Question

For process the QC inspector found that the X bar equals 50.2, UCL equals 50.5, LCL equals 49.5 and Rbar equals 0.7 for n=4 which one is the correct value of 6a

a.1.98
b.2.04
c.2.16
d.2.10

Answer 1

To determine the correct value of 6a, we need to calculate the control limits for the R chart and then compare them to the given value of Rbar

Step-by-step explanation

The control limits for the R chart can be calculated using the following formulas:

UCL(R) = D4 * Rbar

LCL(R) = D3 * Rbar

Where D4 and D3 are constants based on the sample size, n. For n=4, the values of D4 and D3 are typically 2.282 and 0.410, respectively.

Let's calculate the control limits for the R chart:

UCL(R) = 2.282 * 0.7 = 1.5974

LCL(R) = 0.410 * 0.7 = 0.287

Now, we compare the given value of Rbar (0.7) to the calculated control limits for the R chart:

0.287 ≤ Rbar ≤ 1.5974

Since the given value of Rbar (0.7) falls within the control limits, we can conclude that the process is in control for the R chart.

Next, we need to determine the correct value of 6a. For an R chart, 6a is equal to the difference between the UCL and LCL for the R chart.

6a = UCL(R) - LCL(R)

= 1.5974 - 0.287

≈ 1.31

Based on the calculations, the correct value of 6a is approximately 1.31.

Therefore, none of the given options (a, b, c, d) match the correct value of 6a.