Question

1. The net weight (in oz.) of a dry bleach product is to be monitored by X and R and X and S control charts using a sample size of n = 5. Data for 20 preliminary samples are shown below.

   Subgroup Number	X1	X2	X3	X4	X5
   1	12	10	13	15	12
   2	10	7	16	14	8
   3	11	12	10	16	9
   4	8	9	15	13	7
   5	9	10	14	13	16
   6	12	11	10	10	13
   7	16	10	14	9	12
   8	14	9	10	14	13
   9	9	10	13	12	10
   10	15	16	10	13	12
   11	10	12	14	16	11
   12	16	13	9	11	8
   13	16	11	13	15	10
   14	15	13	10	12	9
   15	12	14	8	16	11
   16	15	13	10	14	12
   17	9	11	12	10	14
   18	15	12	10	11	13
   19	14	16	9	12	10
   20	13	10	12	15	9

   Determine the trial central line and control limits for the X and R (24 points).

   UCLX=

   CLX=

   LCLX=

   UCLR=

   CLR=

   LCLR=

Answer 1

The control limits are:

Sample size	5
Number of samples	20
	Mean	Range
Upper Control Limit, UCL	15.47	13.00
Center	11.92	6.15
Lower Control Limit, LCL	8.37	0.00

The calculations are:

Subgroup Number	X1	X2	X3	X4	X5	Xbar	R
1	12	10	13	15	12	12.4	5
2	10	7	16	14	8	11	9
3	11	12	10	16	9	11.6	7
4	8	9	15	13	7	10.4	8
5	9	10	14	13	16	12.4	7
6	12	11	10	10	13	11.2	3
7	16	10	14	9	12	12.2	7
8	14	9	10	14	13	12	5
9	9	10	13	12	10	10.8	4
10	15	16	10	13	12	13.2	6
11	10	12	14	16	11	12.6	6
12	16	13	9	11	8	11.4	8
13	16	11	13	15	10	13	6
14	15	13	10	12	9	11.8	6
15	12	14	8	16	11	12.2	8
16	15	13	10	14	12	12.8	5
17	9	11	12	10	14	11.2	5
18	15	12	10	11	13	12.2	5
19	14	16	9	12	10	12.2	7
20	13	10	12	15	9	11.8	6
					Average	11.92	6.15
			A2	0.577
			A3	1.427
			D3	0
			D4	0.114
		Sample size	5
		Number of samples	20
			Mean	Range
		Upper Control Limit, UCL	15.47	13.00
		Center	11.92	6.15
		Lower Control Limit, LCL	8.37	0.00