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QSO 510 Final Project Case Addendum 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).

2006

Mean 801.1667

Standard Error 24.18766

Median 793

Mode 708 Standard 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

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