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題 名 | 不同機率分配下可靠度壽命估計方法之比較研究=Reliability Estimation Methods under Various Probability Distribution Functions |
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作 者 | 潘浙楠; 陳木彬; | 書刊名 | 中國統計學報 |
卷 期 | 35:2 1997.06[民86.06] |
頁 次 | 頁173-192 |
分類號 | 494.56 |
關鍵詞 | 可靠度壽命估計; 最大概似估計法; 動差估計法; 最小平方法; 貝氏估計法; Reliability life estimation; Method of moments; Method of maximum likelihood; Bayesian estimation method; Method of least squares; |
語 文 | 中文(Chinese) |
中文摘要 | 可靠度壽命測試的目的是為了保證產品出廠後能正常運作而其壽命至少可達到合 約或設計上之要求。由於產品或系統在使用期間之失效情形呈隨機分布,因此不易正確地預 測出產品可能發生失效的時間。一般工業界在預估其產品平均壽命或可靠度時,均假設壽命 試驗所得的至失效所經過之時間 (time to failure ) 數據是指數或韋伯分配,而以圖解之 方式予以概算,其所得之壽命參數估計值並不精確。因此,選擇適當的可靠度壽命估計方法 有其必要。 統計界常用的壽命估計方法有最大概似估計法 (the method of maximum likelihood)、 動差估計法 (method of moments)、 最小平方法 (method of least squares) 以及貝氏估計法 (Bayesian estimation method) 等四種。 為了比較上述四種可 靠度壽命估計方法的差異與優劣, 本研究假設產品壽命在服從指數 (exponential)、 常態 (normal)、韋伯 (Weibull) 以及伽瑪 (gamma) 等四種常見的機率分配下,分別以上述四種 壽命估計方法求算其壽命參數及可靠度函數的估計值;並利用統計模擬的方法,探討產品壽 命之各種分配在不同樣本數的狀況下,其壽命估計值的變化情形及其相對之誤差等性質。本 研究進一步提出一個可供業界在進行可靠度壽命試驗後,在完全失效的型態下,正確預估產 品平均壽命之決策流程。我們針對不同的機率分配利用上述四種方法估計其壽命參數,並以 Fortran 電腦程式語言寫出一套應用程式用以篩選出較精確的壽命參數組合。最後以一組絕 緣纜線 (服從常態分配 ) 及另一組柴油引擎中發電機風扇 (服從韋伯分配 ) 之壽命試驗資 料進行分析與驗證。 |
英文摘要 | The purpose of reliability life test is to ensure that the product will operate without failure during its expected mission life. Since a product/system is subject to failure at random during its useful life period, it is difficult to precisely predict its exact time of system failure. Although the estimation of life parameters is not accurate, most industries normally assume the time-to-failure distributions of their products/components follow exponential or Weibull distribution and use graphical methods to estimate the mean life and reliability function of these products/components. Therefore, it is necessary to select an appropriate reliability estimation method to accurately calculate the life parameter (s) of a given distribution and expected mean life of the system. The following are four common point estimation methods by which the unknown parameter (s) of a given distribution can be estimated: (1) method of moments, (2) method of maximum likelihood, (3) Bayesian estimation method, and (4) method of least squares. Assuming the time to failure distribution of random samples for each product/system follows exponential, normal, Weibull, or gamma distribution, this paper discusses differences and advantages/disadvantages of the above four point estimation methods. In addition, the estimated values of life parameter(s) and the expected mean life for a given distribution are calculated and compared by using the above four estimation methods and statistical simulation techniques with various sample sizes. This paper also provides a statistical decision process in conjunction with a Fortran computer program on how to accurately select the life parameter(s) and predict the expected mean life of a product/system by simultaneously using the above four estimation methods. Finally, a complete failure data analysis using this ttechnique has been demonstrated with a realistic example of the Diesel Engine Fan data. |
本系統中英文摘要資訊取自各篇刊載內容。