Question

4. A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results : Machine #1 measurements [13, 16, 21, 16]; Machine #2 measurements [ 22, 24, 23, 21]; Machine #3 measurements [ 15, 24, 13, 12]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits? Select one:

a. 26.15and 10.51

b. 20.4and 16.26

c. 23.93and 12.74

d. 41.33and -4.667

Answer 1

Note: In case of any doubt, please mention it in the comment so that I can help you. Thank you.

Answer: C (23.93 and 12.74)

Machines					Mean	Range (Maximum - Minimum)
Machine 1	13	16	21	16	16.5	8
Machine 2	22	24	23	21	22.5	3
Machine 3	15	24	13	12	16	12

Overall Mean (
X
) = (16.5 + 22.5 + 16)/3

Overall Mean (
X
) = 18.333

Average Range ($\bar{R}$) = (8 + 3 + 12)/3

Average Range ($\bar{R}$) = 7.666

Number of observations in a sample = 4

* Use mean factor table to find value of A2 at n = 4

Value of A2 = 0.729

$UCL = \bar{\bar{X}}+A_{2}\bar{R}$

UCL = 18.33 + (0.729 × 7.66)

UCL = 23.93

$LCL = \bar{\bar{X}}-A_{2}\bar{R}$

LCL = 18.33 - (0.729 × 7.66)

LCL = 12.74