Question

Problem 10-25

Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. Use Exhibit 10.13.

     To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three-sigma control limits.

SAMPLE NUMBER		READINGS (IN OHMS)
1		976	998	985	979
2		1018	993	974	1025
3		1027	1021	990	1019
4		1015	1028	1027	1009
5		1002	1016	992	972
6		974	981	1009	1006
7		976	1016	1027	1027
8		999	1000	1015	992
9		1024	997	986	979
10		1009	996	987	1028
11		994	974	994	1010
12		977	990	1024	990
13		993	1000	1006	1018
14		1012	1015	1015	1004
15		972	977	1018	1020

a. Calculate the mean and range for the above samples. (Round "Mean" to 2 decimal places and "Range" to the nearest whole number.)

Sample Number	Mean	Range
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

b. Determine X=X= and R−R−. (Round your answers to 3 decimal places.)

X=X=
R−R−

c. Determine the UCL and LCL for a X−X−chart. (Round your answers to 3 decimal places.)

UCL
LCL

d. Determine the UCL and LCL for R-chart. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places.)

UCL
LCL

e. What comments can you make about the process?

	The process is in statistical control.
	The process is out of statistical control.

Answer 1

sample mean = Sum of observations in a sample / 4

Range = Max observation of a sample - Min observation

X-X = Average of all sample means = 1001.617

R-R = Average of all range = 35.667

Please see below images for part A & B

Formula

Part C)

For Sample size N = 4 , constants for X and R charts are

A2 = 0.729

D3 = 0.00

D4 = 2.282

UCL X-X chart = X-X + A2 * R-R = 1001.617 + 0.729 * 35.667 = 1027.618

LCL X-X chart = X-X - A2 * R-R = 1001.617 - 0.729 * 35.667 = 975.616

part d)

UCL R-R Chart = D4* R-R = 2.282*35.667 = 81.392

LCL -R-R Chart = D3 * R-R = 0.00 ( 35.667 = 0

part E) Process is in statistic control as all Sample means and Range are within the UCL and LCL range for X-chart and R-chart.