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# ABC Motor Company installs approximately 10 engines per hour. The...

ABC Motor Company installs approximately 10 engines per hour. The process manager measures the maximum Nitrous Oxide (NOx) emissions of each engine to be installed. As part of the process, a subgroup of n=7 measurements are randomly taken when the engine is tested. This occurs during a 6 minute test on every engine. There was an issue with testing during sample 5 that is under investigation. The results are given in Table Q1.

a) Calculate the upper and lower control limits of X bar and R Charts for the data (10 marks). Note: Constants for calculating the Upper and Lower Control limits for and R Charts are given in the appendix.

b) Plot the X bar and Range charts and hence determine if the process is in control (10marks).

c) Explain why it is not necessary to know the underlying distribution of the process (5 marks).

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Sample Engine Emissions Output (g/min) 1 4.93 4.72 5.01 4.82 4.95 4.83 4.88 2 4.77 4.85 4.67 4.84 4.69 4.92 4.79 3 4.99 4.66 4.87 4.70 4.98 4.79 4.83 4 4.67 5.02 4.73 4.90 4.75 5.05 4.85 5 4.88 6.83 6.98 6.78 6.87 6.82 4.86 6 4.70 4.97 4.77 4.89 4.74 4.96 4.84 7 4.97 4.74 5.05 4.67 4.97 4.74 4.86 8 4.69 5.02 4.75 5.00 4.66 4.88 4.83 9 4.86 4.82 4.95 4.68 4.90 4.73 4.82 10 4.66 4.98 4.81 4.86 4.73 5.06 4.85 Table Q1 - Engine emissions of NOx (g/min)

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d) The car engine was designed to emit less than 5.6 g/min of NOx. The agreed customer defect level is less than 3.4 defects per million engines. Legislation is changed to an emission target of 5.0 g/min. Is your company capable of producing conforming cars with the existing engine? What may be able to be done to help? Explain your answer (5 marks).

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