Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function

Xie, Min; Lai, C. D.

doi:10.1016/0951-8320(95)00149-2

Cited by 400 publications

(221 citation statements)

References 9 publications

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“…In practice, for the majority of mechanical parts, the failure mechanism could be represented by a bathtub curve (Xie and Lai, 1996;Wang et al, 2001). The Weibull distribution is one of the distributions which fit each distinct stage of the bathtub failure patterns.…”

Section: Failure Rate Functionmentioning

confidence: 99%

“…However, such a stationary failure rate cannot explain the failure rates in the early or wear-out stages, which confuses logistical decisions. In fact, the failure rate at each stage of the lifetime of many spare parts might follow a bathtub-shaped curve (Xie and Lai, 1996;Slack et al, 2010). The Weibull failure rate function is generally applicable to the failure rate in the early or wear-out stage, owing to its time-variant (Xie and Lai, 1996;Wang et al, 2001;Wessels, 2007).…”

Section: Introductionmentioning

confidence: 99%

“…In fact, the failure rate at each stage of the lifetime of many spare parts might follow a bathtub-shaped curve (Xie and Lai, 1996;Slack et al, 2010). The Weibull failure rate function is generally applicable to the failure rate in the early or wear-out stage, owing to its time-variant (Xie and Lai, 1996;Wang et al, 2001;Wessels, 2007). The widely used spare parts optimization models such as VARI-METRIC (Sherbrooke, 1986) did not focus thoroughly on such nonstationary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Optimizing Concurrent Spare Parts Inventory Levels for Warships Under Dynamic Conditions

Moon¹,

Lee²

2017

Industrial Engineering and Management Systems

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The inventory level of concurrent spare parts (CSP) has a significant impact on the availability of a weapon system. A failure rate function might be of particular importance in deciding the CSP inventory level. We developed a CSP optimization model which provides a compromise between purchase costs and shortage costs on the basis of the Weibull and the exponential failure rate functions, assuming that a failure occurs according to the (non-) homogeneous Poisson process. Computational experiments using the data obtained from the Korean Navy identified that, throughout the initial provisioning period, the optimization model using the exponential failure rate tended to overestimate the optimal CSP level, leading to higher purchase costs than the one using the Weibull failure rate. A Pareto optimality was conducted to find an optimal combination of these two failure rate functions as input parameters to the model, and this provides a practical solution for logistics managers.

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Section: Failure Rate Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimizing Concurrent Spare Parts Inventory Levels for Warships Under Dynamic Conditions

Moon¹,

Lee²

2017

Industrial Engineering and Management Systems

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“…Nooghabi et al (2012) used the continuous modified Weibull distribution of Lai et al (2003) to propose a new modified version of discrete Weibull distribution (DMW). Bebbington et al (2012) introduced discrete additive Weibull distribution (DAddW) using the continuous additive Weibull distribution of Xie and Lai (1996). Recently, Almalki and Nadarajah (2014) presented a new discrete modified Weibull (NMWD) distribution as a discrete analogue of a recent modified continuous Weibull distribution by Almalki (2013).…”

Section: Introductionmentioning

confidence: 99%

A two-parameter discrete distribution with a bathtub hazard shape

Sarhan

2017

CSAM

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This paper introduces a two-parameter discrete distribution based on a continuous two-parameter bathtub distribution. It is the only two-parameter discrete distribution that shows a bathtub-shaped hazard function. Some statistical properties of the distribution are discussed. Three different methods are used to estimate its two unknown parameters. The point estimators of the parameters have no closed form. The bootstrap method is used to estimate the distributions of these point estimators. Different approximations of the interval estimations for the two-parameters are discussed. Real data sets are analyzed to show how this distribution works in practice. A simulation study is performed to investigate the properties of the estimations obtained and compare their performances.

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“…It comprises three stages: initial stage (or burn-in) with a decreasing failure rate, middle stage with an approximately constant failure rate, and final stage with an increasing failure rate. Many probability distributions have been proposed to fit real life data with bathtub-shaped failure rates (e.g., [1][2][3][4][5]). Chen [6] proposed a two-parameter lifetime distribution (written as CZM( , ) throughout this paper) with bathtub failure rate whose distribution function is…”

Section: Introductionmentioning

confidence: 99%

Statistical Analysis of a Weibull Extension with Bathtub-Shaped Failure Rate Function

Wang

Sha

et al. 2014

Advances in Statistics

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We consider the parameter inference for a two-parameter life distribution with bathtub-shaped or increasing failure rate function. We present the point and interval estimations for the parameter of interest based on type-II censored samples. Through intensive Monte-Carlo simulations, we assess the performance of the proposed estimation methods by a comparison of precision. Example applications are demonstrated for the efficiency of the methods.

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Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function

Cited by 400 publications

References 9 publications

Optimizing Concurrent Spare Parts Inventory Levels for Warships Under Dynamic Conditions

Optimizing Concurrent Spare Parts Inventory Levels for Warships Under Dynamic Conditions

A two-parameter discrete distribution with a bathtub hazard shape

Statistical Analysis of a Weibull Extension with Bathtub-Shaped Failure Rate Function

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