Design specifications require that a key dimension on a product measure 106 ± 11 units. A process being considered for producing this product has a standard deviation of four units. a. What can you say (quantitatively) regarding the process capability? Assume that the process is centered with respect to specifications. (Round your answer to 4 decimal places.) b. Suppose the process average shifts to 97. Calculate the new process capability. (Round your answer to 4 decimal places.) c. What is the probability of defective output after the process shift? (Use Excel's NORM.S.DIST() function to find the correct probability. Round "z" values to 2 decimal places. Round your answer to 4 decimal places.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Design specifications require that a key dimension on a product measure 106 ± 11 units. A process being considered for producing this product has a standard deviation of four units.
a. What can you say (quantitatively) regarding the process capability? Assume that the process is centered with respect to specifications. (Round your answer to 4 decimal places.)
b. Suppose the process average shifts to 97. Calculate the new process capability. (Round your answer to 4 decimal places.)
c. What is the probability of defective output after the process shift? (Use Excel's NORM.S.DIST()
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