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 4972 2814 5411 2874 7678 3774 5774 3247 6007 3107 6290 2776 8332 3571 6107 3354 6729 3513
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