Chapter 9 – Instructor Reserve Problem Solutions
1. Ultraprecision Corp. has historically had processes which operate above the five sigma
level. They have a new process on which they are about to start production. If the
specification for a critical part produced by the process is 3.5 cm ± 0.10 and the standard
deviation for the process is 0.019, at what sigma level is this process operating?
Answer
The specification limits for the process are LSL = 3.40 and USL = 3.60 and if the process
standard deviation is 0.019, then using equation (9.1), we get:
2. Nodroptcalz Cellphone Co. advertises that 99% of their customer’s calls are completed
without interruption. How many dpmo does this claim represent? At what sigma level is
this process operating, assuming a 1.5 sigma offset?
Answer
The defect rate is 1.0 – 0.99 = 0.01. Thus, 0.01 X 1,000,000 = 10,000 dpmo. Using the
3. Jack Frost has used his belt-driven, hand-guided snowblower to clear his driveway for
several winters. Due to a knee replacement, he can’t do the work this winter. He wants to
make a flowchart to assist his 15-year old son in knowing what steps to follow when he
takes over the job. Assume that the blower is stored in the garage. Some of the steps
would include getting it out of the garage, blowing the snow off the driveway, and
putting it back in the garage. Are there other steps that should be included, in order to
have a more complete flowchart? Construct the flowchart, using Excel, or other
appropriate software having drawing tools.
Answer
The flowchart for setting up, operating, and putting away the snowblower is shown below.
4. The times required to assemble a common circuit board at Circuitus Corp. were measured. The
production manager thought that the assembly times increased as the day progressed, due to
worker fatigue. A typical worker was chosen and three assembly times were taken and
averaged for each hour of the workday over a period of 5 workdays. These averages are
provided in the worksheet Prob. 9-4. Construct a histogram and a scatter diagram of the data.
What suggestions would you give the production manager?
Answer
Interpretation of the data is not completely clear. However, the histogram and scatter diagram
do provide some interesting insights.
5. A kiln at Suither Pottery was thought to be unstable, due to the number of defective items that were
being experienced. To test this theory, the temperature was measured every hour over a 36 hour cycle.
The temperature range was required to be 1180 ± 20 deg. C. The results can be found in the
worksheet Prob. 9-5. Construct a scatter diagram for these data. What conclusions can you reach?
Answer
The scatter diagram, shown below, indicates that there is a decline in the mean, starting around the
0
2
4
6
8
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90
Frequency
Cell Upper Limit
Histogram
6. Weights of containers filled with a powdered dietary supplement made by WeightBgone were
measured by taking samples for 30 days consisting of 4 containers, each. The data found in the
worksheet Prob. 9-6 were gathered by a quality analyst. The containers were designed to be filled
with 400 ± 20 grams. Construct a histogram of the data. What can you observe about the shape of
the distribution? What would you recommend to the production manager based on your analysis?
Construct a control chart for the data. What additional information does it provide?
Answer
The histogram, below, shows a distribution which is somewhat skewed to the left. However, the
X-bar and R chart are even more revealing. They reinforce what is seen in the histogram.
Histogram
X-bar Chart Averages
Lower control limit
Upper control limit
35
40
45
R-Chart Ranges
Lower control limit
Upper control limit
Center line
7. The DOT.COM Apparel Company analyzed customer complaint data which revealed
errors in five categories, such as billing, shipping, etc. Data can be found in the
worksheet Prob. 9-7. Construct a Pareto diagram for these data. What conclusions can
you reach?
Answer
The Pareto chart for DOT.COM Apparel Company is shown below. See spreadsheet
Prob09-07IR for details)
DOT.COM Apparel Company
Percent
Cumulative %
Frequency
100.00%
120.00%
35.00%
40.00%
45.00%
Pareto Chart for DOT.COM Apparel Company
Percent
Cumulative %
Electronic charge errors
Shipping errors
Billing errors
Delivery errors
Long delays
Total
8. The manager of the RiosDeLibros bookstore is trying to determine whether sales of a new
children’s book are correlated with the dollars being put into local advertising. Weekly book sales
versus advetising dollars are shown in the worksheet Prob. 9-8. Plot a scatter diagram and
compute the correlation using Excel tools. What do your results indicate?
Answer
The scatter diagram shows an approximately linear relationship between sales and
advertising expenses.
1630
1680
Correlating Advertising & Sales