Question

In order to determine if a process that produces housings for wireless speakers is in control, the following data is collected to construct a control chart. Ten samples of 200 wireless speakers each have been taken and the number of defective housing is: Sample1:3; Sample2:10; Sample3:8; Sample4:2; Sample5:6 Sample6:7; Sample7:4; Sample8:5; Sample9:6;Sample10:7. Based on this data, is the process in control if 2 sigma limits are employed?

a. it is out of control

b. it is in control because the average is within the control limits.

c. it is in control because all points are within the control limits

d. it is out of control because the sample data varies.

e. cannot answer the questions as not enough information is given.

Answer 1

Mean for the samples is : (3+10+8+2+6+7+4+5+6+7)/10

: 5.8

(Standard Deviation)2 = [(3-5.8)2 + (10-5.8)2 + (8-5.8)2 + (6-5.8)2 + (7-5.8)2 + (4-5.8)2 + (5-5.8)2 + (6-5.8)2 + (7-5.8)2 ]/9

= [7.84 + 17.64 + 4.84 + 0.04 + 1.44 + 3.24 + 0.64 + 0.04 + 1.44]/9

=4.129

Standard Deviation: 2.03

Calculating 2 sigma control limits:

Upper Control Limit: 5.8 + (2*2.03)

: 9.86

Lower Control Limit: 5.8 - (2*2.03)

:1.74

a. Sample is out of control is Correct as in two cases the number of defective speakers are beyond the upper control limit. A sample is in control if the variations in defects are in the given control limits

b. Incorrect as some variations are beyond control limits

c. Incorrect as some variations are beyond control limits

d. Incorrect as it is out if control as data varies beyond control limits

e. Incorrect as we have all the data we need to solve this problem