Statistical procedures are presented to evaluate major human errors during the development of a new system, errors that have led or can lead to accidents or major failures. The first procedure aims at estimating the average “residual” occurrence rate for this type of accidents or major failures after several have occurred. The procedure is solely based on the historical record. Certain idealizations are introduced that allow the application of a sound statistical evaluation procedure. These idealizations are practically realized to a sufficient degree such that the proposed estimation procedure yields meaningful results, even for situations with a sparse data base, represented by very few accidents. The “accidents” considered are caused or amplified by human errors, primarily in the design. It is assumed that no accident caused by a human design error is permitted to occur more than once; the cause of every accident is determined, and the design of the system is modified so that this type of accident does not recur. Under the assumption that the possible human-error-related failure times have exponential distributions, the statistical technique of isotonic regression is proposed to estimate the failure rates due to human design error at the failure times of the system. The last value in the sequence of estimates gives the residual accident chance. In addition, the actual situation is tested against the hypothesis that the failure rate of the system remains constant over time. This test determines the chance for a decreasing failure rate being incidental, rather than an indication of an actual learning process. Both techniques can be applied not merely to a single system but to an entire series of similar systems that a technology would generate, enabling the assessment of technological improvement. For the purpose of illustration, the nuclear decay of isotopes was chosen as an example, since the assumptions of the model are rigorously satisfied in this case. This application shows satisfactory agreement of the estimated and actual failure rates (which are exactly known in this example), although the estimation was deliberately based on a sparse “historical” record.