Question

Hour	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6	Sample 7	Sample 8
1	98.2706	98.82376	101.8175	100.1819	102.9594	101.165	95.25957	98.97423
2	100.7166	101.8866	98.56813	98.77126	101.8273	98.20298	101.6975	99.63706
3	98.9922	101.9845	103.7859	97.94211	100.9618	102.5191	97.33631	101.6476
4	103.2479	97.55057	105.5942	99.39358	99.57922	95.39694	96.26237	102.5666
5	100.403	99.99954	100.1254	100.21	93.46717	103.2011	100.1247	101.0385
6	97.26687	101.0598	96.30829	100.2402	98.07447	97.92167	102.4083	104.0686
7	101.2243	98.17466	99.66765	101.106	100.2891	99.37136	99.33442	95.24574
8	99.77304	95.70568	99.5615	99.89883	100.3117	104.133	100.4445	96.28674
9	98.51186	99.89239	101.3762	99.76019	101.5632	97.32041	99.62125	101.4166

a. Construct an R-chart for this process.

b. Does the process appear to be in control? Why or why not?

c. Why must the R chart be read before the x-chart?

Answer 1

Solution :

Now here there are 8 samples each sample has size 9 (Subgroup size)

A) For R chart

1)We find from  the each Sample (Max - Min) in each sample

2) Average Of all this 8 points is Which is also Central line (CL) in R chart .

3) Find LCL = D3 & UCL = D4 ,   Where D3 & D4 is from table.

Calculation:

	Hour	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6	Sample 7	Sample 8
	1	98.2706	98.82376	101.8175	100.1819	102.9594	101.165	95.25957	98.97423
	2	100.7166	101.8866	98.56813	98.77126	101.8273	98.20298	101.6975	99.63706
	3	98.9922	101.9845	103.7859	97.94211	100.9618	102.5191	97.33631	101.6476
	4	103.2479	97.55057	105.5942	99.39358	99.57922	95.39694	96.26237	102.5666
	5	100.403	99.99954	100.1254	100.21	93.46717	103.2011	100.1247	101.0385
	6	97.26687	101.0598	96.30829	100.2402	98.07447	97.92167	102.4083	104.0686
	7	101.2243	98.17466	99.66765	101.106	100.2891	99.37136	99.33442	95.24574
	8	99.77304	95.70568	99.5615	99.89883	100.3117	104.133	100.4445	96.28674
	9	98.51186	99.89239	101.3762	99.76019	101.5632	97.32041	99.62125	101.4166
	MAX - MIN	5.98103	6.27882	9.28591	3.16389	9.49223	8.73606	7.14873	8.82286
CL	Rbar	7.363691
LCL		1.354919
UCL		13.37246

Now control Chart is :

R- chart ,X- Chart Constant value Table is:

B) The Process appears to be in control because all the Values of Range observation lies in between the Lines LCL & UCL This lines are the Control limits.

if any point is go outside of the control limit then process is out of control.

C)

R chart is read before the X chart because process for continuous variables can go out of control in one of the two ways. One way is that the process can drift from the standard mean value. At that situation we use X - chart to check for this behaviour. The other way process can get out of control is that the variable of a process can exceed specifications. The R - chart checks for this.

Also;

In the X- chart for finding the Control limits We need the Value CL of R-chart

Control limits of R - chart :

And

So here R must need.