Question

PLEASE ANSWER IN 45 MINUTES

QC.56 Thirst, an IBC company, wants to serve their customers within a consistent, reasonable amount of time. On each day during their second week of business (5 days total) they randomly timed the wait time of 7 different customers (per day). The table below contains the average wait time (in seconds) for each of these days as well as the minimum and maximum wait times for each day:

Day	Avg Wait	Min Wait	Max Wait
1	79	74	85
2	74	67	79
3	71	63	76
4	72	64	81
5	74	70	81

Using this information (above) and the table at the top of this problem (Factors for Control Charts), set up an x-bar chart and an r-chart.
Hint: Answer the following questions to help you gather the necessary data to complete these problems.

• Is a target wait time given? If not, then you should calculate the sample mean (average of the average times) and use that as the target wait time.
• Do you know what the range is for the wait times each day (the difference between the minimum and maximum times)? How about the average range across all days?
  

What is the upper control limit for the x-bar chart? (Display your answer to two decimal places.
   

What is the lower control limit for the x-bar chart? (Display your answer to two decimal places.)

   

What is the upper control limit for the r-chart? (Display your answer to two decimal places.)
   ​

What is the lower control limit for the r-chart? (Display your answer to two decimal places.)
   ​

Answer 1

# SAMPLE	AVERAGE	RANGE
1	79	11
2	74	12
3	71	13
4	72	17
5	74	11
AVERAGE	74	12.8

X-BAR = AVERAGE OF X VALUES = 74

R-BAR = AVERAGE OF R VALUES = 12.8

A2 VALUE CORRESPONDING TO N = 7 = 0.419

D3 & D4 VALUES CORRESPONDING TO N = 7, D3 = 0.076 & D4 = 1.924

FOR X

UCL = XBAR + (A2 * RBAR) = 74 + (0.419 * 12.8) = 79.36

LCL = XBAR - (A2 * RBAR) = 74 - (0.419 * 12.8) = 68.64

FOR R

UCL = RBAR * D4 = 12.8 * 1.924 = 24.63

LCL = RBAR * D3 = 12.8 * 0.076 = 0.97

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