ABSTRACT
Example 3.1. Cohen (1957) considered a random sample from production of a certain bushing that had been screened through go-no go gauges to eliminate items with diameters in excess of 0.6015 inches or less than 0.5985 inches. Nonconforming items were discarded and no further information was available on either their measurements or their number. For a random sample of 7 5 bushings selected from the screened production, n = 75, i = 0.60014933, T1 = 0.5985, T2 = 0.6015, s2 = 0.000000371187, w = 0.0030, v1 = x-T1 = 0.00164933, vtfw = 0.54978, and s2/w2 = 0.041242. Visual interpolation between the curves of Figure 3.1 gives initial approximations ~? = -2.50 and ~g = 2.00. With these values as approximate coordinates of the intersection of curves of the two estimating equations, we enter Table 3.1 and interpolate as necessary to obtain coordinates of points on the two curves in the vicinity of their intersection. We locate two points on the curve of H 1 (~t. ~2) - vtfw = 0 with coordinates (- 2.5, 1.9734) and (- 2.6, 2.0666), and two points on the curve H2(~ 1 , ~2) - s2/w2 = 0 with coordinates (- 2.5, 2.0364) and (- 2.6, 1.8779). Equations of straight lines through the first two points and through the second two points are
In effect, these two linear equations are replacements for the nonlinear estimating equations (3.2.11) in the vicinity of their common solution. A simultaneous solution of the two linear equations subsequently gives
and
and
f.Lo = 0.600 175 14.
