2.2 The bathtub curve
A characteristic of many products is illustrated in Figure 11, where failure rate is plotted against product lifetime. The so-called bathtub curve shows an early, high mortality (known sometimes as infant mortality), followed by a stable mid-life of random failures, followed by a rise in failures as critical components wear out.
For safety-critical products, any early failures are unacceptable, so all products will be inspected and tested for their key functions before being sold.
Wear-out failures can be avoided by replacing components likely to degrade at pre-determined intervals. Drawing on the car as an example, some of the components replaced at intervals would be:
cooling system seals;
elastomeric hose for coolant, fuel, and brake fluid;
A sensible maintenance policy is to replace sensitive components at regular intervals. For instance, it is a legal requirement in the UK that tyres be replaced when the tread depth reaches 1.6 mm.
For safety-critical components, a regime of testing every component in the factory can nearly eliminate early failures, and reduce random failures. Wear-out can be reduced by replacing parts at a predetermined point in their lifespan. These measures produce the ideal curve shown in Figure 12 (using the same axes as in Figure 11). However, if parts replacement is botched, safety can be severely compromised, as Box 4 relates.
Box 4 Safety-critical seals
Seals in closed fluid systems are often safety-critical components because they prevent escape of the fluid into the outer environment.
An astounding incident was reported in the House of Commons in November 1997, and related to the near disaster that occurred to a BAE 146 aircraft of the Queen's Flight. The four engines cut out one-by-one, with the final engine cutting out just as the pilot landed the aircraft.
Investigation of the engines after the incident showed the engines had experienced a loss of oil pressure, leading to shut-down. None of the sump drain plugs on the engines had been fitted with their O-ring seals, so oil leaked out slowly. It was fortunate the last engine was working during the landing, and the aircraft was not carrying any member of the royal family at the time. No doubt the mechanic was duly admonished. The story is a useful reminder of the safety-critical nature of many seals.
Another example of a seal problem arose in the early 1990s when the hot radiators in numerous hospitals and old people's homes leaked and caused material damage. The radiators had only recently been fitted, and incorporated a new material for the flat circular washers used on the drain plugs. The material was a thermoplastic elastomer: a copolyester with polyether rubbery chains. Such polymers offer advantages because they can be injection moulded quickly and easily, when compared with conventional cross-linked rubbers. They also apparently offered better water resistance than the older fibre washers, and had been used successfully in hot water taps.
The initial report to loss adjusters pointed to two possible causes:
overtightening by the plumber;
undertightening of the drain plugs.
The possible causes of failure on such a large scale had not been considered. While either cause could explain a few failures, it did not explain the many installations by many different plumbers. In addition, the initial investigator ignored key evidence of brittle cracking and hardening of the material.
The conditions of exposure are quite different in radiator seals, compared with hot water taps. Washers in the latter are exposed only intermittently to high water temperatures when a tap is opened, while radiator seals are exposed almost continuously. Examination of the failed washers (Figure 13) showed radial brittle cracks through which the pressurised hot water could leak. The material showed little or no resilience, indicating that crystallisation had occurred, making the polymer hard and unyielding.
The investigations carried out independently by several experts showed the material supplier had printed a technical note to warn customers of the instability of the polymer at high water temperatures. For whatever reason, the note had not been read by the moulder, and it had made millions of the washers for the radiator company.
The civil case was eventually settled for a large sum to compensate for the material damage caused by the leaking water, and for replacing the washer material with another polymer, EPDM rubber.
Surprisingly, this example is not that unusual, because new technology or new materials often create problems of use and application that were not foreseen by their originators. However, most manufacturing companies try to explore the properties and potential problems of new materials before launching a product, both by laboratory testing and by development phases such as prototyping.