This is a very interesting question. Apparently, at the time relays and tubes were used in computational equipment, there were no studies specifically regarding the lifetime of these components in such equipment. The state of the art was advancing at such a pace that relays and tubes were used for only a brief period of time and then left behind after about 1955 to 1960. However, relays which had been used a brief period longer than tubes in computation, had proven useful and durable in telephonic switching equipment. That use would continue long after computational use ended. And, as should be noted, certain specialty tubes were used in computation but apparently only on one platform developed by the Institute for Advanced Study. In answer to the question, was there a study comparing the reliability or lifespan of relays or vacuum tubes used in computers, the answer seems there was none. Nevertheless, there was extensive experience in the use of such devices and their performance capabilities were compared and documented. The following summary of the then state-of-art is offered...
Reliability in computing devices is of the utmost importance, and therefore a serious problem arises with the use of electromechanical relays. Interference with one or more computing operations may result if a particle of dust happens to rest on the contact faces, since electrical contact is made between two points of microscopic size. Since there is no direct way to detect such a failure either before or after it occurs, the use of checking circuits is desirable. Fortunately, it is relatively easy to add contacts to an electromechanical relay for checking purposes. This was done on the Bell Telephone Laboratories machines, and their ability to resume operation quickly after a failure is one of their outstanding features.
A comparison between the electromagnetic relay and the electron tube reveals that the former has a longer life expectancy in operating hours but will operate fewer times than the latter. Furthermore, the electromechanical relay is subject to failure from vibrations and dust on the contact faces and is apt to require more delicate care than a vacuum tube. The relay usually operates on less power than the filaments of a vacuum tube, but the latter can operate on alternating current taken directly from the power mains through step-down transformers. Most fast-acting relays operate on direct current; hence when the rectification conversion loss is taken into account, their power requirements are comparable to those of electron tubes. The two are nearly the same in cost and size. The greatest difference in characteristics is in the maximum speed of operation; the electron-tube relay is at least 10E4 times faster than the electromechanical relay. Therefore, in situations where computing may be done serially, a single tube can perform the same operations in the same time as a large number of relays operating simultaneously in parallel.
Source: Engineering Research Associates (ERA), Inc., 1950. High-Speed Computing Devices. McGraw-Hill Book Company, New York. pp 313-314.
Reading through the ERA text, one thing becomes abundantly clear. For the state of the art in computing existing in 1949, components used in the construction of computing equipment were not designed and life-tested for such use. In essence, parts such as relays and tubes were off the shelf, already available. Manufacturers, sensing the need for durability in relays, began to manufacture equipment that had higher durability than previously. Nevertheless, tubes such as 6SA7 and 6L7, for instance, were just radio-equipment tubes and were manufactured as they had always been. Although similar tube designations may have unique design characteristics (folded vs twisted filaments, for example), their use in computing equipment was always subject to eventual failure. As noted by ERA, for the ENIAC, tube failures usually occurred within the first 250hrs of operation, or after 5000 hours. The ENIAC operating staff was reportedly not in sympathy with replacing a large number of tubes at once, presumably to preclude failure during equipment use.
The most common source of trouble in using the ENIAC related to trouble with the 18,000 vacuum tubes used in the machine. Although the practice was to test several hundred of the 3-tube amplifiers each week, and replace all three tubes if any amplifier was found to not be operating satisfactorily, the quantity of replaced tubes was considerable. ERA reports that during the first 11 months of operation in 1949, about 2000 tubes per month were replaced each month, of which about half were actually bad.
At this particular time, say 1948 to 1950, there were two approaches to reducing equipment failure during operation. One approach was to make components so reliable that they would outlast the useful life of the computing equipment in which they were being used. At this time there were not statistical tests of lifetime durability for these components (except, presumably, by experience gained), but if the expected statistical life expectancy were sufficiently long, the actual failure would have proved to be sufficiently low during the initial years of machine operation. The sense gained from today's view of this approach was that equipment would be replaced or superseded before components substantially failed. The second approach was to extend the operating life of computing equipment as far as possible by detecting incipient failures before they occurred. As an independent and retrospective view 30 years later (about 1980), this approach was used productively with many mainframe systems.
Also at this early-1950s period, computing equipment failures were expensive and annoying given the value of the operating time of these machines. Nevertheless, other failures caused problems, such as those causing intermittent machine errors, for instance. In relay computers, approximately 85 percent of the failures were intermittent. For the ENIAC, the majority of failures were intermittent. To detect this problem, in the Bell Telephone Laboratories machines, continuous automatic checking, or low-level checking, was done at the level of the individual relay. Detection of a failure would cause the results to be held in their respective relays until the fault was cleared, upon which computation would continue with the results obtained previously. For the ENIAC, checks were made of the solutions or partial solutions to problems, a process termed high-level checking. Operation of the ENIAC was so fast that holding results in stasis was deemed impractical and results were recalculated after a failure.
ERA makes the following comment regarding the ENIAC -
It has been estimated that the ENIAC is actually in useful operation on problems about 50 percent of the time and that, allowing for a complete repetition of each problem, it therefore turns out about one-fourth as many useful answers as could an ideal, perfectly reliable, machine with the same basic mathematical characteristics, which required no maintenance whatever. This is an excellent performance record.