The fiber fragment distribution obtained from tensile testing of a single-filament composite contains vital information on the in situ strength of the fiber at short gauge lengths and on the shear stress across the fiber/matrix interface. Here, this fragmentation problem is mapped onto the problem of hard rods distributed randomly along a one-dimensional line, but with a stress-dependent rod length, and is then solved exactly. The solution utilizes the "car-parking" problem of equal sized cars parked along a line and the theory predictions agree well with existing simulation results. The theory also applies to multiple cracking of brittle films on pliable substrates, film coatings on fibers, and matrix cracking in ceramic matrix composites, and now allows the in situ fiber or film statistical strength and interfacial shear strength to be derived from experimental fragment distributions.