At Webster Chemical Company, lumps in the caulking compound could cause difficul

Question

At Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Testing for the presence of lumps destroys the product, so an analyst takes random samples. The following results are obtained: Tube No. Lumps Tube No. Lumps Tube No Lumps 4 4 10 4 12 4 Determine the c-chart two-sigma upper and lower control limits for this process. Is the process in statistical control? The UCLc equals and the LCL equals (Enter your responses rounded to two decimal places.)

Explanation / Answer

Nmumber of tubes = 12

Sum of number of lumps = 5+4+5+7+7+4+2+4+2+1+7+4 = 52

C-bar = Sum of number of lumps / Number of tubes = 52/12 = 4.33

Using a two sigma control limit,the value of Z = 2

UCL = C-bar + [Z(Sqrt of C-bar)]

= 4.33 + [2(Sqrt of 4.33)]

= 4.33 + (2X2.08)

= 4.33 + 4.16

= 8.49

LCL = C-bar - [Z(Sqrt of C-bar)]

= 4.33 - [2(Sqrt of 4.33)]

= 4.33 - (2X2.08)

= 4.33 - 4.16

= 0.17

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