在有關產品可靠度問題之研究中，通常需要做產品抽樣壽命試驗。由於壽命試一般屬 於破壞性試驗，且費時頗久，成本支出甚鉅。因此，如何快速且有效地得到試驗結果 ，作為評估及改善產品可靠度的依據，以供決策參考，便極為重要。 一般在研究產品壽命時，大部份選擇產品壽命為指數分布。指數壽命分布適用於故障 率穩定的產品，但由於生產環境的不同，或製造過程中所容許的變動，導致混合母體 的故障率是隨機的。本文即是假設每條生產線之產品壽命皆指數分布，而由不同生產 線產出之產品故障率為GAMMA 分布，於是混合各生產線之產品後，其產品壽命為柏拉 圖分布。 本文討論在母體壽命為柏拉圖布時，研究如可以早期發生故障之樣本壽命觀測值來求 得其後發生故障之樣本觀測值的點預測及區間預測。 本文架構如下： 第一章為緒論，說明研究的動機與目的，研究的範圍及限制。 第二章討論當柏拉圖分布的形狀參數已知時，位置參數和尺度參數的最大概似估計式 ，最佳線性不偏估計式及最佳線性不變估計式。 第三章研究如何利用早期發生故障的樣本觀測值，來求其後發生故障之第Ｓ個樣本觀 測值的最佳線性不偏點預測，最佳線性不變點預測及終極線性不偏點預測。 第四章則研究以早期發生故障的樣本觀測值，來發現其後第Ｓ個發生故障之樣本觀測 值的預測區間及大樣本時的近似預測區間。 第五章為結論。

人口預期壽命的變化一直以來皆被視為是人類發展與進步的指標之一，其成長更為人們所樂見。當人類預期壽命普遍成長且達一定壽命水準時，兩性存活年數的差距仍為一常見的現象。假設社會的發展與變遷對同一社會中的兩性人口造成相異的衝擊，此種差異性會進一步透過兩者間壽命差距的狀況加以反映時，在追求兩性平等與均衡發展此社會目標之驅動下，對兩性壽命水準差距狀況的瞭解乃為提升兩性存活狀況、創造均衡之兩性社會並進而採取相關策略前重要的一步。 本研究利用內政府統計處所編列之台灣地區簡易生命表做為主要的分析資料，從透過對台灣地區兩性壽命差距於國民政府遷台後之1950起至2004年此55年間變化之關注做為出發點，發現兩性壽命於55年間其增長變化上雖然呈現相似的變動狀態，然而女性於各時期內優於男性之成長幅度則是造成日趨擴大之兩性壽命差距之由來。又兩性出生時平均餘命其變動上所呈現的階段性則與兩性壽命差距水準變化上所出現的四階段有其關聯性。此外，兩性於各年齡別平均餘命之增長，大致來說，主要發生在10-60歲組中，70歲以後之較高年齡組中，兩性存活餘命的成長則較不顯著，且兩性餘命差距隨著年齡別的增加而減少。兩性於各年齡別上餘命之差距，在研究觀察的55年間呈現穩定，只是，1960年以前兩性出生時平均餘命與其他較高年齡組上之平均餘命間呈現較為特殊的型態，此乃說明造成兩性壽命差距之年齡別死亡率有異。 本研究將Arriaga(1984)所提，用以分解兩相異之平均餘命，而以不同年齡別中兩性死亡率差異分別對兩性預期壽命差距所作之貢獻加以表示時，發現，兩性在40-79歲間死亡率的差異是造成兩性壽命差距最主要的貢獻年齡別，其中以60-69歲組為最。此外，面對0-9歲組中兩性死亡率差異狀況對該時期兩性預期壽命差距之貢獻型態於1960年前後所呈現之相異性時，一方面有對該時期兩性死亡率之資料加以檢定之必要性外，其所可能象徵之女性生存狀況受其地位改善之影響，抑或為男性存活狀況變化等推測的驗證雖不在本研究所觸及之範圍內，然而透過本研究分析結果中所掌握造成兩性壽命差距之年齡組別，則有助於日後在企圖釐清造成兩性壽命差距之因以進一步改善兩性存活狀況時一切入點。 / Life Expectancy of human beings, one of the indices of human development, has been generally growing since the beginning of the 20th century and the increase in the life span of human is also taken as the result of the improved medical techniques and social conditions. In the face of the growth in life expectancy at birth both of the male and female populations in Taiwan during the past 55 years, 1950-2004, the gender differential of life expectancy at birth or at any other specific age still exited and even got expanding. The difference in life expectancy at birth between the male and the female was 2.64 years and in the year of 2004, it came to be 6.24 years. Suppose the growth of human life expectancy at birth or at any specific age in both female and male populations implies that social changes and developments brought positive impacts not only on the female but also on the male during the observation period of 55 years. Obviously, the existing and expanding gender differences in life expectancy somewhat indicates that the impact of the social changes and developments on the male and the female weren’t comparable in qualities. The main concern of this article is about the change of the differences in life expectancy at birth between the male and the female in Taiwan during the past 55 years, 1950-2004. Dismissing the discussion and investigation of the practical and real causes of the gender difference in life expectancy, the researcher intended to give the reason to the expanding gender difference in life expectancy by comparing the way male and female life expectancies evolved. In addition, adopting the decomposition method developed by Arriaga(1984) originally for decomposition of changes in expectation of life at birth, the researcher was using this method to decompose the gender differential in life expectancy at birth and evaluated the contribution of the gender differential in mortality within each specific age group to the ultimate differential in life expectancy at birth between the male and the female each year during the observation period and the shifts in the significance of these age groups in the past 55 years. In this article, the researcher separated a person’s life into several age groups,0-9,10-19,20-29,30-39,40-49,50-59,60-69,70-79 and 80 above, to symbolize the different stage of a person’s life. The male and the female experienced similar pattern in the changes of life expectancy. However, the improvement of female life expectancy was greater than that of the male’s in any specific period of the past 55 years , which caused the increasing difference in life expectancy between the male and female in Taiwan. The higher the age is, the less the gender difference in life expectancy at that specific age is. As the male is able to live long enough to a higher age, they are more likely to overcome the survival predominance of the female and the gender difference in life expectancy at a specific age would diminish. In addition, as for the contributions made by each specific age group, during the observation period of 55 years, gender differential life expectancy at birth had been coming from the gender differential in death rates within 40 to 80 years old. The contribution made by the age group of 60-69 made had been the most significant one. Mostly, the living ability of the female was much more superior to that of the male at any specific age even if the significance, each age groups held, somewhat had been shifting during the 55 years. Noticeably, the type of the contribution, age group of 0-9 made, was very different after 1960. Before 1960, men demonstrated a better survival ability than women did within this age group; however, after 1960, the superiority of men came into disappearance. As for the change of the contribution this age group of 0-9 made, we need to have more information and data to gain the further ideas it might bring about.

電子產品一向是我國外銷市場中的主力，因此為了提升外銷競爭的能力，必須不斷的 改善產品品質，從而提高其平均壽命和可靠度，其中壽命試驗正是了解可靠度問題的 重要步驟。 但由今日電子產品的可靠度提高，平均壽命較長，用傳統的壽命試驗，很難在短時間 內獲致結果，故通常以加速壽命試驗的方式取而代之。所謂加速壽命試驗是採用較高 的環境應力，在不改變產品失效模式的原則下，縮短產品的壽命和試驗時間，進而推 估產品在正常使用條件下的壽命分配。此外，加速試驗亦有助於預燒工作的進行，將 有助於剔除產品早期故障以提高產品品質。 除了加速壽命試驗之外，使用截略抽樣資料以及較佳的試驗計劃，均可節省時間、金 錢。因而本文研究的目的，乃以可代表電子產品壽命在正常操作期之指數分配為例， 配合加速壽命試驗，決定各組應力的截略數和樣本數，從而設計出最佳的壽命試驗計 劃。 文中，以固定的總截略數為控制成本，欲使所估計之正常使用下的瞬間故障率之變異 數為最小，並分三種情形討論之。一、只固定較高應力，則發現較低應力愈接近正常 應力時，變異愈小。二、固定二組較高及較低應力，則在較應力的組別，應配置較多 的截略樣本。三、在二組應力之間，增加第三組應力，此舉雖增加變異數，但較具有 穩健的功能。而一旦決定各組的截略數之後，可以控制其期望值和完成試驗之期望值 之比例，進而求得所需的樣本數。本文的結果和以前的文獻在型Ⅰ截略抽樣計劃下的 實驗設計，大致上能夠相符合，並進一步對型Ⅱ截略抽樣計劃下，各組應力之截略數 不同配置的情形，作了一番比較探討。

突變生成(mutagenesis)的方式有許多種，其中insertional mutagenesis為果蠅上常使用建立突變株的方式，本篇論文利用p[GawB]隨機插入果蠅genome中產生大量突變株，並篩選出會影響壽命的突變果蠅M2。進一步的實驗發現M2果蠅為Vha16-1基因的突變，並造成其mRNA表現量的下降，且在低卡路里(5% yeast、5% dextrose)與高卡路里(15% yeast、15% dextrose)的環境下homozygous mutant果蠅皆有減少平均壽命的現象。 Vha16-1所表現的蛋白為Vacuolar-type H+-ATPase (V-ATPase)上的subunit c，V-ATPase主要的功能為藉由消耗ATP來運送氫離子，並可調節胞器或胞外腔室的酸鹼平衡。V-ATPase主要表現在果蠅腸道的copper cell上，此細胞的功能類似於哺乳動物的胃壁細胞(parietal cells)，與胃酸的分泌有關，我們發現M2 homozygous mutant果蠅因Vha16-1基因的缺失而有減少腸道酸化的情形發生，符合我們觀察到其在腸道上的表現。此一現象亦在另一株突變果蠅Vha16-1EP2372上加以證實。先前研究顯示果蠅腸道酸鹼平衡的破壞會影響到對養分的吸收，而Vha16-1的缺失亦導致M2果蠅體重與三酸甘油酯的上升，並增加對飢餓的耐受性，而這些代謝上的變化並不會改變M2果蠅對食物的攝取量或者生育能力。綜合這些實驗結果，我們推測Vha16-1基因的缺失會改變腸道功能，並影響果蠅體內代謝的狀態，表現出類似肥胖(obesity)的性狀，而終導致平均壽命的縮短。 / Mutagenesis can be induced by many ways and one of the most common approaches used in Drosophila is insertional mutagenesis. In this study, we screened pGawB insertion lines and identified M2 as a novel mutant with affected lifespan. The mutant allele of M2 carried a pGawB inseration at the 5’ end of the Vha16-1 gene, which caused a reduced Vha16-1 mRNA expression level and a shorten lifespan in homozygous mutants under both low calorie (5% yeast and 5% dextrose) and high calorie (15% yeast and 15% dextrose) foods. Vha16-1 encodes the c subunit of the Vacuolar-type H+-ATPase (V-ATPase) which is known to regulate pH homeostasis by pumping protons across organelle and plasma membranes. V-ATPase is highly expressed by the Copper cells which are located at the Drosophila middle midgut and functionally similar to the gastric acid producing parietal cells in mammals. Along the same line, we found that Vha16-1 pGawB drives GFP reporter was observed along the Drosophila gastrointestinal tract. M2 as well as the other Vha16-1 hypomorphic mutant line, EP2372, also showed reduced midgut acidification. This disrupted pH homeostasis in the Drosophila midgut region may be associated with increased body weight, triglyceride, and starvation resistance that observed in M2 mutants. The feeding behavior and reproductive function, however, were not affected in M2 mutant flies. In summary, our data suggested Vha16-1 deficits may alter normal intestinal function or internal metabolic status that ultimately induces obesity phenotypes with reduced lifespan.

水丁香在台灣已被廣泛用作為香料和中草藥。目前已經被證實擁有許多生物活性，例如抗氧化、抗肝毒性、抗菌及抗癌等。在本研究中，我們利用兩種不同果蠅株w1118和Canton-S(CS)餵食兩種不同的飲食條件，分別為標準食物配方(15% yeast和15% dextrose)及卡路里節制(calorie restriction, CR)食物配方(5% yeast和5% dextrose)，來評估水丁香水萃取物對果蠅老化的影響。我們測試不同水丁香水萃取物濃度(0.1% 及0.5％)的食物對於果蠅的壽命、食物攝取量、下蛋率、活動能力、學習記憶、氧化壓力和基因表現等影響。我們發現水丁香水萃取物在標準食物配方下對於兩種品系的母果蠅均有延長壽命的表現，但並不影響果蠅的下蛋率及活動能力，另外水丁香水萃取物明顯的延緩了老化過程中學習能力退化的情況。然而於CR食物中添加水丁香水萃取物，其延長果蠅壽命的現象則消失，顯示水丁香水萃取物延長果蠅壽命的現象可能透過卡路里節制相關路徑。水丁香水萃取物可增加果蠅抵抗paraquat所引發的氧化壓力，並且降低抗氧化基因如superoxide dismutase(sod1及sod2)、catalase以及果蠅類胰島素胜肽(Drosophila insulin-like peptide, dilp2及dilp3) mRNA的表現。 綜合以上實驗結果我們推測，水丁香水萃取物延長壽命可能的作用機制為：(1)透過卡路里節制的路徑。 (2)影響類胰島素生長因子的訊號傳導(Insulin/IGF-1 signaling)。(3)增加抗氧化壓力的能力。 / Ludwigia octovalvis (Jacq.) P. H. Raven has been widely used as a spice and herbal medicine in Taiwan. It has been proved to possess many biological activities, antioxidative, anti-hepatotoxic, anti-bacterial and anticancer properties, for example. In this research, Ludwigia octovalvis extract (LOE) was used in two different diet conditions, one is standard diet (15% yeast and 15% dextrose), and the other is calorie restriction (5% yeast and 5% dextrose). The effect of LOE on the lifespan of the flies was estimated using w1118 and Canton-S strains of Drosophila melanogaster. We also evaluated the effects of 0.1% or 0.5% of LOE on food intake, fecundity, locomotor activity, cognitive performance, anti-oxidative stress and age-related gene expression in flies under standard diet. Our results showed that LOE could extend the lifespan of female flies on both species without affecting the fecundity and locomotor activity. Intriguingly, LOE attenuated the cognitive decline in both male and female flies. The longevity effect of LOE, however, was vanished when the lifespan of the flies was examined under CR diet, suggesting that LOE may extend lifespan through a CR-related pathway. LOE also increased resistance of paraquat-induced oxidative stress and down regulated the mRNA expression of sod1, sod2, cat, dilp2 and dilp3 in the flies. In summary, our results indicated that LOE may extend lifespan through: (1) a CR-related pathway. (2) regulation of Insulin/IGF-1 signaling. (3) increase of anti-oxidative stress.

死亡壓縮(Mortality Compression)意指死亡年齡更集中，是最近廣受注意的研究議題，和生存曲線矩形化（Rectangularization）關係密切，以統計分佈的角度描述，則是死亡年齡會逐漸退化到某個特定年齡。換言之，如果死亡壓縮和壽命有上限兩者都成立，以統計術語而言，代表壽命的期望值有上限、變異數會收斂，可藉由死亡年齡分配探討壽命變化。 本文希望以統計方法與資料品質等兩個面向探討死亡壓縮與延壽之間的關係。除了過去使用的無母數方法，如檢視各年度生命表上死亡分佈的最短區間（25%、50%及75%）與死亡人數最多的年齡（Modal Age）的變化，探討死亡壓縮與壽命是否有延長；另一方面，也將對死亡曲線作參數設定，觀察死亡年齡分佈的標準差變化。由於過往的研究多使用的生命表資料，本研究將比較使用生命表資料（死亡資料經過修勻）或原始死亡人數資料對結果的影響。 本研究藉由電腦模擬比較各種估計標準差方法的差異，包括Kannisto (2000) 提出的SD(M+)法與本文考量的非線性極值法(Nonlinear-Maximization)，衡量何者具有較小的均方誤差，並探討錯誤設定分配偵誤的敏感度；另外，本文可討論使用經過修勻的死亡率及原始死亡率對於估計結果的影響。除了電腦模擬，本研究也套入實際死亡資料（如臺灣、美國、…等國資料，資料來源：Human Mortality Database），檢視死亡壓縮是否存在。 / Mortality compression is one of the popular research issues in longevity risk. It means that the age-at-death would concentrate on a narrower range, and it is also related to the concept of rectangularization of survival curve. In terms of statistical distribution, mortality compression indicates that the age-at-death degenerates to a certain age, and it can be used to study changes of lifespan. If the lifespan has a limit, or mortality compression does exist, this suggests that the life expectancy has a limit and the variance of age-at-death would converge. In the study, we evaluate the mortality compression using the statistical methods and considering the issue of data quality. In addition to the nonparametric methods used in the previous studies, such as shortest confidence interval on the distribution of age-at-death and the modal age, we consider optimization methods for estimating the standard deviation of age-at-death distribution. In specific, we compare the SD(M+) proposed by Kannisto (2000) and the method of Nonlinear-Maximization, and check which method has a smaller MSE (Mean Squared Error). For the issue of data quality, we compare the estimation results of using mortality rates from life table data with those using the raw data. In addition to computer simulation, we consider the sensitivity analysis of age-at-death distribution, to evaluate the estimation method. Furthermore, based on the data from Human Mortality Database, we apply the method of Nonlinear-Maximization to life table data (i.e., graduated mortality rates) and raw data, and check if there are significant differences. The estimation results of empirical study are also used to evaluate if there is mortality compression and if there is a longevity limit.

本文所探討的中心為貝氏模型運用於加速壽命試驗，並且假設受測項目之壽命服從Weibull分配。加速實驗環境有三種，其中第二種環境代表正常狀態，採用加速壽命試驗的方式涵蓋了三種：固定應力、漸進之逐步應力和變量曲線之逐步應力。對於先驗參數，並不是直接給予特定的值，而是透過專家評估，給定各種環境之下的產品可靠度之中位數或百分位數，再利用這些資訊經過數值運算解出先驗參數。資料的型態分成兩種，一為區間資料，另一為型一設限資料，透過蒙地卡羅法模擬出後驗分配，並且估計正常環境狀態的可靠度。 / This article develops a Bayes inference model for accelerated life testing assuming failure times at each stress level are Weibull distributed. Using the approach, there are three stressed to be used, and the three testing scenarios to be adapted are as follows：fixed-stress, progressive step-stress and profile step-stress. Prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known Markov Chain Monte Carlo methods to derive posterior approximations.