Question

found by a. 3. Three temperature sensors measure temperatures at 3 different places in the processing room. The measurements are taken five times (samples) during a day. [24 pts] a. What is the sample size? Compute sample means and ranges b. Compute the upper and lower control limits for a X-bar chart. ("A2 1.023) c. Sketch the X-bar chart. Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sensor 1 65 72 68 55 60 Sensor 2 70 50 54 60 69 Sensor 3 57 67 70 58 72

Answer 1

a)

here, total number of sample is 5

Sample Means and Ranges computed in the below table - column -  Mean Value or X Bar and Column - Range

b) Upper control limit and lower control limit computed for X Bar Chart, here

formula = UCL = X Double Bar + (1.023*R Bar)

LCL= X Double Bar - (1.023*R Bar)

1	B	C	D	E	F	G	H
2	Sample	Sensor 1	Sensor 2	Sensor 3	Mean Value or X Bar	Range	Upper control Limit of X Bar Chart
3	1	65	70	57	64.00	13	77.05
4	2	72	50	67	63.00	22	Lower Control Limit of X Bar Chart
5	3	68	54	70	64.00	16	49.22
6	4	55	60	58	57.67	5
7	5	60	69	72	67.00	12
8					X Double Bar	R Bar
9					63.13	13.6

Formula:

1	B	C	D	E	F	G	H
2	Sample	Sensor 1	Sensor 2	Sensor 3	Mean Value or X Bar	Range	Upper control Limit of X Bar Chart
3	1	65	70	57	=AVERAGE(C3:E3)	=MAX(C3:E3)-MIN(C3:E3)	=F9+(1.023*G9)
4	2	72	50	67	=AVERAGE(C4:E4)	=MAX(C4:E4)-MIN(C4:E4)	Lower Control Limit of X Bar Chart
5	3	68	54	70	=AVERAGE(C5:E5)	=MAX(C5:E5)-MIN(C5:E5)	=F9-(1.023*G9)
6	4	55	60	58	=AVERAGE(C6:E6)	=MAX(C6:E6)-MIN(C6:E6)
7	5	60	69	72	=AVERAGE(C7:E7)	=MAX(C7:E7)-MIN(C7:E7)
8					X Double Bar	R Bar
9					=AVERAGE(F3:F7)	=AVERAGE(G3:G7)

c) X Bar Chart using MiniTab, Manually can be computed using above table data,

Xbar-R Chart of Sensor 1, ..., Sensor 3 UCL-77.05 Sample Mean X-6313 Cl=49 22 Sample