Question

Problem 1.

Resistor 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.

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:

Sample #	Readings (in ohms)
1	1010	991	985	986
2	995	996	1009	994
3	990	1003	1015	1008
4	1015	1020	1009	998
5	1013	1019	1005	993
6	994	1001	994	1005
7	989	992	982	1020
8	1001	986	996	996
9	1006	989	1005	1007
10	992	1007	1006	979
11	996	1006	997	989
12	1019	996	991	1011
13	981	991	989	1003
14	999	993	988	984
15	1013	1002	1005	992

1. (10 points) Calculate control limits for R-chart.
2. (10 points) Calculate control limits for x̄ - chart.
3. (20 points) From the charts, what comments can you make about the process? and why?

Answer 1

Formula

a)

R-chart

UCL = D4*R-bar [For sample size 4, D4 = 2.282]
=2.282*21.73333333 = 49.59546666

LCL = D3*R-bar [For sample size 4, D3 = 0] = 0

b)

x-bar-bar chart

UCL = x-bar-bar+A2.R-bar [For sample size 4, A2 = 0.729]

=999.1+0.729*21.73333333

=1014.9436

LCL = x-bar-bar-A2.R-bar [For sample size 4, A2 = 0.729]

=999.1-0.729*21.73333333

= 983.2564

c)

The process is in control in terms of R-chart and x-bar-bar chart as all the sample means and ranges are within control limits