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A study on estimation of reliability of a coherent system under field condition

An engineered system is a functionally related group of components, and thus estimation of its reliability depends on the estimation of the reliability of its components. The component reliabilities are estimated usually under a laboratory set up while the system may be installed to work under a different condition, called field condition. The difference may arise due to the change in temperature, humidity, voltage, friction, etc. The cause of the difference may be attributed to a random variable, known as an environmental variable, which affects the functioning of the system. The presence of this variable makes the component failure-times dependent, and hence they behave differently from what they would have behaved under independent set up. Naturally, this change in the behavior of the components affects the estimates of system reliability. Thus, under such situation, if the reliability of a system is not estimated considering the conditions under which it actually works, there will be an upward or downward bias in estimation. Here we make an attempt to study the effect of an environmental variable on the reliability estimation of a complex coherent system, and try to find out the conditions under which the system performance is optimized. A simulation study has been included to see the crossing behavior of the reliability function, which describes the nature of the reliability curves under laboratory and field conditions, at different time points, in particular, when they cross each other.