Problems(20 points) A part for an automobile should have a length of 4.00 in. The following is a summary table of the mean (x-bar) and range (R) for the observations in each sample, where there were four readings of the length (observations) in each sample.

Mean RangeSample 1 4.01 0.04Sample 2 3.98 0.06Sample 3 4.00 0.02Sample 4 3.99 0.05Sample 5 4.03 0.06Sample 6 3.97 0.02Sample 7 4.02 0.02Sample 8 3.99 0.04Sample 9 3.98 0.05Sample 10 4.01 0.06

x-bar-bar = …………. R-bar = …………. n (number of observations in a sample) = …………

Calculate the upper and lower control limits for the R chart.

R-bar = ………………………………………………………………………………………. (1 point)UCLR = ……………………………………………………………………………………… (2 points)LCLR = ……………………………………………………………………………………… (2 points)

Calculate the upper and lower control limits for the x-bar chart.

X-bar- bar = …………………………………………………………………………. .…… (1 point)UCLxbar = ……………………………………………………………………………….… (2 points)LCLxbar = ………………………………………………………………………………..… (2 points)

Plot the charts, including UCL, mean, and LCL. (4 points)

R Chart Xbar ChartIs this process in control? …………………………………………… (2 points)Why or why not? …………………………………………………………………….…………………………………………………………………………………………… (2 points)

(6 points) The specification for a plastic handle calls for a length of 6.0 inches ± 0.2 inches. However, the actual process, as just recently measured, has an average length of 6.07 inches. The UCL of the process is 6.22 inches and the LCL is 5.92 inches.

What is the Cpk for this process?

Cpk = ……………………………………………………………………………………………..….……………………………………………………………………………………………… (4 points)

Is this process capable of producing the desired part? Why?…………………………………………………………………………….…………….. (2 points)

(7 points) A local convenience store makes personal pan pizzas. Currently, their process makes complete pizzas, fully cooked, for the customer. This process has a fixed cost of $20,000 and a variable cost of $1.75 per pizza. The owner is considering a different process that can make pizzas in two ways: completely cooked (as before), or partially cooked and then flash frozen, for the customer to finish at home. This alternate process has a fixed cost of $24,000, but a lower variable cost (because much less energy is used in baking) of $1.25 per pizza. He sells the Pizzas for $5 each.

What is the crossover point in pizzas between the existing process and the proposed process? (4 points)

If the owner expects to sell 9,000 pizzas, should he get the new process (1 point) and why (2 points)?

(9 points) A new route easing to air traffic controlWall Street Journal 12 May 2009The FAA is phasing in a new navigation system that has already proved it can reduce weather delays, shave minutes off flight times, and reduce ground noise pollution.Required Navigation Performance (RNP) is in use in China, Australia, Canada, and Alaska. The FAA will expand it soon to all major airlines. SouthWest Airlines will have all its planes and pilots ready by next year. Reagan National airport has RNP in place. The plan is to start with the most congested airports first, starting with New York and Chicago.RNP is a plane based, computer driven, precision navigation system that enables aircraft to fly an exact path with a deviation less than the wingspan of the plane. RNP needs no ground equipment. The plane’s autopilot puts the aircraft at an exact position and height at an assigned time. Half the US fleet is already equipped with RNP. With RNP, aircraft can land at the same rate in bad weather as in good. With the old ground based systems, the landing rate can halve in bad weather. RNP reduces fuel usage, noise, and flight times. More takeoffs and landings are possible with RNP.RNP is beyond the test phase. RNP is technically ready to go. Naverus developed RNP for planes landing in Juneau. They then developed RNP for Canada, China, and Australia. For full benefit, airlines must upgrade old planes to RNP and train all its pilots. Once this happens, (together with satellite based navigation or RNAV), there will be a huge difference for passengers, according to the FAA.Why is RNP advantageous to airlines? (3 points)

Why is RNP advantageous to the FAA? (3 points)The biggest problems with moving to RNP are ….? (3 points)Where n is the number of observations in the sample, not the number of samples!

Cpk = Min ((USL-xbar)/(UCL- xbar),(xbar -LSL)/(xbar -LCL))

Where SL = Specification Limit; CL = Control Limit;U = Upper, L = Lower,

TCA = FCA + VCA * nWhere TCy = Total cost for alternative y; VCy = Variable Cost per unit for alternative y;FCy = Fixed Cost for alternative y; n is number of units produced.

TRA = PA * n

Where TRx = Total Revenue for product x and Px = Price per unit of product x.

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