基於伽瑪分配之壽命績效指標發展重覆遞交與重複群集驗收抽樣計畫

Developing Resubmitted and Repetitive Group Acceptance Sampling Plans Based on the Lifetime Performance Index Under Gamma Distribution

劉丞軒(Liu, Cheng Hsuan)

指導教授 ： 吳建瑋

國立清華大學/工學院/工業工程與工程管理學系/碩士(2016年)

摘要

隨著科學技術與生活水準的提升，人們對於品質的概念越加重視，品質也成為各企業的競爭關鍵，而評估產品之品質最常利用的方法為製程能力指標（process capability indices），但是大多數的製程能力指標皆假設其品質特性屬於常態分配，而在現實當中，並非所有的品質特性皆服從常態分配，像是產品的壽命、電壓、黏性…等，其中又以產品壽命為最多人所關注的，故為了有效衡量產品壽命，壽命績效指標（lifetime performance index）CL因而被發展出來。
而在高品質產品時代，使用傳統的檢驗方法成本很高，故業界現在普遍使用驗收抽樣計畫來做為檢驗的方法，驗收抽樣計畫在滿足與保障買賣雙方風險的情況下，同時能夠降低抽樣的樣本且有效反映出產品的品質，並提供評斷該產品是否該允收的決策準則。本研究即針對當產品之壽命服從伽瑪分配時，利用壽命績效指標 之均勻最小變異數不偏估計量來發展重覆遞交與重複群集驗收抽樣計畫，而為了實務上應用，分別條列出其操作程序並彙整不同的品質水準(AQL、RQL)、買賣雙方所能承受之風險(alpha,beta)與伽瑪分配形狀參數 等組合下之計畫參數表，使用者可以透過此表得知所需抽樣之樣本數與相對應之允收臨界值來進行貨批的決策。接著，利用求解出之結果來與單次驗收抽樣計畫來進行比較與分析，最後，利用實際的案例來說明此計畫應如何與產業做結合並提供給業界參考如何正確使用此驗收抽樣計畫。

關鍵字

驗收抽樣計畫 ； 壽命績效指標 ； 伽瑪分配 ； 允收機率

並列摘要

As technology and living standards improved, people gradually attach importance to the quality. Quality becomes the key of the corporation competitiveness. Process capability indices are effective means of measuring process performance. Most process capability indices have been developed under the assumption that the quality characteristics are normally distributed. However, the voltage, stickiness and lifetime of products generally may possess an non-normal distribution. People are interesting in the lifetime of products so a lifetime performance index CL was proposed and used as a means of measuring product lifetime performance.
In the era of high quality, use traditional testing methods need more costs, so acceptance sampling plans are widely used by industry to do the inspection. It protects the risks of producer and customer, reduce the sample size, effectively reflect the quality and provides a decision criteria about accepting the product or not. This study considers the product lifetime with a gamma distribution and uses the uniformly minimum-variance unbiased estimator (UMVUE) of the lifetime performance index to develop resubmitted and repetitive group sampling plans. For the practical purpose, this study presents a step-by-step procedure and tabulates the plan parameters for various combinations of acceptable, rejectable quality levels, producer’s and consumer’s risks and shape parameter. Thus, practitioners can easily know the number of product required for inspection and the corresponding critical value for decision making. Furthermore, this study also uses the results to compare with the single sampling plans. Lastly, provide a practical example to illustrate how to apply this acceptance sampling plans.

並列關鍵字

Acceptance sampling plans ； Lifetime performance index ； Gamma distribution ； Probability of accepting

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