Mission-Based Component Testing for Series Systems

Mission-Based Component Testing for Series Systems

Abstract We consider the component testing problem of a device that is designed to perform a mission consisting of a random sequence of phases with random durations. Testing
is done at the component level to attain desired levels of mission reliability at minimum
cost. The components fail exponentially where the failure rate depends on the phase of the
mission. The reliability structure of the device involves a series connection of nonidentical
components with different failure characteristics. The optimal component testing problem
is formulated as a semi-infinite linear program. We present an algorithmic procedure to
compute optimal test times based on the column generation technique, and illustrate it with
numerical examples.
Keywords Component testing · Phased-mission systems · Mission reliability ·
Semi-infinite linear programming

1 Introduction
Component testing poses an interesting statistical decision making problem that has been
gaining more importance in recent years. It involves testing the components of a complex
device separately because the whole system can not be tested. System testing may sometimes be economically infeasible or even impossible. Current international agreements, for
example, ban testing of nuclear devices and weapons of mass destruction. This is an extreme
but typical example where one needs to obtain required levels of reliability without testing
it. Instead, testing is done on individual components, at minimum cost, to make sure that reliability requirements are satisfied. Also, in many cases, life testing data on the components
is made available by the producers. An interesting question now is, how should the available resources be efficiently allocated among the tests of different component types so that
a certain level of inference on reliability is obtained. This problem, which is the experimental design converse of using component test data to estimate reliability, has been known as
the system based component test problem. The reader is referred to Gal (1974), Mazumdar
(1977), Easterling et al. (1991), Altınel (1994), Altınel and Özekici (1998) and Altınel et al.
(2001) for historical developments and some recent literature. This approach is applicable
in cases where reliability is defined as the probability of failure free operation of the device
for a prespecified fixed amount of time. There are many applications, however, where this is
not appropriate.



References

https://link.springer.com/article/10.1007%2Fs10479-010-0816-9