Question

The management of the Diners Delight restaurant chain is in the process of establishing quality control charts for the time that its service people give to each customer. Management thinks the length of time that each customer is given should remain within certain limits to enhance service quality. For simplicity, the data from three samples are displayed below. In each sample, five service people were randomly selected, and the customer service they provided was observed. The time (in seconds) to service each customer was recorded as below.

Service person	Sample 1 (morning)	Sample 2 (afternoon)	Sample 3 (evening)
#1	202	196	201
#2	204	206	210
#3	208	208	211
#4	195	202	206
#5	200	203	202

What is the upper control limit of the X-bar chart for a 99.73% (3-sigma) quality limit?

Numbers only, keep 3-decimal if not exact, either round up or down is ok.

Answer 1

Grand mean = ( 199.6666667 + 206.6666667 + 209 + 201 + 201.6666667 ) 5

Grand mean = 203.6

Grand range = ( 6 + 6 + 3 + 11 + 3 ) 5

= 5.8

Upper control limit of the X-bar chart = + A₂

Upper control limit of the X-bar chart = 203.6 + 1.023 5.8

Upper control limit of the X-bar chart = 209.533

-----------------------------------------------------------------------------------------------

The value of A₂ is obtained using the the control chart table for a subgroup size of 3. A₂ = 1.023