Design specifications require that a key dimension on a product measure 99 ± 11

Question

Design specifications require that a key dimension on a product measure 99 ± 11 units. A process being considered for producing this product has a standard deviation of five 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.) Process capability index b. Suppose the process average shifts to 96. Calculate the new process capability(Round your answer to 4 decimal places.) New process capability index c. What is the probability of defective output after the process shift? (Use Excel's NORM.S.DISTO function to find the correct probability. Round "z" values to 2 decimal places. Round probabilities to 4 decimal places (0.### ) Probability of defective output

Explanation / Answer

a) For centered process, Cp = (UCL-LCL)/(6*SD)

UCL = 99+11 = 110

LCL = 99-11 = 88

SD = 5

Cp = (110-88)/(6*5) = 0.7333

As the value is less than 1, it is not capable

b) New Mean = 96

Cpk = Min((UCL-Mean)/(3*SD), (Mean-LCL)/(3*SD)) = Min((110-96)/(3*5), (96-88)/(3*5)) = Min(0.9333, 0.5333) = 0.5333

c) Z value can be computed as:

Values less than 88 with Mean as 96:

Probability = NORM.S.DIST(88,96,5,1) = 0.0548

Values greater than 110 with Mean as 110:

Probability using NORM.S.DIST(110,96,5,1) = 0.9974

Hence, probability of values between LCL & UCL = 0.9974 - 0.0548 = 0.9426

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