Question

Based on your recommendations, Mr. Miller improved shop operations and successfully reduced the number of customer complaints. To maintain good service, Mr. Miller asked you to keep monitoring the wait times of oil change customers at the shop.

First, you decide to create an x-bar chart to monitor the central tendency (i.e., mean). But you know that we sometimes overlook a problem if we use only an x-bar chart. Therefore, you decide to create an R-chart to monitor the process dispersion (i.e., variance) as well. To create these charts, you start collecting 10 customer wait times every day and record them in Table 1.

Table 1: Customer Wait Time (in minutes) at the Downtown Lube & Oil

	SAMPLE
	Day 1	Day 2	Day 3	Day 4
Wait Time (minutes)	25	28	28	28
	28	33	30	37
	21	24	26	39
	32	27	28	38
	28	37	34	36
	22	29	36	43
	34	29	28	33
	25	30	34	30
	24	27	25	36
	29	33	44	45

1.

Calculate the average of the sample means (x-double-bar). Round your answer to two decimal places.

1. 29.70 minutes
2. 31.08 minutes
3. 32.30 minutes
4. 33.80 minutes
5. 36.50 minutes

2.

Calculate the sample range (R) for Day 1. Don’t round your answer.

1. 11 minutes
2. 12 minutes
3. 13 minutes
4. 14 minutes
5. 15 minutes

3. Calculate the average of the sample ranges (R-bar). Don’t round your answer.

1. 11.5 minutes
2. 12.5 minutes
3. 13.5 minutes
4. 14.5 minutes
5. 15.5 minutes

4.

Calculate the lower control limit for the x-bar chart. Round your answer to the nearest whole number.

1. LCL=20
2. LCL=22
3. LCL=24
4. LCL=26
5. LCL=28

5.

Calculate the upper control limit for the x-bar chart. Round your answer to the nearest whole number.

1. UCL=34
2. UCL=36
3. UCL=38
4. UCL=40
5. UCL=42

6.

Calculate the lower control limit for the R-chart. Round your answer to the nearest whole number.

1. LCL=0
2. LCL=1
3. LCL=2
4. LCL=3
5. LCL=4

7.

Calculate the upper control limit for the R-chart. Round your answer to the nearest whole number.

1. UCL=28
2. UCL=30
3. UCL=32
4. UCL=33
5. UCL=35

8.

Based on the x-bar chart and R-chart, is the process in control? If not, which day(s) is not in control?

1. Yes. The process is in control.
2. No. Day 4 is not in control.
3. No. Day 3 and Day 4 are not in control.
4. No. Day 2, Day 3 and Day 4 are not in control.
5. No. All days are not in control.

Answer 1