Consider the design problem in Section 1.4. Suppose the design decision does not completely specify x in (1.4.1), but the designer only knows that if a value xˆ is specified then x ∈ [.99 ˆx,1.01 ˆx]...

Consider the design problem in Section 1.4. Suppose the design decision does not completely specify x in (1.4.1), but the designer only knows that if a value xˆ is specified then x ∈ [.99 ˆx,1.01 ˆx] . Suppose a uniform distribution for x is assumed initially on this interval and that the designer can alter the design once after manufacturing and testing N axles out of a total predicted demand of 1,000 axles. The designer assumes that her posterior distribution on the actual mean relative to ˆx would not change if she adjusts the target diameter ˆx after observing the first N axle diameters. With these assumptions, formulate a Bayesian model to determine an initial specification ˆx1 and N followed by a second specification ˆx2 for the remaining 1000−N axles