Management Chapter 17 Homework The case describes an automobile tire manufacturer that uses statistical process control to monitor the product quality of the tires the produce

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by hand using the formulas in the chapter. If any special causes are identified, remove

them from the data and construct a revised control chart.

Use Equations 17.4 -= 17.6.

On average, this insurance claim process generates 2.4% errors. Portions of the Excel

template are shown below:

p-Chart Copyrigh

This spreadsheet is designed for up to 50 samples. Enter data only in yellow cells. Not for c

Some resizing or rescaling of the chart may be needed.

Sample size 80

Number of samples 25

Average (p-bar) 0.024

Number Fraction Standard

Sample Nonconforming Nonconforming Deviation LCLp CL UCLp

12 0.0250 0.017111 0 0.024 0.0753

21 0.0125 0.017111 0 0.024 0.0753

30 0.0000 0.017111 0 0.024 0.0753

43 0.0375 0.017111 0 0.024 0.0753

13 10 0.1250 0.017111 0 0.024 0.0753

14 2 0.0250 0.017111 0 0.024 0.0753

15 1 0.0125 0.017111 0 0.024 0.0753

16 4 0.0500 0.017111 0 0.024 0.0753

17 0 0.0000 0.017111 0 0.024 0.0753

18 3 0.0375 0.017111 0 0.024 0.0753

Based on the control limits, we would expect a maximum of about 7.5% errors. Samples

13 and 19 are outside of the control limits and are most likely due to a special cause. It is

assumed that an improvement team was set up to investigate samples 13 and 19 and a

0.1000

0.1200

0.1400

Attribute (p) Chart Fraction

nonconforming

Instructors might also show students that they can simply delete the data for samples 13

and 19 in column B of the template) – and change the number of samples from 25 to 23 –

to display the revised chart, connecting samples 12 and 14, and 18 and 20 automatically in

the chart.

p-Chart Copyrigh

This spreadsheet is designed for up to 50 samples. Enter data only in yellow cells. Not for c

Some resizing or rescaling of the chart may be needed.

Sample size 80

Number of samples 23

Average (p-bar) 0.016304348

Number Fraction Standard

Sample Nonconforming Nonconforming Deviation LCLp CL UCLp

12 0.0250 0.014159 0 0.016 0.0588

21 0.0125 0.014159 0 0.016 0.0588

30 0.0000 0.014159 0 0.016 0.0588

43 0.0375 0.014159 0 0.016 0.0588

13 2 0.0250 0.014159 0 0.016 0.0588

14 1 0.0125 0.014159 0 0.016 0.0588

15 4 0.0500 0.014159 0 0.016 0.0588

16 0 0.0000 0.014159 0 0.016 0.0588

17 3 0.0375 0.014159 0 0.016 0.0588

0.0400

0.0500

0.0600

0.0700

Attribute (p) Chart Fraction

nonconforming

43. An Internet service provider (ISP) measures the proportion of peak period time when a

customer is likely to receive busy signals. Data on the number of busy signals received from

samples of 500 calls over a 30-day period can be found in the worksheet C17 Excel P43

Data in MindTap. Construct and interpret a p-chart for these data.

Portions of the Excel template are shown below:

The process appears to have shifted considerably around sample 16. This might represent

a technology issue or a staffing issue (perhaps several customer service representatives

44. Data showing the number of errors per thousand lines of code for a software development

project are given in the worksheet C17 Excel P44 Data in MindTap. Construct a c-chart and

interpret the results.

Portions of the Excel template c-Chart are shown next.

On average, the process generates c-bar = 14.65 errors per 1,000 lines of code.

Statistically, the number of errors should range from 3.1 to 26.13. Sample #7 exceeds the

upper control limit, so this process is not in statistical control. The reason for the high

value for sample #7 should be investigated. In any event, having this many errors in

software coding is probably not acceptable, and the project manager should take steps to

understand the root causes and reduce the incidence of errors.

45. A mail-order prescription drug vendor measured the number of errors per standard order

Note that in calculating the lower control limit using the formula in the book, the value

turns out negative, so 0 is used.

The process appears to be in control; however, an order with 3 errors or more should

trigger investigation. Nevertheless, every effort should be made to reduce the number of

errors to zero, especially considering that they may affect patient’s health. Also, point out

46. Use the data from the machining process in Excel problem 40 (worksheet C17 Excel P40

Data in MindTap) to calculate Cp , Cpl , Cpu, and Cpk , assuming that the specifications are

3.75 ± 1.25. Interpret the results for the manager of this process.

Using the Process Capability Excel template, we obtain the following:

The overall capability indexes is marginal, but the lower index suggests that there is a

problem meeting the lower specification.

47. The worksheet C17 Excel P47 Data in MindTap provides sample times in hours for

processing and shipping orders from a web-based retailer. The retailer advertises that

orders are shipped within four hours of receipt. What is the capability of the process to

achieve this standard? Explain your conclusions.

Teaching Note: Eckhardt Hospital

Overview

The Joint Commission on Accreditation of Healthcare Organizations (JCAHO) monitors and

evaluates health care providers according to strict standards and guidelines. Improvement in

Case Questions for Discussion:

1. Using the data in Exhibit 17.8, what is the average percentage of infections?

The average percentage of infections is the total number of infections divided by the total

number of surgeries = 55/[(36)(200)] = 0.0076 or 0.76 percent. This is also calculated in the

template.

2. Construct an appropriate control chart, compute the upper and lower control limits, plot

the data on the control chart, and determine if the process is in statistical control. Based

on your analysis, what action, if any, should management take?

A p-chart is the correct chart to use.

Although month 12 has a higher rate of infections, none of the data points fall above the upper

control limit, indicating that the variation each month is due purely to chance and that the

3. What threshold for evaluation should management use to monitor future samples as a

basis for taking action?

The upper control limit is 0.026 or 2.6%. The upper control limit would be a logical TFE to use,

Teaching Note: Goodman Tire and Rubber Company

Overview

The case describes an automobile tire manufacturer that uses statistical process control to

monitor the product quality of the tires the produce. The case data are available in MindTap.

The case asks students to examine the distribution of the data (for example, how does it

compare to the specification limit cited in the case?).

Some students might address normality of the data. The histogram is clearly not normal. This

as a lognormal distribution, individual charts, chi-square goodness of fit tests, assume gamma

or Weibull distributions, and multivariate control charts. You might simply tell your students

that there are statistical process control methods for non-normal distributions but they require

advanced knowledge to understand them, and may or may not provide better insights than we

produce in this SPC analysis.

Case Questions for Discussion:

1. Draw a histogram of these data. What can you conclude (if anything) about the

distribution of the tread wear?

Using the Statistical Analysis template:

The distribution of the data does not appear to be normal; it is somewhat symmetric, but the

tails do not die off as a normal distribution would. However, normality is not a requisite for

using control charts, although it can improve the results. This, however, is beyond the scope of

the text.

2. Construct x-bar and R-charts for these data. Is the production process in control?

Not for commercial use.

This spreadsheet is designed for up to 50 samples, each of a constant sample size from 2 to 10. Enter data only in yellow cells

Charts are displayed below the calculations. Some resizing or rescaling of the charts may be required.

Number of samples (<= 50) 25

Sample size (2 – 10) 3

Grand Average 28.43 A2 D3 D4 d2

Average Range 11.84 1.023 0 2.574 1.693

DATA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

131 26 25 17 38 41 21 32 41 29 26 23 17 43 18 30 28 40 18 22 18 24 27 39 17

242 18 30 25 29 42 17 26 34 17 31 19 24 35 25 42 36 29 29 34 24 28 32 26 32

328 35 34 21 35 36 29 28 33 30 40 25 32 17 29 31 32 31 28 26 30 19 20 19 27

R-Chart Ranges

Lower control limit

Upper control limit

Center line

The R-chart is in statistical process control since all points fall within the control limits. There is

no discernable pattern in the plot of sample means for the R-chart.

The x-bar chart might appear to be in statistical process control. However, there appears to be

a downward shift since samples #19 to #25 are all below the centerline (x-bar) and the

3. Provide two examples of each of the four major categories of quality costs applicable to

this situation (i.e., prevention, appraisal, internal and external failure costs).

Prevention – frequent calibration of tire making equipment, checking raw material quality

levels, frequent training equipment operators, quality design planning, training equipment

4. What are the process capability indexes for this process to meet design specifications?

What do you recommend?

Using the Process Capability template, we have

Cp = (34-22)/43.51 = 0.276 which is much less than 1.0. That is, the process is not capable and

tires will not all meet the 60-month lifetime! This may result in excessive warranty (external

failure) costs. A Kaizen event should take place to identify the root cause and fix it. The root

cause could be the raw materials from the supplier, changes in production procedures or

Therefore, the process is slightly off center, closer to the USL, and not capable.

This template is designed to handle up to 150 observations. Enter data only in yellow cells.

Not for commercial use.

Nominal specification 28

Upper specification limit 34

Lower specification limit 22

DATA 1 2 3 4 5 6 7 8 9 10 11 12 13

131 26 25 17 38 41 21 32 41 29 26 23 17

242 18 30 25 29 42 17 26 34 17 31 19 24

328 35 34 21 35 36 29 28 33 30 40 25 32

Integrative Case – Hudson Jewelers

A complete teaching note for all chapters is available in the Instructor Resources online.

Instructors should read the entire case and most of the case assignments at the end of each

chapter. Then decide if you want to assign all or part of the case questions.

Chapter 17 Case Questions for Discussion:

1. Research and acquire the criteria for diamond appraisals and critique these criteria in

terms of objectivity, measurement, and overall accuracy. Are diamond quality criteria as

specific and measurable as for manufactured parts? Explain.

Criteria:

Color

Diamond color can range from steel gray, white, blue, orange, red, green, pink, purple, brown,

Carat

Each carat weight is subdivided into 100 points. For example, a diamond that is 0.75 carats is a

Cut

Possible diamond cuts or shapes include princess (square), cushion (oval), heart, pear, Radiant

and Asscher (hexagons), emerald (rectangle), and oval. In addition, each part of the diamond

Clarity

The grading system includes these clarity categories:

Flawless (FL) – no external blemishes or internal inclusions visible using a 10x magnification.

Slight Included – (SI1 and SI2) – diamond has noticeable inclusions that are easy to see using

10x magnification.

Included – (I1, I2, and I3) – diamond has obvious inclusions that are clearly visible using 10x or

visible without magnification or have inclusions that threaten the long term viability of the

stone such as possible fractures.

Measurability:

Diamond quality criteria are specific with criteria like cut and carat weight being very

measurable. However, color and clarity are more human judgment criteria. Only with multiple

2. Develop p-charts for the diamond blemish and inclusion data found in the worksheet

Hudson Jeweler Blemish and Inclusion Data in MindTap, which documents the quality of

the diamonds on “clarity and defects” coming from two different diamond mines

(suppliers) – one in Asia and one in Africa. What do you conclude?

You might want to go over the diamond criteria for “Clarity” defined in the previous question.

Assuming the same diamond experts did the clarity grading for these two different mines, the

conclusion is the Africa diamonds in this carat range are of higher quality.

For Asia Supplier:

The p-chart for the Asia Supplier is below with p-bar = 0.616 and the control chart is fairly

random with samples 13 and 20 outside the upper control limit. And samples 14 to 18 are all

For the African supplier:

The p-chart for the African Supplier is with p-bar = 0.539 and the control chart is random with

no sample outside the control limits. Technically, this p-chart is in statistical process control.

One can conclude that for this sampling plan, assuming they were administered the same way,

the African diamonds in this carat range of 1.0 to 1.5 carats are better (clearer) diamonds than