Question

A new machine has just been installed to cut and rough-shape large slugs. The slugs are then transferred to a precision grinder. One of the critical measurements is the outside diameter. The quality control inspector randomly selected five slugs each half-hour, measured the outside diameter, and recorded the results. The measurements (in millimeters) for the period 8:00 a.m. to 10:30 a.m. follow.

		Outside Diameter (millimeters)
Time		1		2		3		4		5
8:00		87.1		87.4		87.9		87.1		87.0
8:30		86.9		88.5		87.6		87.5		87.4
9:00		87.5		88.4		86.8		87.5		88.0
9:30		86.0		88.0		87.2		87.6		87.1
10:00		86.9		87.2		87.1		87.0		86.8
10:30		88.2		86.3		87.2		87.2		87.6

Click here for the Excel Data File

a.	Determine the control limits for the mean and the range. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)

=	LCL =	UCL =
=	LCL =	UCL =

c-1.	Are any means out of control?
	(Click to select)  No  Yes

c-2.	Are any ranges out of control?
	(Click to select)  No  Yes

Answer 1

Time		1		2		3		4		5	mean	Range
8:00		87.1		87.4		87.9		87.1		87	87.3	0.9
8:30		86.9		88.5		87.6		87.5		87.4	87.58	1.6
9:00		87.5		88.4		86.8		87.5		88	87.64	1.6
9:30		86		88		87.2		87.6		87.1	87.18	2
10:00		86.9		87.2		87.1		87		86.8	87	0.4
10:30		88.2		86.3		87.2		87.2		87.6	87.3	1.9
										AVERAGE	87.333	1.4

CONTROL limit for mean,

   x̅̅ =   87.33333333
   R̅ =   1.40
   A2=   0.577
UCLx =    x̅̅ +A2 * R̅ )=   88.14
LCLx =    x̅̅ - A2*R̅ )=   86.53

================

control limit for Range,

D4=   2.114  
D3=   0  
UCLr = D4*R̅ =        2.96
LCLr = D3*R̅ =       0.00

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c-1.	Are any means out of control?
	No

c-1.	Are any means out of control?
	NO

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