Case- Vice-president Arun Mittra speculates
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).
Mean
801.1667
Standard Error
24.18766
Median
793
Mode
Standard Deviation
708
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
SUMMARY
Groups Count Sum Average Variance
2006 12 9614 801.1667 7020.515
2007 12 10784 898.6667 18750.06
2008 12 11884 990.3333 21117.88
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups
214772.2
2 107386.1 6.870739 0.003202 3.284918
Within Groups
515773
33 15629.48
Total 730545.2 35
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
6792
3513
Questions
Produce a spreadsheet that provides justification of the appropriate statistical tools that are needed to analyze the company’s data, a hypothesis, the results of your analysis, any inferences from your hypothesis test, and a forecasting model that addresses the company’s problem.
2. Identify statistical tools and methods to collect data: Short answers to the following are okay as I can build upon the basic idea
A. Identify the appropriate family of statistical tools that you will use to perform your analysis. What are your statistical assumptions concerning the data that led you to selecting this family of tools? In other words, why did you select this family of tools for statistical analysis?
B. Determine the category of the provided data in the given case study. Be sure to justify why the data fits into this category type. What is the relationship between the type of data and the tools?
C. From the identified family of statistical tools, select the most appropriate tool(s) for analyzing the data provided in the given case study.
D. Justify why you chose this tool to analyze the data. Be sure to include how this tool will help predict the use of the data in driving decisions.
E. Describe the quantitative method that will best inform data-driven decisions. Be sure to include how this method will point out the relationships between the data. How will this method allow for the most reliable data?
3. Analyze data to determine the appropriate decision for the identified problem:
A. Outline the process needed to utilize your statistical analysis to reach a decision regarding the given problem.
B. Explain how following this process leads to valid, data-driven decisions. In other words, why is following your outlined process important?
C. After analyzing the data sets in the case study, describe the reliability of the results. Be sure to include how you know whether the results are reliable.
D. Illustrate a data-driven decision that addresses the given problem. How does your decision address the given problem? How will it result in operational improvement?
4. 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.
Submit your statistical analysis report and recommendations to management. It should be a complete, polished artifact containing all of the critical elements of the final product.Vice-president Arun Mittra speculates:
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.
