General Overview Of Failure Kinetics

There is a striking similarity between living organisms and technical devices in the general age pattern of their failures—in both cases the failure rate usually follows the so-called bathtub curve (Figure 5.4).

The bathtub curve of failure rate is a classic concept presented in all textbooks on reliability theory (Ayyub and McCuen, 2003; Barlow and Proshan, 1975; Rausand and Hoyland, 2003).

The bathtub curve consists of three periods. Initially the failure rates are high and decrease with age. This period is called the "working-in" period and the period of "burning-out" of defective components. For example, the

Age in median lifespan scale

Figure 5.4. Bathtub mortality curves for humans and fruit flies. Mortality is estimated on a daily basis; age is expressed in a median lifespan scale (a similar approach was used by Pearl and Miner, 1935 and Carnes et al., 1998). Mortality for Drosophila melanogaster was calculated using data published by Hall (1969). Mortality for humans was calculated using the official Swedish female life table for 1985 (ages 0-80 years), and the 1980-90 decennial life table for Swedish females available in the Kannisto-Thatcher Database on Old Age Mortality, http://www.demogr. mpg.de/databases/ktdb (ages over 80 years), Source: Gavrilov and Gavrilova, 2005.

Age in median lifespan scale

Figure 5.4. Bathtub mortality curves for humans and fruit flies. Mortality is estimated on a daily basis; age is expressed in a median lifespan scale (a similar approach was used by Pearl and Miner, 1935 and Carnes et al., 1998). Mortality for Drosophila melanogaster was calculated using data published by Hall (1969). Mortality for humans was calculated using the official Swedish female life table for 1985 (ages 0-80 years), and the 1980-90 decennial life table for Swedish females available in the Kannisto-Thatcher Database on Old Age Mortality, http://www.demogr. mpg.de/databases/ktdb (ages over 80 years), Source: Gavrilov and Gavrilova, 2005.

risk for a new computer to fail is often higher at the very start, but then those computers that did not fail initially work normally afterwards. The same period exists early in life for most living organisms, including humans, and it is called the ''infant mortality'' period. Then follows the second period called ''the normal working period,'' corresponding to an age of low and approximately constant failure rates. This period also exists in humans, but unfortunately it is rather short (10-15 years) and ends too soon. Then the third period, ''the aging period,'' starts, which involves an inexorable rise in the failure rate with age. In most living organisms, including humans, this rise in failure rates follows an explosive exponential trajectory (the Gompertz curve). For humans, the aging period lies approximately within the interval 20-100 years. Thus there is a remarkable similarity in the failure patterns of technical and biological systems. This similarity is reinforced further by the fact that at extreme old ages there is one more, the fourth period common to both technical devices and living organisms (Economos, 1979). This period is known in biology as a period of late-life mortality leveling-off (Carey and Liedo, 1995; Clark and Guadalupe, 1995; Economos, 1979; Fukui et al., 1993; 1996; Vaupel et al., 1998), and also as the late-life mortality deceleration law (Fukui et al., 1993; 1996; Khazaeli et al., 1996; Partridge and Mangel, 1999).

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