Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)

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for this problem.

Thirty-five samples of size

Sample Size, n	Mean Factor, A2	Upper Range, D4	Lower Range, D3
2	1.880	3.268	0
3	1.023	2.574	0
4	0.729	2.282	0
5	0.577	2.115	0
6	0.483	2.004	0
7	0.419	1.924	0.076
8	0.373	1.864	0.136
9	0.337	1.816	0.184
10	0.308	1.777	0.223
12	0.266	1.716	0.284

7

each were taken from a fertilizer-bag-filling machine. The results were: Overall mean =

54.75

lb.; Average range

R

=

1.64

lb.

a) For the given sample size,

the

control limits for 3-sigma

x

chart are:

Upper Control Limit

(UCLx)

=

nothing

lb. (round your response to three decimal places).

Lower Control Limit

(LCLx)

=

nothing

lb. (round your response to three decimal places).

b) The control limits for the 3-sigma R-chart are:

Upper Control Limit

(UCLR)

=

nothing

lb. (round your response to three decimal places).

Lower Control Limit

(LCLR)

=

nothing

lb. (round your response to three decimal places).