Posted: December 4th, 2014

Machine Production Records

Case: http://www.mhhe.com/business/opsci/bstat/bryantcases/samplecase11.mhtml.

Machine Production Records
Background on Case: http://www.mhhe.com/business/opsci/bstat/bryantcases/samplecase11.mhtml.

Here is the case background (taken almost verbatim from Bryant, P. G., and Smith, M. A. (1998), Practical Data Analysis: Case Studies for Business Statistics (2nd ed.), New York: McGraw Hill):
Helen managed a major manufacturing facility that was devoted largely to producing millions of identical small metallic parts. While the parts produced were intended to be identical, the facility produced them by using hundreds of presses, of three different types (which we’ll call types 1, 2, and 3). The rated production rates for machine types 1, 2, and 3 were 700, 200, and 155 parts per minute, respectively, but actual production rates varies. Helen felt that factors such as the quality of input material, worn or “changed-out” dyes, and dirty or poorly maintained presses would probably affect production.

The facility had always kept daily production records, but from what Helen could tell, no one had ever consulted them. She thought that in principle she should be able to monitor production rates, identify any machines that seemed to be in need of adjustment, and characterize the amount of down time to be expected. Accordingly she extracted one day’s production records for 116 presses at her facility.

The machines were scheduled for a shift of 7.75 hours each day. The operators recorded the hours of operation manually on clipboards kept near each machine. The actual quantities of parts produced were determined from automatic counters on the machines.

Data File: Econ2100_CaseStudy2Data.xlsx
Column A (OBS) simply indicates the observation number.
Column B (MTYPE) indicates the machine type (1, 2, or 3).
Column C (PROD) indicates the number of parts produced.
Column D (HRSWRK) indicates the hours of production time.
Column E (HRSDOWN) indicates the hours that the press was down, or inoperative, for any reason.

PART 1: Preliminary exploratory data analysis  (10 points)
DUE: Wed/Thur November 19/20
DATA: Econ2100_CaseStudy2Data.xlsx
SUBMIT: (1) Word document with tables and figures and summary.  Hard copy in class. Only thing graded
(2) Electronic word document with tables and figures clearly labelled.  Upload on Canvas
(3) Electronic version of Excel file with tables and figures clearly labelled.  Upload on Canvas

The first step in data analysis is to explore the data by creating various tables and figures and making brief notes about the exploratory data analysis.  This includes:
•    Calculating summary statistics for each variable in your analysis
•    Examining the distribution of each variable by constructing histograms
•    Constructing a frequency table for categorical variable
•    Looking for outliers (min/max seem extreme?). Do there appear to be any outliers?  Are data entered correctly?
•    Creating any additional variables.  Do any variables need to be created?  If so, be sure to calculate summary statistics for it/them
•    Looking for inconsistencies in data. Are the variables consistent with each other?
Create a standalone (ie no need to reference Excel file, only the hard copy will be graded) document containing tables and figures.  Clearly label each table and figure.  Underneath each, include one or more brief bullet points of your findings.
Although this analysis is preliminary, all tables and figures should be in “final report” formatting.  This means, all numbers should be rounded properly, everything should be labelled properly, and all formatting done.

PART 2: Report  (40 points)
DUE: Wed/Thur December 3
DATA: Econ2100_CaseStudy2Data.xlsx
SUBMIT:
(1) Electronic version of report on Canvas; (name file: CaseStudy2_NAME.docx or CaseStudy2Report_NAME.pdf, where you replace NAME with your Last name.)
(2) Hard copy of report at the start of class on the due date

ASSIGNMENT:
As a statistician working for the manufacturing facility involved in the case, prepare a report for Helen. Although it may be informative to look at graphs, present only numerical results as well as your own observations about the data. Specifically:
•    Present appropriate summaries of the day’s production records. Present these descriptive statistics without omitting any outliers.
o    If you believe that the results are influenced by outliers, indicate which observations are outliers and discuss the effects of these outliers on your results.
o    Note, you do not need to include all of the tables from Part 1 of the assignment.  Do not present figures. Choose which statistics are most relevant and how to present them
•    Compare the machines’ production rates with their official ratings. Identify any specific machines or machine types that appear to be performing poorly.
•    For each machine type, test whether the average production differs from the official rating at the 5% level of significance. For this analysis, do not omit any outliers. Do you have to make any assumptions in order to conduct these tests? Are any statistically significant differences large enough to be practically significant?
•    Indicate one potential problem with the data collection. Be specific.
•    Given your findings, advise Helen on how to proceed.

Helen has a conceptual understanding of descriptive statistics and hypothesis testing, but she is very busy. Please limit the report to a maximum of 1.5-2 single-spaced pages. The report should look like something you would submit to a colleague, not like a homework assignment.

See following page for Scoring Rubric (in electronic version)
Scoring Rubric:
Descriptive Statistics
Corrections from Part 1 were made and numbers updated.  Selectively chose key descriptive statistics to include in final report
4 = all errors corrected. Only key statistics included
3 or 2 = some errors remain.  Some key statistics omitted or too many included.
1 = errors remain and/or all tables included in final report.
0 = still use incorrect statistics

The report presents a table with descriptive statistics (mean, median, standard deviation, minimum, and maximum) for the most important variables for each machine type (without omitting outliers). These descriptive statistics are accurate. They are rounded consistently and appropriately. The discussion of outliers is accurate.
6 = all appropriate descriptive statistics are reported accurately; rounding is consistent and appropriate;
the discussion of outliers is brief but accurate
5 or 4 = all appropriate descriptive statistics are reported; all are accurate; there are problems with rounding and/or the discussion of outliers
4 = most descriptive statistics are reported; all of those reported are accurate; rounding is consistent and appropriate
4 = all appropriate descriptive statistics are reported; most are accurate; mistakes are very minor; rounding is consistent and appropriate; the discussion of outliers is brief but accurate
3 or 2 = most descriptive statistics are reported; all of those reported are accurate; there are problems with rounding and/or the discussion of outliers
3 or 2 = all appropriate descriptive statistics are reported; mistakes are major or conceptual; rounding is consistent and appropriate
1 = bona fide attempt but many problems
0 = missing

The report includes a brief discussion of these descriptive statistics. This discussion highlights selected findings rather than mechanically discussing each statistic. As part of this discussion, the report compares the machines’ production rates with their official ratings. In particular, the report compares the mean and median production rates for each machine type to its official rating. It also identifies any particular underperforming machines (only the minimum values are reported in the table so this requires an examination of the raw data).
4 = brief, accurate, relevant, interesting discussion of descriptive statistics; discussion compares the mean and median production rates for each machine type to its official rating; the report accurately identifies underperforming machines
3 = discussion of descriptive statistics is accurate and relevant but uninteresting or mechanical; comparisons to official ratings are appropriate; identification of underperforming machines is appropriate
2 or 1 = there are more serious problem with the discussion
0 = missing

Hypothesis Tests
The report presents a table summarizing the hypothesis tests described in the assignment. This table presents the null and alternative hypotheses, the t statistics, and the p-values. The hypotheses, t statistics, and p-values are accurate. The t statistics and p-values are rounded appropriately and consistently.
WARNING: Accurate results depend on accurate descriptive statistics.
6 = all information is presented; all is accurate; rounding is appropriate and consistent
5 = all information is presented; all is accurate; rounding is inappropriate or inconsistent
4 = all information is presented; most is accurate; any errors are minor; rounding is appropriate and consistent
3 = all information is presented; most is accurate; errors are major or conceptual
2 = there are more serious problem(s) such as missing information
1 = the author made a bona fide attempt but many problems remain
0 = missing

The report discusses at least two important implicit assumptions behind these hypothesis tests
4 = discussion reflects a solid understanding of two implicit assumptions; discussion addresses two issues other than the potential problem with the data collection
2 = discussion reflects a solid understanding of at least one implicit assumption
0 = missing

The report discusses the statistical significance of the findings.
4 = the author accurately interprets the statistical significance of the findings
3 or 2 = there are minor problems with the discussion of the statistical significance
1 = there are more serious problems
0 = missing

The report discusses whether any statistically significant findings are large enough to be practically significant.
2 = discussion of practical significance is reasonable and reflects an understanding of the difference between practical and statistical significance
1 = minor problem
0 = serious problem or missing

Caveats
The report discusses one potential problem with the data collection.
2 = the problem addressed is relevant and it is clearly explained
1 = the caveat could be explained more clearly
0 = the discussion is off target

Recommendation
The report makes an appropriate recommendation based on the findings.
2 = the recommendation is appropriate in light of the findings
1 = the recommendation could be explained more clearly
0 = the recommendation is off target

Quality of the Presentation and Writing
The report looks professional. It does not look like a homework assignment.
The report does not contain sentence-level errors. It is well-organized and clearly written.
The report is written from the perspective of a statistician employed by the manufacturing facility.
The report targets the appropriate audience (Helen, the busy manager described in the assignment).
The report does not exceed 1.5-2 single-spaced pages with reasonable margins and font sizes.
6 = all of the above criteria are satisfied; the report would impress Helen
5 = there are one or two minor issues with the writing or presentation; otherwise the report would impress Helen
4 = there are more than two minor issues
3 or below = there are serious problems; the report is not satisfactory

_____Total (40 possible points)

OBS    MTYPE    PROD    HRSWRK    HRSDOWN
1    1    320242    7.75    0
2    3    54311    7.75    0
3    2    60820    7.75    0
4    1    230679    5.16    2.5
5    1    253855    5.67    2
6    1    142151    3.57    4
7    3    16118    0.58    7.17
8    1    267881    7    0.75
9    2    25295    4.08    3.67
10    2    59360    7.75    0
11    3    65201    6.83    0.92
12    2    20521    3    4.75
13    2    22916    3    4.75
14    1    315124    7.75    0
15    3    47854    6    1.75
16    2    59868    7.62    0.13
17    3    75393    6.83    0.92
18    2    51374    7.25    0.5
19    3    30372    4.34    3.41
20    3    42784    5.75    2
21    1    202003    6    1.7
22    2    54597    7.75    0
23    2    59066    7.75    0
24    3    83712    7.75    0
25    3    20530    2.5    1.25
26    3    18188    2.17    5.58
27    3    87400    7.75    0
28    1    311877    7.75    0
29    2    15783    1.75    6
30    1    259945    7.58    0.17
31    2    31034    4.83    2.92
32    3    25569    4.17    3.58
33    2    15771    2.67    5.08
34    2    6899    1.5    6.25
35    3    82837    7.75    0
36    2    58349    7.75    0
37    3    68899    7.75    0
38    3    41909    5.25    2.5
39    1    127686    3.75    4
40    3    60159    7.58    0.17
41    3    48111    6    1.75
42    3    22461    2.5    1.25
43    1    308209    7.58    0.17
44    3    82915    7.58    0.17
45    2    53671    7.42    0.33
46    2    50006    6.95    0.8
47    1    214085    6    1.7
48    2    53614    6.83    0.92
49    3    82810    7.75    0
50    1    109567    3    4.7
51    1    245819    6.5    1.2
52    3    74643    7.75    0
53    3    30111    3.67    4.08
54    3    30561    3.75    0
55    3    47696    4.41    3.34
56    2    40289    5.75    2
57    1    297330    7.75    0
58    3    31593    3.5    0.25
59    3    46471    4.75    3
60    3    31499    3.5    0.25
61    3    60469    7.33    0.42
62    3    63703    7.75    0
63    2    19769    2.92    4.83
64    1    212743    7.75    0
65    2    55767    7.75    0
66    3    15038    1.75    2
67    3    31556    3.5    0.25
68    3    30380    3.42    0.33
69    3    68982    6.58    1.17
70    2    59850    7.7    0.05
71    1    300891    7.75    0
72    2    56431    7.75    0
73    3    83171    7.75    0
74    3    16650    2.25    5.5
75    2    52644    7.43    0.32
76    3    8954    1.08    2.67
77    1    316080    7.75    0
78    2    20200    2.93    4.82
79    2    61050    7.65    0.1
80    2    30459    4.47    3.28
81    2    25061    2.83    4.92
82    2    60224    7.75    0
83    3    60935    7.5    0.58
84    3    31233    3.75    0
85    3    20237    1.92    5.83
86    1    283785    7.25    0.5
87    2    49499    6.75    1
88    3    59722    6.67    1.08
89    1    271276    6.58    1.1
90    3    62762    7.75    0
91    2    61075    7.75    0
92    1    220686    6.83    0.92
93    3    78103    7.75    0
94    2    51300    7.54    0.21
95    3    40967    3.25    4.5
96    3    31056    3.5    0.25
97    3    61092    7.5    0.25
98    3    87114    7.75    0
99    3    8675    1.08    2.67
100    1    301077    7.5    0.2
101    3    5084    0.58    3.17
102    2    55753    7.62    0.13
103    1    285831    7.75    0
104    1    302774    7.75    0
105    2    57083    7.25    0.5
106    1    281949    7.25    0.5
107    3    40469    6.08    1.67
108    1    300039    7.75    0
109    3    88634    7.67    0.08
110    1    312501    7.75    0
111    3    75455    6.83    0.92
112    2    27600    3.63    4.12
113    1    273486    7    0.75
114    3    52164    6.67    1.08
115    2    29367    5.05    2.7
116    3    8142    1.08    2.67

In this case study, there are 3 variables: number of parts produced, hours that they spent, and hours that the press was down.
Mtype    Frequency    Percent
700 PPM    28    24.1
200 PPM    35    30.2
155 PPM    53    45.7
Total    116    100.0

This table calculates the summary statistic for each variables.
Variable    Statistic    Value
No. of parts produced    Mean    97610.26
Median    58707.50
Variance    9600782707.9
SD    97983.584
Std. Error    9097.547
Minimum    5084
Maximum    320242
Interquartile Range    57286
Hours of production time    Mean    5.7784
Median    6.8300
Variance    4.886
SD    2.21045
Std. error    .20524
Minimum    .58
Maximum    7.75
Interquartile Range    4.06
Hours that the press was down    Mean    1.4859
Median    .5400
Variance    3.422
SD    1.84984
Std. error    .17175
Minimum    .00
Maximum    7.17
Interquartile Range    2.67

Variables    Mtype    No.    Mean    SD    Standard Error
No. of parts produced    1    28    259627.54    58444.892    11045.046
2    35    43210.43    17238.352    2913.813
3    53    47940.64    24976.660    3430.808
Total    116    97610.26    97983.584    9097.547
Hours of production time    1    28    6.7668    1.38309    .26138
2    35    5.8906    2.16969    .36674
3    53    5.1821    2.41612    .33188
Total    116    5.7784    2.21045    .20524
Hours that the press was down    1    28    .9593    1.35500    .25607
2    35    1.8594    2.16969    .36674
3    53    1.5175    1.81441    .24923
Total    116    1.4859    1.84984    .17175

There are 3 histogram which show us the distribution of each variable.

This table shows the highest value in each variable.
Value
No. of parts produced        Highest    320242
316080
315124
312501
311877
Lowest    5084
6899
8142
8675
8954
Hours of production time        Highest    7.75
7.75
7.75
7.75
7.75a
Lowest    .58
.58
1.08
1.08
1.08
Hours that the press was down        Highest    7.17
6.25
6.00
5.83
5.58
Lowest    .00
.00
.00
.00
.00b

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