Process/Queue Analysis, R-Chart Analysis, X -Chart Analysis, (Calculate)

Section 2. Problems (55 points)
Please show all work for partial credit.
1. (25 points) You manage a service center that provides call center support to a variety of different clients. Your organization tracks call center arrival and service time across individual clients as well as for the whole call center.
a. (3 points) The call center on average receives a call every 2 seconds, what is ƛ (include units)?
b. (3 points) If a call has just been answered, what is the probability another call will arrive within the next 1 minute?
c. (3 points) For the call center, what is the probability of 15 calls being received within the next 30 minutes?
d. (3 points) The call center tracks data for all arrival and service times and recognizes they follow an exponential distribution for both arrival and service variance, normal for this type of operation. The call center typically employees 50 customer service technicians to answer calls. You are an operations consultant engaged to help analyze the call center queueing dynamics. How would you describe this system in Standard Queue Notation?
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e. (3 points) You recognize the call center staff are highly trained and on average resolve a call within 1.5 minutes.
What is μ for this call center (with units)?
f. (3 points) What is the utilization for this call center?
g. (3 points) In your opinion as a consultant, is this utilization figure good or bad? Why?
h. (4 points) The sales department for the call center secures a huge new client, and they estimate a call will now be
received every 1 second (instead of every 2 seconds). Based on your calculation for current utilization, they
propose hiring another 30 customer service technicians to handle the additional volume, assuming average service
time (and thus μ) will remain unchanged. You are asked to analyze their projections and advise if they are
sufficient. What is your recommendation (this should be straightforward and supported with quantitative
analysis)?
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2. (10 points) To progress your analysis of the call center, you decide to collect samples for call times to ensure the
the process is in control. You decide on a sample size of 7, the minimum to ensure a D3 value greater than. The data
collected is as follows:
Call time, sec
Technician Sample 1 Sample 2 Sample 3
Kristen 78 74 101
Julia 91 80 91
Brent 88 80 101
Eric 85 83 95
Morgan 86 91 95
Ashley 87 81 101
Ryan 90 88 102
a. (5 points) Conduct R-chart analysis for this data (including, and the corresponding UCL and LCL.
Based on your findings, is the process variability in control, why or why not (be specific)?
b. (5 points) As a 2nd step, conduct x̄ -chart analysis for this data (including and the corresponding UCL
and LCL). Based on your findings, is processed in control (be specific in stating why or why not!)
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3. (10 points) Moving forward, you decide to help the call center by leading a Six Sigma project to help optimize their
performance. As part of that process, you start data collection after the new technicians have started working. The
the goal is to ensure call service times take an average of 2 minutes and that the process is in control. You collect the
following data:
Sample Size 1,000
Average Call Time (s) 122
Standard Deviation (s) 10
Upper Tolerance (s) 130
a. (4 points) What is the z-value for this data set?
b. (3 points) What percentage of calls take too long? (For this problem, NORMSDIST(Z) calculates the
percentage of call times that occur below the Upper Tolerance level)
c. (3 points) The observed average (122 seconds) is pretty close to the desired average (120 seconds). Based
on your answer to b) above, do you think the process is in good shape or needs significant work? Why?
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4. (20 points) A continuing theme in this course is how Service Operations are unique from those of Manufacturing.
Select 5 ways Service Operations are distinct and give an explanation of how what the effect is or why it is important
to Service Managers. (4 pts per)