Question

The following data represents sample data of 6 oz. bottles of after-shave. Develop the X-bar and R control charts (mean chart and range chart) for the following sample. A process that is considered to be in control measures an ingredient in ounces. Below are the samples taken from the process.

Sample	1	2	3	4	5	6	Sum	X-bar	R
1	6.00	5.90	6.00	5.90	6.00	5.90
2	6.00	6.00	6.30	6.04	6.02	6.00
3	5.90	6.00	6.06	5.90	6.00	5.90
4	5.88	6.00	6.03	5.90	6.05	5.92
5	6.10	6.00	5.96	6.00	6.10	6.02
							Average=

a) What are the control limits for the mean chart? (4 points)

b) What are the control limits for the range chart? (4 points)                       

c) Is the process in control? Show your explanation. (2 points)

Answer 1

Solution:

# SAMPLE	1	2	3	4	5	6	AVERAGE	RANGE
1	6	5.9	6	5.9	6	5.9	5.95	0.1
2	6	6	6.3	6.04	6.02	6	6.06	0.3
3	5.9	6	6.06	5.9	6	5.9	5.96	0.16
4	5.88	6	6.03	5.9	6.05	5.92	5.963	0.17
5	6.1	6	5.96	6	6.1	6.02	6.03	0.14
AVERAGE							5.993	0.174

XBAR = 5.993

RBAR = 0.174

A2 VALUE CORRESPONDING TO N = 6 = 0.483

D3 & D4 VALUES CORRESPONDING TO N = 0, 2.003

CONTROL LIMITS FOR XBAR

UCL X = XBAR + (A2 * RBAR) = 5.993 + (0.483 * 0.174) = 6.077

LCL X = XBAR - (A2 * RBAR) = 5.993 - (0.483 * 0.174) = 5.909

CONTROL LIMITS FOR RBAR

UCL R = RBAR * D4 = 0.174 * 2.003 = 0.349

LCL R = RBAR * D3 = 0.174 * 0 = 0

2. YES, SINCE ALL THE POINTS ARE WITHIN THE CONTROL LIMITS, IT SHOWS THAT THE PROCESS SHOWS NATURAL VARIATION AND IS IN CONTROL.

NOTE:: I hope this answer is helpfull to you......**Please suppport me with your rating

**Please give me"LIKE".....Its very important for me......THANK YOU