Suppose that it is known that the ξi are non-negative, that ξi = 1 , and that ¯ ξ(2) i = XXXXXXXXXXIn this case, we would like an upper bound on the expected performance E(g(ξ)) . We construct a bound...

Suppose that it is known that the ξi are non-negative, that ξi = 1 , and that ¯ ξ(2) i = 1.25 . In this case, we would like an upper bound on the expected performance E(g(ξ)) . We construct a bound by first finding ηi(ξi) as in (5.37). This problem may correspond to determining a performance characteristic of a part machined by two circular motions centered at (0,0) and (1,0), respectively. Here, the performance characteristic is proportional to the distance from the finished part to another object at (2,1). The square of the radii of the tool motions is ξi +1 , where ξi is a non-negative random variable associated with the machines’ precision.