; Elfaki, Faiz Ahmed Mohamed; Hrairi, Meftah; Adegboye, Oyelola A.

doi:10.1155/2020/8248640

Cited by 5 publications

(4 citation statements)

References 20 publications

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“…Utilizing the Clayton [13] formula, suppose the observed data is D = N ij (t), Y ij (t), X where N ij (t) represents the counting process of failures due to cause j, occurring up to time t and Y ij (t) being the at risk indicator for cause j. Note that the same formulation was used in Yousif et al [10]; however, the definition of Y ij (t) is quite different. Let dN ij (t) be a small increment of N ij (t) over interval [t, t + dt).…”

Section: Bayesian Analysismentioning

confidence: 99%

“…Earlier, Miyakawa [9] discussed this type of data by considering parametric and non-parametric approaches to reliability estimation. Previously, we developed a Bayesian approach to estimate the effect of explanatory variables motivated by incomplete data with masked causes of failure [10,11]. We discussed the effect of covariates on CIF in the presence of a moderate masking level, and preliminary results were introduced [11].…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Analysis of Masked Competing Risks Data Based on Proportional Subdistribution Hazards Model

et al. 2022

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Masked issues can emerge when dealing with competing risk data. Such issues are exemplified by the cause of a particular failure not being directly exhibited for all units to observe but only proven to be a subset of possible causes of failure. For assessing the impact of explanatory variables (covariates) on the cumulative incidence function (CIF), a process of Bayesian analysis is discussed in this paper. The symmetry assumption is not imposed on the masking probabilities and independent Dirichlet priors assigned to them. The Markov Chain Monte Carlo (MCMC) technique is utilized to implement the Bayesian analysis. The effectiveness of the developed model is tested via numerical studies, including simulated and real data sets.

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Section: Bayesian Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Masked Competing Risks Data Based on Proportional Subdistribution Hazards Model

et al. 2022

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“…Second, the scarcity of data is a recurrent problem when dealing with life-long products or high MTBF equipment. Recent references (Zhang et al, 2019;Leoni et al, 2021, Yousif et al, 2020 calculate point and interval estimation for the Weibull model according to Bayesian, MLE, and LSE methods. Although the differences fall within a reasonable range for limited censored times, the first performs better, which suggests its use in further research.…”

Section: Preventivementioning

confidence: 99%

Maintenance Strategy Choice Supported by the Failure Rate Function: Application in a Serial Manufacturing Line

Sellitto

Pinho

2022

Period. Polytech. Soc. Man. Sci.

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The purpose of this article is to choose a maintenance procedure for the critical equipment of a forging production line with five machines. The research method is quantitative modelling and simulation. The main research technique includes retrieving time between failure and time to repair data and find the most likely distribution that has produced the data. The most likely failure rate function helps to define the maintenance strategy. The study includes two kinds of maintenance policies, reactive and anticipatory. Reactive policies include emergency and corrective procedures. Anticipatory policies include predictive and preventive ones combined with a total productive maintenance management approach. The most suitable combination for the first three machines is emergency and corrective choice. For the other machines, a combination of total productive maintenance and a predictive approach is optimal. The study encompasses the case of a serial production manufacturing line and maximum likelihood estimation. The failure rate function defines a combination of strategies for each machine. In addition, the study calculates the individual and systemic mean time to failure, mean time to repair, availability, and the most likely number of failures per production order, which follows a Poisson process. The main contribution of the article is a structured method to help define maintenance choices for critical equipment based on empirical data.

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“…A considerable number of studies have been carried out on parameter estimation using mask data based on ORTs since it was first introduced by [1,2]. Considering different failure distributions, Guess et al [23][24][25][26][27][28][29][30][31][32][33] utilizes the MLE technique for estimating model parameters for a single component or a series or parallel systems of two or three components, whereas Reiser et al [34][35][36][37][38][39][40][41][42][43] considered BE technique based on different priors. As it was discussed earlier, many real-life systems or machines these days are made of hybrid structures which are a combination of series and parallel subsystems.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

Kamal¹

2022

Computer Modeling in Engineering &Amp; Sciences

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In general, simple subsystems like series or parallel are integrated to produce a complex hybrid system. The reliability of a system is determined by the reliability of its constituent components. It is often extremely difficult or impossible to get specific information about the component that caused the system to fail. Unknown failure causes are instances in which the actual cause of system failure is unknown. On the other side, thanks to current advanced technology based on computers, automation, and simulation, products have become incredibly dependable and trustworthy, and as a result, obtaining failure data for testing such exceptionally reliable items have become a very costly and time-consuming procedure. Therefore, because of its capacity to produce rapid and adequate failure data in a short period of time, accelerated life testing (ALT) is the most utilized approach in the field of product reliability and life testing. Based on progressively hybrid censored (PrHC) data from a three-component parallel series hybrid system that failed to owe to unknown causes, this paper investigates a challenging problem of parameter estimation and reliability assessment under a step stress partially accelerated life-test (SSPALT). Failures of components are considered to follow a power linear hazard rate (PLHR), which can be used when the failure rate displays linear, decreasing, increasing or bathtub failure patterns. The Tempered random variable (TRV) model is considered to reflect the effect of the high stress level used to induce early failure data. The maximum likelihood estimation (MLE) approach is used to estimate the parameters of the PLHR distribution and the acceleration factor. A variance covariance matrix (VCM) is then obtained to construct the approximate confidence intervals (ACIs). In addition, studentized bootstrap confidence intervals (ST-B CIs) are also constructed and compared with ACIs in terms of their respective interval lengths (ILs). Moreover, a simulation study is conducted to demonstrate the performance of the estimation procedures and the methodology discussed in this paper. Finally, real failure data from the air conditioning systems of an airplane is used to illustrate further the performance of the suggested estimation technique.

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A Bayesian Approach to Competing Risks Model with Masked Causes of Failure and Incomplete Failure Times

Cited by 5 publications

References 20 publications

Bayesian Analysis of Masked Competing Risks Data Based on Proportional Subdistribution Hazards Model

Bayesian Analysis of Masked Competing Risks Data Based on Proportional Subdistribution Hazards Model

Maintenance Strategy Choice Supported by the Failure Rate Function: Application in a Serial Manufacturing Line

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

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