Recently, a research paper in Nature claimed that the maximum human life span is 115 years old, with very little chance to attain 125 years of age. Although demographers and biologists are arguing that increases in human longevity continue, some researchers have pointed out that the human lifespan reached its peak in the 1990s, based on an analysis of demographic data of more than 40 countries in the Human Mortality Database, and attributed this to the progress of science and medical technology. However, others have pointed out that although scientists claimed that the upper limit of human life is 65, 85 or even 105 years in the past, all these assertions were later overturned. Critics of the study point out that it did not use demographic and statistical data to verify the accuracy of the relevant hypotheses, saying that ＂this kind of studies do not provide any scientific evidence for how long people would live.＂ In Taiwan, the national income and living and medical standards have reached the level of developed country in the past two decades. Although the life expectancy in 2015 was 80.2 years old, the life expectancy growth rate has been limited recently. In 2013-2014, there was even a slight decline in life expectancy. This paper intends to use the statistical data on life expectancy in Taiwan by means of the idea of randomization in statistics to explore (1) trend of life table changes, 1953-2015, (2) the sum of life expectancy in birth, middle age and old age with life table entropy, and (3) trends of the gains of life expectancy by elimination of the causes of death to discuss related issues about the maximum life span. Our study reveals the maximum life span in Taiwan is about 93 and 95 years of age for males and females respectively.