Question

A telephone customer service center wants to ensure that the majority of customer calls are answered within a reasonable amount of time. Based on customer feedback, the company has determined that this wait time is between 10 and 45 seconds. A large sample of data points collected reveal an average wait time of 31 seconds with a standard deviation of 4.5 seconds.

Calculate the process capability index AND advise if the process is at an acceptable level for an existing process (defend your answer). Please show all calculations.

Answer 1

average wait time	31	seconds
std dev	4.5	seconds
specification limits= mean(+/-)z*std dev
for 6 sigma chart, z=3
USL=31+3*4.5	44.5	seconds
LSL=31-3*4.5	17.5	seconds
Process Capability Index, Cp = (USL-LSL)/(6*std dev)
	1.00
A process capability index is used to estimate if the process is capable of producing results well between the specification limits.
Higher the capability index, better the process control, but any value >1.33 is considered good for process capability (for two-sided specifications).
A capability index of 1 is a good value, but to get the process at an acceptable level, the system needs more control, hence, either the variation in the wait time values have to be reduced, or the specification limits have to be expanded.

formulae used: