C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 2 + 0.07 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 2.001 inches with a standard deviation of 0.030 inch. Calculate the Cpk for this machine. (Round your answer to 3 decimal places.) Cpk
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- Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations. a. The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. b. Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. c. What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?An existing robot is used in a commercial material laboratory to handle ceramic samples in the hightemperature environment that is part of several test procedures. Due to changing customer needs, the robot will not meet future service requirements unless it is upgraded at a cost of $2,000. Because of this situation, a new advanced technology robot has been selected for potential replacement of the existing robot. The accompanying estimates have been developed from information provided by some current users of the new robot and data obtained from the manufacturer. The firm’s before-tax MARR is 25% per year. Based on this information,should the existing robot be replaced? Assume that a robot will be needed for an indefinite period.A manufacturing firm just received a shipment of 20 assembly parts, of slightly varied sizes, from a vendor. The manager knows that there are only 15 parts in the shipment that would be suitable. He examines these parts one at a time.a. Find the probability that the first part is suitable. (Round your answer to 2 decimal places.) b. If the first part is suitable, find the probability that the second part is also suitable. (Round your answer to 4 decimal places.) c. If the first part is suitable, find the probability that the second part is not suitable. (Round your answer to 4 decimal places.)
- Herme, the quarry supervisor for Espinosa Stone, wants to select the more economical of two alternatives for quarry dust control. Help him perform a spreadsheet-based AW evaluation for the estimates with MARR = 12% per year.Vernon Inc. has analyzed the setup time on its computer-controlled lathe. The setup requireschanging the type of fixture that holds a part. The average setup time has been 140 minutes,consisting of the following steps: Turn off machine and remove fixture from lathe 15 minutesGo to tool room with fixture 15Record replacement of fixture to tool room 18Return to lathe 20Clean lathe 20Return to tool room 20Record withdrawal of new fixture from tool room 12Return to lathe 15Install new fixture and turn on machine 5Total setup time 140 minutesa. Why should management be concerned about improving setup time?b. What do you recommend to Vernon Inc. for improving setup time?c. How much time would be required for a setup, using your suggestion in (b)?In a manufacturing process the assembly line speed (feet per minute) was thought to affect the number of defective parts found during the inspection process. To test this theory, managers devised a situation in which the same batch of parts was inspected visually at a variety of line speeds. They collected the following data: Develop a scatter chart with line speed as the independent variable. What does the scatter chart indicate about the relationship between line speed and the number of defective parts found? Use the data to develop an estimated regression equation that could be used to predict the number of defective parts found, given the line speed. What is the estimated regression model? Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? How much of the variation in the number of defective parts found for the sample data does the model you estimated in part (b) explain?
- A mechanical engineer is considering two types of pressure sensors for the low-pressure steam lines in several of the company plants. Piezoresistive sensors use the change in conductivity of semiconductors to measure the pressure. Fiber optic sensors use the properties of fiber optic interferometers to sense nanometer scale displacement of membranes. The costs for each system are shown below. Which should be selected based on a present worth comparison at an interest rate of 1% per month?The production department is proposing the purchase of an automatic insertion machine. It has identified three machines and has asked the accountant to analyze them to determine which one has the best average rate of return. Machine A Machine B Machine C Estimated average income $45,593.52 $70,301.40 $72,086.10 Average investment 325,668.00 234,338.00 480,574.00The production department is proposing the purchase of an automatic insertion machine. It has identified three machines and has asked the accountant to analyze them to determine which one has the best average rate of return. Line Item Description Machine A Machine B Machine C Estimated average income $47,060.44 $72,961.50 $73,785.60 Average investment 336,146.00 243,205.00 491,904.00 a. Machine C b. Machine A c. Machines B and C have the same preferred average rate of return. d. Machine B
- Dunlop company conducts tests on tires life . For a particular tires, the standard deviation is 6000 kilometers,and the 68% of tires life failed between two values (102000 , 78000) what is the value of the mean life of dunlop tires ?The firm, Bolta Ltd, manufactures high precision specialized nuts and bolts that are customized for the needs of specific applications. It has received an enquiry from the Spaceways Company to supply high precision bolts that are needed for their new spacecraft designed to take passengers for a flight over the earth to the limit of earth’s atmosphere of 100 kms and back, hopefully alive and safe. Special bolts are needed that will not be affected by the temperature difference as the spacecraft goes up to the outer atmosphere and on its decent back to the ground. It is expected that the requirements will be about 3 million units in year 1, which will increase by 15% for 2 years up to year 3, and then decrease by 15% for another 2 years. Current plans foresee demand for these specialized nuts for only 5 years. The price per bolt in year 1 is expected to be $ 50 which will increase by 8% each year to account for inflation. Variable cost is 50% of sales. Fixed cost is $ 6 million in year 1…A process control manager is considering two robots to improve materials handling capacity in the production of rigid shaft couplings that mate dissimilar drive components. Robot X has a first cost of $84,000, an annual M&O cost of $31,000, a $40,000 salvage value, and will improve revenues by $96,000 per year. Robot Y has a first cost of $146,000, an annual M&O cost of $28,000, a $47,000 salvage value, and will increase revenues by $119,000 per year. The company’s MARR is 15% per year and it uses a 3-year study period for economic evaluations. Which one should the manager select (a) on the basis of ROR values, and (b) on the basis of the incremental ROR value? (c) Which is the correct selection basis? Perform the analysis by hand or spreadsheet, as instructed.