利用逐步右型二設限樣本評估具有韋伯分配的產品壽命績效指標

Assessing the Lifetime Performance Index of Products with the Weibull Distribution under Progressively Type II Right Censored Samples

陳佳君(Chia-Chun Chen)

指導教授 ： 陳景祥

淡江大學/管理學院/統計學系碩士班/碩士(2012年)

https://doi.org/10.6846/TKU.2012.00826

摘要

由於科技日新月異，許多複雜且精密的高科技產品被發明與創新，製造商如何藉由提升產品的品質、壽命、性能及製程良率來加強產業競爭力，並提高顧客購買意願，是一個重要的課題。近年來，製程能力指標(PCI)被製造商廣泛應用在品質監控上。製程能力指標是以量化的方式來衡量產品的特性是否符合製造商或顧客所設定的規格界限，並藉由指標值來評估製程能力的好壞。有關製程能力指標的文獻大多假設產品的品質特性服從常態分配，然而，在實際上產品的壽命往往是服從非常態分配，例如： Pareto、Weibull及Gamma分配等等。本研究探討當產品壽命服從韋伯分配下，利用壽命績效指標來衡量產品的壽命績效。此外，在壽命試驗當中，常因時間限制或其他限制(如成本限制或人為疏忽等)而無法取得完整的樣本資料，然而取得設限樣本，也可減少試驗時間及降低成本。
為了使製程能力指標可以更合理、更準確的評估產品的壽命績效，本篇主要探討產品壽命來自韋伯分配下的逐步右型二設限樣本，建構出壽命績效指標C_L的最大概似估計量，進而發展出一個新的假設檢定程序做為產品的績效評估，可以提供給製造商去評估他們的製程是否能夠滿足顧客需求水準。

關鍵字

韋伯分配 ； 逐步右型二設限樣本 ； 壽命績效指標 ； 最大概似估計量

並列摘要

Many high-tech devices have been inventing as well as innovating with the rampant change of the technology. However, it is important for manufacturers to improve the quality, lifetime, performance and conforming rate of the productions because these will raise the purchase intentions of customers. The process capability indices (PCIs) have been applied by the manufacturers’ surveillance quality widely. The indices are to evaluate the production characteristics by way of the quantity; in addition, they will be checked whether they are correspond to the specification limit designed by the manufacturers and customers.
Most of the research papers on the quality performance assessment have proposed all sorts of hypotheses to explain the quality characteristics on the normal distribution. However, the fact is the lifetime of many products frequently follows non-normal distribution, such as Pareto, Weibull, Gamma distribution etc.. This paper is to explore the product lifetime controlled by the factors of Weibull distribution. Under the limitation, the lifetime performance index assesses the product lifetime performance. Also, considering the cost and artificial negligence during the experiments, we will use the censored samples to reduce the experiment time and decrease the cost.
In order to get the reasonable and correct PCIs on the lifetime performance, the aim of this research constructs a maximum likelihood estimator (MLE) of C_L based on the progressive type II right censored sample from the Weibull distribution. The MLE of C_L is then utilized to develop a new hypothesis testing procedure. Finally, according
to the experiment analysis, the data will tell how to use the procedures to evaluate the lifetime performance. It will offer a process for the manufacturers determine whether the lifetime performance of products adhere to the required level.

並列關鍵字

Weibull distribution ； Progressively right type Ⅱ censored sample ； Lifetime performance index ； Maximum likelihood estimator

參考文獻

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