Addendum
We have always estimated how many transformers will be needed to meet demand. The usual method is to look at the sales figures of the last two to three months and also the sales figures of the last two years in the same month. Next make a guess as to how many transformers will be needed. Either we have too many transformers in stock, or there are times when there are not enough to meet our normal production levels.
It is a classic case of both understocking and overstocking. Ratnaparkhi, operations head, has been given two charges by Mittra. First, to develop an analysis of the data and present a report with recommendations. Second, "to come up with a report that even a lower grade clerk in stores should be able to fathom and follow."
In an effort to develop a report that is understood by all, Ratnaparkhi decides to provide incremental amounts of information to his operations manager, who is assigned the task of developing the complete analyses
A-Cat Corporation is committed to the pursuit of a robust statistical process control (quality control) program to monitor the quality of its transformers. Ratnaparkhi, aware that the construction of quality control charts depends on means and ranges, provides the following descriptive statistics for 2006 (from Exhibit 1).
| |
2006 |
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| |
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| Mean |
|
801.1667 |
| Standard Error |
24.18766 |
| Median |
|
793 |
| Mode |
|
708 |
| Standard |
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| Deviation |
83.78851 |
| Sample Variance |
7020.515 |
| Kurtosis |
|
-1.62662 |
| Skewness |
0.122258 |
| Range |
|
221 |
| Minimum |
695 |
| Maximum |
916 |
| Sum |
|
9614 |
| Count |
|
12 |
The operations manager is assigned the task of developing descriptive statistics for the remaining years, 2007-2010, that are to be submitted to the quality control department.
A-Cat's president asks Mittra, his vice-president of operations, to provide the sales department with an estimate of the mean number of transformers that are required to produce voltage regulators. Mittra, recalling the product data from 2006, which was the last year he supervised the production line, speculates that the mean number of transformers that are needed is less than 745 transformers. His
analysis reveals the following:
t = 2.32
p = .9798
This suggests that the mean number of transformers needed is not less than 745 but at least 745 transformers. Given that Mittra uses older (2006) data, his operations manager knows that he substantially underestimates current transformers requirements. She believes that the mean number of transformers required exceeds 1000 transformers and decides to test this using the most recent (2010) data.
Initially, the operations manager possessed only data for years 2006 to 2008. However, she strongly believes that the mean number of transformers needed to produce voltage regulators has increased over the three-year period. She performs a one-way analysis of variance (ANOVA) analysis that follows:
| 2006 |
2007 |
2008 |
| 779 |
845 |
857 |
| 802 |
739 |
881 |
| 818 |
871 |
937 |
| 888 |
927 |
1159 |
| 898 |
1133 |
1072 |
| 902 |
1124 |
1246 |
| 916 |
1056 |
1198 |
| 708 |
889 |
922 |
| 695 |
857 |
798 |
| 708 |
772 |
879 |
| 716 |
751 |
945 |
| 784 |
820 |
990 |
| Anova: Single Factor |
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| SUMMARY |
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Groups |
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Count |
Sum |
Average |
Variance |
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2006 |
12 |
9614 |
801.1667 |
7020.515 |
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2007 |
12 |
10784 |
898.6667 |
18750.06 |
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2008 |
12 |
11884 |
990.3333 |
21117.88 |
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| ANOVA |
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Source of Variation |
|
SS |
df |
MS |
F |
P-value |
F crit |
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Between Groups |
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214772.2 |
2 |
107386.1 6 |
6.870739 |
0.003202 |
3.284918 |
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Within Groups |
|
515773 |
33 |
15629.48 |
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Total |
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|
730545.2 |
35 |
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|
The results (F = 6.871 and p = 0.003202) suggest that indeed the mean number of transformers has changed over the period 2006-2008. Mittra has now provided her with the remaining two years of data (2009 and 2010) and would like to know if the mean number of transformers required has changed over the period 2006-2010.
Finally, the operations manager is tasked with developing a model for forecasting transformer requirements based on sales of refrigerators. The table below summarizes sales of refrigerators and transformer requirements by quarter for the period 2006-2010, which are extracted from Exhibits 2 and 1 respectively.
| Sales of Refrigerators |
Transformer Requirements |
| 3832 |
2399 |
| 5032 |
2688 |
| 3947 |
2319 |
| 3291 |
2208 |
| 4007 |
2455 |
| 5903 |
3184 |
| 4274 |
2802 |
| 3692 |
2343 |
| 4826 |
2675 |
| 6492 |
3477 |
| 4765 |
2918 |
| 4972 |
2814 |
| 5411 |
2874 |
| 7678 |
3774 |
| 5774 |
3247 |
| 6007 |
3107 |
| 6290 |
2776 |
| 8332 |
3571 |
| 6107 |
3354 |
| 6729 |
3513 |
Instruction
Submit a statistical analysis report and recommendations to management. It must be 10-12 pages in length (plus a cover page and references) and must be written in APA format
Include at least six references , cited in APA format.
Specifically, the following critical elements must be addressed:
V. Recommend operational improvements to stakeholders:
A. Summarize your analysis plan for both internal and external stakeholders. Be sure to use audience-appropriate jargon when summarizing for both groups of stakeholders
B. Explain how your decision addresses the given problem and how you reached that decision. Be sure to use audience-appropriate jargon for both groups of stakeholders.
C. Justify why your decision is the best option for addressing the given problem to both internal and external stakeholders and how it will result in operational improvement. Be sure to use audience-appropriate jargon when communicating with stakeholders.