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CHAPTER $3$

Probability and Statistics

CASE STUDY

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Slicky Lube Oil Products

Background

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John McCowski founded Slicky Lube in $1918.$ As the market for automobiles grew during the early turn, expanded to meet this growth. Expansion into a range of other markets led Slicky Lube to and mid$-1900$s$,$ the demand for specialty additives for lubricating oils also grew. Slicky Lube, in become a market leader within the fluid sector. The company's major goal is to develop r

and additives that are of high quality, yet environment$-$friendly.

new oils

The largest market segment of the fluid sector $(61\%)$ is the automobile market. However, this the testing of new oils be highly accurate and very timely. The case study's tasks are to help Harold market is also the most competitive. As a result, it is crucial to Slicky Lube's continued success that statistics and create processes for analyzing the field test data from all taxis in both New York and Scott, the Senior Chemical Engineer, analyze the data set using simple descriptive and inferential

San Francisco in a more reasonable time frame.

The Operational Environment$-$Testing and Vehicle Specifications

In $1998$ Slicky Lube signed a deal with General Motors $($GM$).$ GM was to deliver $80$ brand new Chevrolet automobiles to the Yellow Cab Cooperative in two different cities, New York and San Francisco. Because of their infamous reputations in regard to city driving conditions, New York and San Francisco were chosen as the test locations for new products. Each city would receive $40$ new vehicles. The Chevrolet automobile utilized is a standard cab with a $4\mathrm{.}8-$liter, $140-$horse$-$ power engine.

The new oil$/$additive that Slicky Lube wished to test had to be used under severe operating conditions. This was necessary to find out whether it would perform better or worse in compari$-$ son to the existing products already on the market. The units operated $7$ days a week, $24$ hours a day $(2\backslash$times $12-$hour shifts$).$ The sample oil was not replaced during the test period. Approximately every $10,000$ miles, samples of the oil sludge would be taken and sent to an independent testing laboratory for testing and decomposition.

Testing Process and Procedures

The tests themselves are performed in the following manner: upon completion of the field$-$tests $($approximately $12$ months for total completion$),$ samples of the lubricant and sludge deposits are taken from test vehicles and sent to independent laboratories for decomposition and analy$-$ sis. Hard copies of the lab results are mailed via the surface mail postal system to Slicky Lube headquarters, where they analyzed by a group of $20$ to $25$ in$-$house technical specialists. U or unexpected results and typographical errors in the lab reports are identified and highlighted before being sent to data entry clerks for entry into Excel spreadsheets. These spreadsheets a of errors, the spreadsheets are handed over to the Statistical Analysis Division of Slicky Lube for returned to the technical specialists for further analysis. When the data are deemed to be free

additional analysis.

Unusual

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