Problem description: You oversee a manufacturing facility that produces an automotive part (steel shaft for the gearbox). The acceptable dimension of the shaft is 2.5±0.05 inches in diameter with the most desirable product being exactly 2.5 inches. Two vendors are trying to sell their equipment for the shaft-machining task to your company, Automotive Parts Corporation. You have been asked to assess the equipment from each vendor, and to make a recommendation on which one to make the purchase from, supported by a justification for your decision.
You asked both vendors to supply data on the machining accuracy of their equipment for the given task. Both vendors machined 100 shafts, collected data, plotted histograms, fitted the histograms with normal distributions and supplied you with their findings
Let X= diameter in inches of the gearbox shaft
Ace Machines: X has a normal distribution with mean 2.48 and variance 0.001
Best Machinery: X has a normal distribution with mean 2.51 and variance 0.002
When you are completing your memorandum be sure to address the following:
Recommend a vendor using the given information, develop and discuss your approach (give all details including quantitative justification). Your response to this question must be directed to the audience described below.
Examine the scenario as described and discuss what additional information would be helpful to make this recommendation a stronger selection, and why that information would be useful. Be careful not to negate your recommendation as you explain this.
Include your calculations as a titled addendum on its own page at the end of your document.
Audience: You are creating this document for the company’s Chief Operating Officer, Lin Gerard, and copying the Chief Financial Officer, Aileen Kitts. Documents involved in major financial decisions like this may also be distributed by the addressees to other executives and the corporate board members.
Document: Complete this assignment as a memorandum. Follow the guidance for business memorandum provided in your reading. Utilize clear, professional language, including setting your Word preferences to check for a more professional writing approach. Examples of professional language constraints would include:
Utilize plain language.
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Links to an external site.
Develop the document around a direct, coherent message (thesis
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) and clear analysis
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to support it.
Do not use contractions, slang or colloquialisms, clichés
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, abbreviations, or text message shortcuts.
file:///C:/Users/hotpi/AppData/Local/Packages/Microsoft.MicrosoftEdge_8wekyb3d8bbwe/TempState/Downloads/How%20to%20Write%20a%20Business%20Memorandum%20%20(1).pdf
This is an answer for problem above:
It would be useful to get metrics like distribution quantiles, range or median. Also the most important aspect would be to get distribution fit statistics such as goodness of fit for normal distribution being fitted to the data in addition to Q-Q plots for normal distribution compared with the data.
A has mean of 2.48 and variance of 0.001 and hence sd 0.032 ( sd : standard deviation). B has mean of 2.51 and variance of 0.002 and hence sd 0.045. Since the means of both are similar in terms of magnitude of difference from the desired level of 2.50, sd plays a pivotal role here. Since 0.045 is quite higher than 0.032, B will have a slight preference. If we compute the tolerance intervals, that is the intervals based on the normal distribution x-sigma limits where x=1,2,3,4,5,6 we see as the x increases the interval widens but the interval width or variability is more in case of A than in B. The overall mean of the tolerance intervals stay quite close to the desired level of 2.5. Here, in simpler terms the issue of accuracy or unbiasedness is similar for both A and B with not a significant difference. However, the precision, consistency or variability of A and B are quite different. The better precision of A makes it a more preferred choice over B. Hence the vendor of choice with just the given information and no additional information would be A.