A spot of an upside down bathtub failure rate lifetime distribution in the wild

Abstract

Lifetime distributions are characterised by their behaviour of the coinciding failure rate as increasing (wear), decreasing (early failures) or bathtub (typical behaviour with three phases). Some distributions have upside down bathtub shaped (UBT) failure rates, which is often associated with overload of a component or a subsystem. Many models of UBT distributions can be found, but not many practical examples.Analyzing a large sample of washing machines over a lifetime, a distribution with UBT shaped failure rate has been found. The failures occurred too early and not all machines were subject to this type of failure. A technical investigation has been carried out to reveal the failure process. It turned out, that too much grease has been used, causing pollution of the commutators of the electrical motor. This pollution increased as long as oil was bleeding out of the grease. The commutator demonstrated a kind of self-cleaning property, if no more oil polluted the commutator. The polluted commutator caused increased electrical discharges at the commutator. These electrical discharges caused instabilities in the controller of the machine leading to failures requiring intervention of a repair technician. The cause was insufficient protection of the controller board against ripple voltage transmitted via the connecting lines. As long as the grease was bleeding out oil, the risk of failure increased. After the quantities of oil decreased, caused by the self-cleaning of the brushes of the motor, electrical discharges and therefore also failures of the machines decreased.A mathematical model has been developed to describe this entire process. As a result, a UBT shaped failure rate has been derived which fitted quite well a large set of data (about several ten thousands of failures). The model allows to explain the observed failure data in terms of the physical failure process and to better understand the application of lifetime distributions with UBT failure rates. Future work could be dedicated to other, simpler failure type distributions with UBT failure rate and to simplify the given model, which is still quite close to physical processes.