利用逐步第一失敗設限樣本對具有柏拉圖分配之產品的壽命績效指標做統計推論

Statistical inference for the lifetime performance index of products with the Pareto distribution based on the progressively first-failure-censored sample

梁德澍(De-Shu Liang)

指導教授 ： 吳錦全

淡江大學/商管學院/統計學系碩士班/碩士(2014年)

https://doi.org/10.6846/TKU.2014.00788

摘要

近年來，製程能力指標被製造商廣泛用在品質監控方面，藉由指標值評估製程能力是否合乎水準。大多數的製程能力指標都是假設產品的品質特性具有常態分配；然而在實務上，產品的壽命並非服從常態分配，例如:柏拉圖分配、韋伯分配、浴缸型分配等等。在製造業中，製程能力指標常被用來評估產品品質是否達到所要求的水準，而壽命績效指標C_L就是評估工具之一，其中L為規格下界。在進行產品可靠度的分析及改善時，通常需要做產品的抽樣壽命實驗，希望能利用已觀測到的產品壽命資料來估計參數與評估產品品質是否達到所要求的水準。本文考慮以逐步第一失敗設限計畫，利用柏拉圖壽命分配取得的設限樣本觀測值，探討具有柏拉圖壽命分配之產品的壽命績效指標，並對壽命績效指標做統計推論。
本文主要以服從柏拉圖壽命分配的逐步第一失敗設限樣本，來建構壽命績效指標C_L之最大概似估計量(MLE)，進而利用C_L之MLE求得壽命績效指標C_L之信賴區間，同時發展一檢定程序以評估產品之壽命是否達到所要求的水準，再針對壽命績效指標的檢定力及信賴區間進行蒙地卡羅模擬。最後，透過實例分析，說明各種程序與方法的運用，以提供製造商評估產品的壽命是否達到所要求的水準。
表單編號：ATRX–Q03–001–FM030–01

關鍵字

逐步第一失敗設限 ； 柏拉圖分配 ； 壽命績效指標 ； 蒙地卡羅模擬 ； 最大概似估計量

並列摘要

In recent years, many process capability indices (PCIs) have been widely used in quality monitoring by many manufacturing industries. Most PCIs asuume that the quality characteristic has a normal distribution. However, the lifetime of many products frequently possesses non-normal distribution, such as Pareto, Weibull or Bathtub-shape distribution etc. Process capability indices are often used to assess whether the product quality to meet the required level, and the lifetime performance index is the tools to evaluate the performance indicators, where L is the lower specification limit. During the analysis and improvement of product’s reliability, we usually need to do sampling test. We can take advantage of the product life who has been observed characteristic to estimate parameters and to assess whether the product quality to meet the required level. In this article, we consider the progressive first-failure-censored plan using the censored sample observations from Pareto distribution to explore the statistical inference for the lifetime performance index of products.
This research constructs a maximum likelihood estimator (MLE) of based on the progressive first-failure-censored sample from the Paereto distribution. The MLE of is then utilized to develop the confidence interval in the condition of known L and the hypothesis testing procedure to determine whether the lifetime performance of products adhere to the required level. And using the Monte Carlo simulation to study lifetime performance index power and confidence level. Finally, we use the numerical examples to illustrate how to apply the proposed method to analyze the performance index to assess the product's life to meet the required level.
表單編號：ATRX–Q03–001–FM031–01

並列關鍵字

progressively first-failure-censoring ； Pareto distribution ； lifetime performance index ； Monte Carlo simulation ； maximum likelihood estimator

參考文獻

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