A2/D3/D4 Table

Factors for Calculating Three-Sigma Limits for the x-bar Chart and R-Chart

Size of Sample (n)	Factor for UCL and LCL for x-bar-Charts A2	Factor for LCL for R-Charts D3	Factor for UCL for R-Charts D4
2	1.880	0	3.267
3	1.023	0	2.575
4	0.729	0	2.282
5	0.577	0	2.115
6	0.483	0	2.004
7	0.419	0.076	1.924
8	0.373	0.136	1.864
9	0.337	0.184	1.816
10	0.308	0.223	1.777

Source: 1950 ASTM Manual on Quality Control of Materials, copyright American Society for Testing Materials. Reprinted with permission.

(LO2DM1) Jus de Fruit Co. has set up for automated production of its new bottled Triple Berry Colada. Five samples were taken during the first week of production. The OM team wants to check if the central tendency of the process is in control. What will be the upper and lower control limits, respectively?

Sample	Bottle 1	Bottle 2	Bottle 3
1	20.1	20.1	19.8
2	20.0	19.1	20.0
3	19.9	20.1	19.4
4	18.0	21.8	20.5
5	20.0	19.7	20.0

A 20.59 and 19.21

B 21.13 and 18.67

C 2.54 and 0

D 20.1 and 16.7

E 3.09 and 0