## Quality Management – Sampling and Tolerance Acceptance

01 Apr

1
MBA Operations Management Workshop
Instructor: Roman Wong, PhD, CPA, CVA
Quality Management – Sampling and Tolerance Acceptance
1. The temperature control of the dying process of the ABC Textile Company has to be
controlled. The target temperature is 140 degrees F. A +/- 5 degrees can be tolerated.
The company’s goal is to have 99.7% of all dyeing processes be within the acceptable
temperature range. The process statistics show that standard deviation of the dye
process temperature to be 2.14 degrees. Evaluate the process capability.
2. The temperature control of the dying process of the ABC Textile Company has to be
controlled. The target temperature is 140 degrees F. A +/- 5 degrees can be tolerated.
The company’s goal is to have 99.7% of all dying processes be within the acceptable
temperature range. The process statistics show that standard deviation of the dye
process temperature to be 2.14 degrees and the mean temperature in reality 142
degrees instead of 140. Evaluate the process capability provided that the tolerance of
the temperature requirement is non-bias (i.e. below specification is just as bad as
above). What if the process is more tolerable for lower-than-specification
temperature than otherwise? Would your conclusion be different? Show your
evaluation based on the reliance of the process capability index.
3. BHC produces bags of cement. The stated weight for a bag of cement is 100 lbs.
Customers will accept an occasional bag weighing as little as 98 lbs. as long as the
average weight is at least 100 lbs. At the same time, BHC doesn’t want to give away
cement, so it has set an upper tolerance limit of close to 102 lbs. Such setting results
in the current filling process having an actual process mean of 101 lbs. and a standard
deviation of 0.7 lb.
a. Does the company have the capability of meeting the tolerance limits more
than 99.7% of the time? Show your computations and briefly explain your
calculated results.
b. Now suppose BHC re-centers the manufacturing process so that the process
mean is exactly 100 lbs, while the standard deviation remains the same.
Calculate the process capability ratio. Is the process still capable of meeting
the tolerance limits more than 99.7% of the time? Show your calculation and
Project Management – Program Evaluation and Review Technique (PERT)
1. What is the earliest that activity D can start if A is 3
days, B is 5, days C is 7 days, and D is 4 days long?
2. What is the latest that activity B can start if A is 3
days, B is 5, days C is 7 days, and D is 4 days long?
3. By which time can activity D be completed if A is 3
days, B is 5, days C is 7 days, and D is 4 days long?

2
4. The project has activity lengths in days, precedence and crash costs as shown in the
table below. Evaluate the project by mapping out the network, computing the ES/EF
and LS/LF times for all activities, identifying the critical path, and the slack that each
activity may have. What is the cheapest completion cost for the project if the
contractor must complete all work in 45 days?

 Activity Duration (Days) Precedence Max # Days of Reduction Crash Cost per Day A 10 None 2 \$250 B 16 A 4 \$400 C 12 A 3 \$100 D 17 B, C 1 \$320 E 14 B 1 \$300 F 6 D, E 2 \$350

Inventory Management
1. Ollah’s Organic Pet Shop sells about 4,000 bags of free-range dog biscuits every
year. The fixed ordering cost is \$15, and the cost of holding a bag in inventory for a
year is \$2. What is the economic order quantity for the biscuits?
Suppose Ollah decides to order 200 bags at a time while keeping a safety stock at the
level of 100 units. What would the total ordering and holding costs for the year be?
2. Pam runs an e-Bay business for gym equipment. Annual demand for the TricoFlexers
is 16,000. Pam is currently paying \$30 per unit. The annual holding cost per unit is
15% of its cost, and the cost to place an order is \$500. In order to save some ordering
cost, Pam currently orders 4,000 units each time. What is the total inventory cost to
Pam?
Pam’s friend, who is an MBA, suggests her to consider using the EOQ as the ordering
size. What is the economic order quantity for Pam based on the current demand and
costs? Will changing from the current order size to EOQ save her some inventory
expenses?
Assuming the same holding and ordering costs, suppose demand is now changed to
32,000. Will the EOQ be different? Is it going to be double? Why or why not?
The manufacturer of TricoFlexers has agreed to offer Pam a price discount of 1% if
she buys 8,000 units each time. Assuming annual demand is still 16,000 units and
that the holding cost per unit remains the same as normal, should Pam order based on
the discount-order size?

3
Waiting-Line Questions
1. Wong runs a small hot dog stand in downtown Miami. On average, it takes Wong 2
minutes to serve a hot dog. During lunchtime, customers randomly arrive at the rate
of one per five minutes.
Required:
a. On average, how many customers are in the hot dog stand and how many are waiting to
be served?
b. On average, how much time, in minutes, does a customer spend at the hot dog stand?
c. On average, how much time, in minutes, does a customer have to wait for service?
2. The following arrival and service data were taken from one of the groups’ class
projects. Table 1 is sample arrival data capturing the number of cars arrived per each
5-minute interval. Table 2 is sample service data capturing the number of seconds a
service station spent on servicing each car.

 Table 1 Table 2 Interval of 5 min # of Cars Service # Service Time (sec) 1 5 1 56 2 4 2 67 3 3 3 59 4 5 4 32 5 3 5 35 6 5 6 37 7 4 7 6 8 1 8 4 9 1 9 64 10 2 10 55

Based on the sample data provided in Table 1 and Table 2, complete the ‘Answer’
column of the following:

 Supporting Work Answer Utilization ρ Arrival Rate λ Service Rate µ Average Customers in System Cs Average Customers in Waiting Cw Average Time Spent in System (in seconds) Average Time Spent in Waiting (in seconds)