HVAC Manufacturing produces parts and materials for the heating, ventilation, and air conditioning industry. One of its facilities produces metal ductwork in various sizes for the home construction market. One particular product is 6-inch diameter round metal ducting. It is a simple product, but the diameter of the finished ducting is critical. If it is too small or large, contractors will have difficulty fitting the ducting into other parts of the system. The target diameter is 6 inches exactly, with an acceptable tolerance of ±.03 inches. Anything produced outside of specifications is considered defective. The line supervisor for this product has datashowing that the actual diameter of the finished product is 5.99 inches with a standard deviation of .01 inches.a. What is the current capability index of this process? What is the probability of producing a defective unit in this process?b. The line supervisor thinks he will be able to adjust the process so that the mean diameter of output is the same as the target diameter, without any change in the process variation. What would the capability index be if he is successful? What would be the probability of producing a defective unit in this adjusted process?c. Through better training of employees and investment in equipment upgrades, the company could produce output with a mean diameter equal to the target and a standard deviation of .005 inches. What would the capability index be if this were to happen? What would be the probability of producing a defective unit in this case?
HVAC Manufacturing produces parts and materials for the heating, ventilation, and air conditioning industry. One of its facilities produces metal ductwork in various sizes for the home construction market. One particular product is 6-inch diameter round metal ducting. It is a simple product, but the diameter of the finished ducting is critical. If it is too small or large, contractors will have difficulty fitting the ducting into other parts of the system. The target diameter is 6 inches exactly, with an acceptable tolerance of ±.03 inches. Anything produced outside of specifications is considered defective. The line supervisor for this product has datashowing that the actual diameter of the finished product is 5.99 inches with a standard deviation of .01 inches.a. What is the current capability index of this process? What is the probability of producing a defective unit in this process?b. The line supervisor thinks he will be able to adjust the process so that the mean diameter of output is the same as the target diameter, without any change in the process variation. What would the capability index be if he is successful? What would be the probability of producing a defective unit in this adjusted process?c. Through better training of employees and investment in equipment upgrades, the company could produce output with a mean diameter equal to the target and a standard deviation of .005 inches. What would the capability index be if this were to happen? What would be the probability of producing a defective unit in this case?
HVAC Manufacturing produces parts and materials for the heating, ventilation, and air conditioning industry. One of its facilities produces metal ductwork in various sizes for the home construction market. One particular product is 6-inch diameter round metal ducting. It is a simple product, but the diameter of the finished ducting is critical. If it is too small or large, contractors will have difficulty fitting the ducting into other parts of the system. The target diameter is 6 inches exactly, with an acceptable tolerance of ±.03 inches. Anything produced outside of specifications is considered defective. The line supervisor for this product has datashowing that the actual diameter of the finished product is 5.99 inches with a standard deviation of .01 inches.a. What is the current capability index of this process? What is the probability of producing a defective unit in this process?b. The line supervisor thinks he will be able to adjust the process so that the mean diameter of output is the same as the target diameter, without any change in the process variation. What would the capability index be if he is successful? What would be the probability of producing a defective unit in this adjusted process?c. Through better training of employees and investment in equipment upgrades, the company could produce output with a mean diameter equal to the target and a standard deviation of .005 inches. What would the capability index be if this were to happen? What would be the probability of producing a defective unit in this case?
HVAC Manufacturing produces parts and materials for the heating, ventilation, and air conditioning industry. One of its facilities produces metal ductwork in various sizes for the home construction market. One particular product is 6-inch diameter round metal ducting. It is a simple product, but the diameter of the finished ducting is critical. If it is too small or large, contractors will have difficulty fitting the ducting into other parts of the system. The target diameter is 6 inches exactly, with an acceptable tolerance of ±.03 inches. Anything produced outside of specifications is considered defective. The line supervisor for this product has data showing that the actual diameter of the finished product is 5.99 inches with a standard deviation of .01 inches. a. What is the current capability index of this process? What is the probability of producing a defective unit in this process? b. The line supervisor thinks he will be able to adjust the process so that the mean diameter of output is the same as the target diameter, without any change in the process variation. What would the capability index be if he is successful? What would be the probability of producing a defective unit in this adjusted process? c. Through better training of employees and investment in equipment upgrades, the company could produce output with a mean diameter equal to the target and a standard deviation of .005 inches. What would the capability index be if this were to happen? What would be the probability of producing a defective unit in this case?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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