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Abstract:
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When replacement times of one component are reported, lifetimes are easily calculated as the times between replacements. If there is more than one component, lifetimes are also easily obtained provided that all components are identified. It is common to have situations, however, where there are several identical components, where replacement times are reported, but where it is not specified which specific component was replaced. For example, consider the case where there are six identical light bulbs in a conference room and we know every instance when a bulb is replaced---but not which bulb is it. Without this last piece of information, it is not possible to calculate lifetimes. However, the parameters of the lifetime distribution can still be estimated, as this presentation explains. Most of the theory is intractable but simulations show good properties for the proposed methods.
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