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			87.3			87.5			87.9			87.2			87.0
8:30			86.9			88.5			87.6			87.5			87.4
9:00			87.7			88.5			86.7			87.5			88.2
9:30			86.0			88.0			87.2			87.6			87.1
10:00			86.9			87.3			87.2			87.3			87.2
10:30			88.2			86.5			87.3			87.2			87.8

1. 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.)

	Mean of the sample means = LCL = UCL = Mean of the sample ranges = LCL = UCL =

1. c-1. Are any means out of control?

Yes

No

1. c-2. Are any ranges out of control?

Yes

No

Answer 1

(a)

Mean of the sample means:  LCL =86.60, UCL=88.22

Mean of the sample ranges : LCL =0, UCL=2.96

here $\bar{x}$=87.41 and $\bar{R}$=1.40

x-bar chart (for n=5, A2=0.577)

LCL=$\bar{x}$-A2*$\bar{R}$=87.41-0.577*1.40=86.60

UCL=$\bar{x}$+A2*$\bar{R}$=87.41+0.577*1.40=88.22

R-bar chart (for n=5, D3=0 , D4=2.114)

LCL=D3*$\bar{R}$=0.*1.40=0

UCL=D4*$\bar{R}$=2.114*1.40=2.96

Time/sample	1	2	3	4	5	mean	range
8:00	87.3	87.5	87.9	87.2	87	87.38	0.90
8:30	86.9	88.5	87.6	87.5	87.4	87.58	1.60
9:00	87.7	88.5	86.7	87.5	88.2	87.72	1.80
9:30	86	88	87.2	87.6	87.1	87.18	2.00
10:00	86.9	87.3	87.2	87.3	87.2	87.18	0.40
10:30	88.2	86.5	87.3	87.2	87.8	87.40	1.70
					mean=	87.41	1.40

(c1) NO, any means is not out of control

since all the means are within the LCL and UCL, so system is not out of contorll

x-bar chart mean mean CL LCL *UCL 1 2 3 4 5 6 sample

(c2)NO, any range is not out of control

since all the means are within the LCL and UCL, so system is not out of contorll

R-control chart Range range CL LCL UCL 1 2 3 4 5 6 7 sample