Question

Step 3: Monitoring the process 5. Subsequently, samples of 4 bottles were taken from filling line. The fillings and the following results were obtained. Use these data to check for process control. Is the process in control? Why? were measured Hypothesis conclusions Decision Units Sample stats Sample 1 2 3 4 Decision Decision about X-bar about the about R chart chart (in control or process out of control)(in control or out of control) (in control or out of control) R X-bar 1 12.08 12.00 11.97 12.1 12.038 2 11.94 11.96 11.978 11.91 12.1 3 11.7 12.10 12.10 12.0 11.968 Conoonto

Answer 1

Given :n=4(the subgroup sample size)

Xbar of sample 1 =AVERAGE(C4:F4)=12.038

(Drag this cell formula down for rest of the samples)

Range of sample 1 =MAX(C4:F4)-MIN(C4:F4)=0.13

(Drag this cell formula down for rest of the samples)

X-double bar=AVERAGE(G4:G6)=12.00

Rbar=AVERAGE(H4:H6)=0.24

In X chart ,

UCLx=X-bar bar +A2*Rbar=H9+H11*H10=12.2

LCLx=X-bar bar -A2*Rbar=H9-H11*H10=11.8

In R chart,

UCLr=D4 *R-bar=2.282*0.24=0.55

LCLr=D3*R-bar=0*0.24=0

Based on X-bar chart ,all the sample means(Xbar values) are within the control limits.Hence,the process is in control.

Based on R chart ,all the sample ranges are within the control limits.Hence,the process is in control.

Therefore,the process is in control.

Calculations are as shown below:

fo H9+H11*H10 C12 A B C E E G H J K 1 Hypothesis conclusions Sample stats 2 Units Decision Decision Decision about Xbar about R about the chart Sample Number Xbar chart 3 1 2 3 4. Range process 4 12.038 1 12 11.97 12.1 12.08 0.13 0.19 In-control In-control In-control 11.91 5 11.94 12.1 11.96 11.978 11.975 6 12.1 11.7 12 12.1 0.40 8 X-bar bar 9 12.00 R-bar 10 0.24 11 A2 0.729 12 UCLX 12.2 D4 2.282 13 11.8 D3 C 14 UCLR 15 0.55 16 LCLR 0 st