SOLUTIONS TO PROBLEMS
3
The Wall Street Journal reported on February 15, 2000, that about 750,000
airplane components are manufactured, machined, or assembled for Boeing
Co. by workers from the Seattle Lighthouse for the Blind. A Boeing
spokeswoman noted that the parts have an “exceptionally low” rejection rate
of one per thousand. At what sigma level is this process operating?
ANS. There is no indication of how many opportunities for defects there are
per component, so we will have to assume that the defect rate is 1 per 1000
units produced. Therefore, only 750 defective items (0.001 X 750,000) were
produced. To calculate dpmo, we see:
dpmo = (1/1000) X 1,000,000 = 1000, which is slightly better than 4.5 sigma
with off centering of 1.5 sigma.
4. Over the last year 1,054 injections were administered at the Mustard clinic.
Quality is measured by the proper amount of dosage as well as the correct
drug. In two instances, the incorrect amount was given, and in one case, the
wrong drug was given. At what sigma level is Mustard’s process?
ANS We use 3/1054 to get the number of defects per unit (DPU’s). However,
there are 2 opportunities per injection (wrong drug, wrong dosage) to make an
error. They must be considered, in order to calculate dpmo.
dpmo = (3/1054) X 1,000,000/2 = 1423.1, which is slightly less than 4.5 sigma
with off centering of 1.5 sigma.
5.
Outsel Microprocessor Corporation (OMC) sells 1500 specialized computer
processing chips each month at a price of $1200 each.
Variable costs amount
to $1,000,000, and fixed costs are $400,000. Currently the company has a
defect rate of 8 percent (which are chips returned by customers, scrapped by
OMC, and replaced). Note that the variable costs include the cost of producing
the defective chips.
a. What is the hidden cost to the company of making this rate of defectives
instead of 1500 good chips each month?
b. Suppose a Six Sigma effort can reduce the defects to a six sigma level
(assume for simplicity that the defective rate is essentially zero). What is the
impact on profitability?
ANS. In order to produce and sell 1,500 good computer chips, OMC must
start 1,500/0.92 = 1,631 chips into production. However, since the variable
cost of $1,000,000 includes the cost of making scrap, the unit variable cost is
therefore not $1,000,000/ 1,500 = $666.67 but $1,000,000/1,631 = $613.12.
Thus the price paid for poor quality, sometimes called the hidden factory, is
131 x $613.12 = $80,319. This additional cost is incurred to make useless
products that can’t be sold.
If a quality improvement initiative achieves a six sigma defect level, the
defective rate is essentially zero. This will remove the variable cost of making
the 131 defective units. The table below shows that the $80,319 poor quality
cost is eliminated from the variable costs, and the saved money trickles falls to
the bottom line to increase profits. Thus, the profit increased to $480,319. The
8% reduction in operational costs produced a 20% increase in profit ($80,319/
$400,000).
Monthly Baseline
Monthly Six Sigma Result
Sales
1500 X $1200.00 =
1800000
Sales
1500 X $1200.00
1631 X $ 613.12 =
1000000
Variable Cost
1500 X $ 613.12 =
=1800000
Variable Cost
919682
Contribution margin
800000
Contribution margin
880319
Fixed cost
400000
Fixed cost
400000
Net Profit
480319
Net Profit
Profit margin
400000
0.222
Profit margin
ANSWERS TO CASE QUESTIONS
II. The PIVOT Initiative at Midwest Bank – Part II - The MAIC Process
1. It appeared fairly difficult to find the true “root causes” of the problem. This
was illustrated by the fact that manual strapping errors were not initially found
to be a significant problem. Also, it was necessary to prepare over 100
different graphical analyses before patterns could begin to be found. It is likely
0.267
that the “tribal knowledge” that everyone believed to be true, had flaws which
temporarily sidetracked the investigation.
2. Data gathering and analysis should have been (and probably was) used to
prove the feasibility of each of the solutions selected for implementation. The
most expensive solution was, no doubt, the purchase of the strapping machine.
Cost-benefit and/or return on investment analysis should be made. The
customer charge for incorrect deposits was also one that required analysis of
error patterns and possibly a customer survey to determine the impact of
implementing the charge. Eliminating double keying should be reasonably
easy to test, since a pilot operation could be set up in parallel with the current
operations. The vacation scheduling policy change could be tested using both
an employee survey and a pilot test. The dollar loss corrective action should
also be subjected to cost-benefit analysis.
3. The two most difficult areas in which to “hold the gains” would probably be in
the personnel areas. Thus the dollar loss corrective action would be difficult to
administer and could cost both supervisors and employees a great deal of
discomfort and uncertainty. Also, while not as uncomfortable, the vacation
policy schedule change could be irritating to employees and provide
temptations for supervisors to make numerous exceptions.