On a Weibull related distribution model with decreasing, increasing and upside-down bathtub-shaped failure rate

Tieling Zhang, R. Dwight, K. El-Akruti
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引用次数: 11

Abstract

A lifetime distribution model was proposed by Dimitrakopoulou, et al. in 2007 [1]. This model has three parameters and includes the Weibull distribution as a special case. Therefore, this is a Weibull related distribution model and it has decreasing, increasing, bathtub and upside-down bathtub-shaped failure rate. Since this distribution model has more flexibility than the conventional 2- and 3-parameter Weibull distributions in modeling the lifetime data, it is of interest to have a study on its statistical characteristics and explore the real application of the model to modeling time to failure data. The objective of this paper is to investigate the parameter estimation of this 3-parameter Weibull related model by graphical approach with short discussion on its statistical characteristics. The procedure in detail for parameter estimation of the model is presented and its usefulness is demonstrated by two real examples.
浴缸形故障率减小、增大和倒立的威布尔相关分布模型
Dimitrakopoulou等人在2007年提出了一个生命周期分布模型[1]。该模型有三个参数,并将威布尔分布作为一个特例。因此,这是一个威布尔相关分布模型,它具有减小、增大、浴缸形和倒立浴缸形故障率。由于该分布模型在建模寿命数据方面比传统的2参数和3参数威布尔分布具有更大的灵活性,因此研究其统计特性并探索该模型在建模失效时间数据中的实际应用具有重要意义。本文的目的是研究这种三参数威布尔相关模型的参数估计,并简要讨论其统计特征。给出了模型参数估计的详细步骤,并通过两个实例说明了该模型的有效性。
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