In previous chapters, our discussion has been focused on balanced RSS. In this chapter, we turn to unbalanced RSS. For a given statistical problem, the amount of useful information contained in one order statistic is not necessarily the same as in the others. Thus, it is desirable to quantify the order statistics with the highest amount of information, which gives rise to an unbalanced RSS. In certain practical problems, though RSS does not come into play, the data has the structure of an unbalanced RSS sample. Take, for example, the reliability analysis of the so-called *r*-out-of-*k* systems which are of great use for improving reliability by providing component redundancy. An *r*-out-of-*k* system consists of *k* independently functioning identical components. The system functions properly if and only if at least *r* of its components are still normally functioning. The system fails when the number of its failed components reaches (*k* − *r* + 1). Thus, the lifetime of an “r-out-of-k” system is, in fact, the (*k* − *r* + 1)st order statistic of *k* independent identically distributed component lifetimes. Thus, a sample of system lifetimes can be treated as an unbalanced RSS sample while only the (*k* − *r* + 1)st order statistic is quantified in each ranked set of size *k*, see Kvam and Samaniego [85] and Chen [33]. Another example is the so-called nomination sampling. In certain social surveys, psychological factors often play a role as to whether or not reliable information can be extracted from the sampling units. Nomination sampling, which takes into account the psychological factors, is designed to observe only the maximum or the minimum of a simple random sample. For more details of nomination sampling, the reader is referred to Willemain [170], Tiwari [168] [169].