Dumplings -To-Go (DTG)provides take-out dumplings and noodle dishes to customers at its chain of drive-through restaurants.The target for a customer's waiting time is 3.0 minutes +/- 1 minute.Each month,one of the managers observes the drive-through process and collects a sample of 4 waiting times a day over a 6 day period.The data for one restaurant appears below.Calculate the process capability ratio.Is this restaurant capable of meeting DTG standards?
A)yes
B)no
C)Cannot be determined from the above information

Question

Dumplings -To-Go (DTG)provides take-out dumplings and noodle dishes to customers at its chain of drive-through restaurants.The target for a customer's waiting time is 3.0 minutes +/- 1 minute.Each month,one of the managers observes the drive-through process and collects a sample of 4 waiting times a day over a 6 day period.The data for one restaurant appears below.Calculate the process capability ratio.Is this restaurant capable of meeting DTG standards? 
A)yes 
B)no 
C)Cannot be determined from the above information

Quizplus · Accepted Answer

To calculate the process capability ratio, we need to first determine the process mean and standard deviation.

Process Mean (X-bar) = (3.5+4.0+3.5+3.0+4.5+4.0)/6 = 3.83 minutes

Process Standard Deviation (s) = √[(Σ(X-X-bar)²)/(N-1)] = √[(0.67²+0.17²+0.67²+0²+1.67²+1.17²)/(6-1)] = 0.78 minutes

Process Capability Ratio (Cp) = (USL - LSL) / (6σ) = (4 - 3) / (6 x 0.78) = 0.85

Since the process capability ratio is less than 1, this implies that the process has a high probability of producing defects and is not capable of meeting DTG standards. Therefore, the correct answer is B (no).

Dumplings -To-Go (DTG)provides Take-Out Dumplings and Noodle Dishes to Customers