Adult tissue stem cells, such as hematopoietic stem cells (HSCs), are distinguished from mature cells by the ability to generate all mature cell-types of a particular tissue (multi-potency). To generate mature cells, HSCs differentiate into cells of lower potency. The resulting loss of stem cells must be compensated for by self-renewal, i.e. cell divisions which preserve the multi-potential differentiation capacity of the ancestral HSC. The reliability with which HSCs can transfer their identity and maintain self-renewal upon proliferation has been of keen interest to the field 
. Important questions are: Are daughter HSCs “as good as old” after self-renewal? How often can individual HSCs self-renew? Do different HSCs have different self-renewal capacities? What controls the fidelity of self-renewal? These questions remain incompletely understood.
Because of their extensive self-renewal capacity, HSCs were initially thought to be immortal. This view was supported by the observation that populations of HSCs could be serially transplanted for a very long period of time - exceeding the normal lifespan of the donor 
. However, when HSCs were examined on the clonal level, extensive heterogeneity in lifespan was revealed 
. A detailed analysis of a large panel of HSCs showed that the lifespan of individual HSCs is mathematically predictable 
. HSCs with lifespans from 10 to nearly 60 months were found side-by-side in the same donor 
, indicating that the lifespan is pre-determined on the level of each HSC. Because lifespans of single transplanted HSCs are predictable from few initial values of their repopulation kinetic, the lifespan is a programmed HSC-specific property 
. The population dynamics, therefore, predict that the molecular machinery which preserves self-renewal, will ultimately fail.
Several hypotheses have been developed to identify and explain how HSCs limit their lifespan. The generation-age hypothesis 
states that for every cell division, an HSC loses some quality that is referred to as “stemness”.
According to Hayflick's hypothesis 
, the probability that somatic cells produce viable daughter cells which can themselves divide, decreases as the number of divisions increases. The decrease might be caused by progressive telomere shortening 
. Hence, an extension of Hayflick's hypothesis predicts that stem cell self-renewal capacity should be self-limiting at the level of individual HSCs.
Yet, HSCs and other stem cells, express telomerase 
. This enzyme repairs telomere damage and, thus, aids in preserving genomic integrity. Thus, telomere shortening alone is unlikely to explain a limited lifespan of HSCs. Indeed, mice that have been homozygously ablated for telomerase activity show only mild effects and need to be severely stressed to reveal deficiencies in the hematopoietic system 
. Potentially in line with these findings in mice are clinical data. It was suggested that telomerase expression declines in the long-run and may be a cause for late bone marrow transplant failure 
. Declining telomerase expression may act in conjunction with the high stressor load imposed by the many co-morbidities affecting transplant patients 
Another proposal suggested that, in conjunction with oxidative stresses, high levels of reactive oxygen species (ROS) could be a damaging force acting on the long-term repopulating capacity of HSCs 
. The corresponding restoring force is provided by Forkhead box class O (FoxO) transcription factors. FoxO transcription factors increase the expression of genes whose products blunt the effects of elevated ROS 
. That different sources of self-renewal failures could be causally co-dependent is suggested by findings that oxidative stress could shorten telomeres 
Along-side genome stability, the preservation of epigenetic patterning is an important prerequisite to reliably produce functional daughter HSCs upon self-renewal. It has been suggested that both maintenance and de novo methylation are needed to maintain epigenetic stability 
. The expression levels of DNA methyltransferases 
responsible for maintenance (DNMT1) and de novo methylation (DNMT3a and DNMT3b) could be important for restoring HSC multi-potency 
. Quantitative work has suggested that small failures may accumulate over time in the DNMT1 pathways leading to the loss of maintenance methylation and, ultimately, epigenetic stability 
. Yet, neither of these mechanisms and hypotheses explain how HSCs with different lifespans co-exist in a single host.
It was suggested that HSCs could preserve their functional integrity over long periods of time by alternating between two states, called resting or quiescent, and active, respectively 
. This idea poses that intermittent transitions to quiescence could provide the time needed to minimize the detrimental effects of repeated DNA replication and other stresses on the HSC population as a whole 
. Elegant mathematical models of this idea have been formulated 
. Surprisingly, quiescence may leave HSCs more vulnerable to mutations following DNA repair 
. Quiescent and active HSCs may use different DNA repair mechanisms and the restoring pathway used by quiescent HSCs may lead to higher differentiation probabilities following re-activation. Never-the-less, when HSC quiescence was inhibited by the expression of the Wnt inhibitor Dickkopf-1, the HSC pool exhausted prematurely 
. This suggests that periods of rest in the niche are essential for controlling HSC lifespan - supporting the idea that repair is necessary to maintain HSC lifespan.
Mathematically, the lifespan of populations has been addressed in manufacturing, engineering, actuarial and biological applications of reliability theory 
. Reliability theory was first developed as a quality control tool to predict the time-to-failure - the manufacturing term for lifespan - of manufactured goods to determine warranty times. When examined as a population, the lifespan of manufactured goods proceeds through well-defined phases (). First, a decline in population size is found, which is interpreted as failure due to factory error. Second, there is a period of little change, known as the useful phase of the population of goods. Thereafter, the population size declines again, this time caused by age-related failure of essential machine components (wear-out phase). The second phase can be prolonged, if goods are repaired. If repairs occur repeatedly, the useful life will be extended, yet the population of goods will fail in the end, because of a general deterioration of many essential parts. In biology, failure theory has been applied to develop general laws of aging and longevity 
, respector-ligand dissociation 
, or genome instability 
. Here, we show that the principles of reliability and failure can be exploited to craft a new model of HSC self-renewal suggesting that HSCs differ a priori in the number of (self-)repair cycles they can undergo.
Failure Rate Kinetics of Machine and Clonal Blood Cell Populations.