Design specifications require that a key dimension on a product measure 102 ± 15

Question

Design specifications require that a key dimension on a product measure 102 ± 15 units. A process being considered for producing this product has a standard deviation of eight 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 94. 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.DIST() 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)

Process capability index (Cp) = (USL - LSL) / 6 = 30 / (6 x 8) = 0.625

Since the Cp value is less than 1.0, we conclude that the process is incapable based on 3 control limits.

(b)

New process mean = 94

Process capability index (Cpk) = min{(USL - Mean)/3, (Mean - LSL)/3} = min{(117-94)/24 , (94-87)/24}

or, Cpk = min(0.9583, 0.2917) = 0.2917

(c)

P(Dimension USL) = 1 - NORMDIST(117, 94, 8, TRUE) = 0.0020

P(Dimension LSL) = NORMDIST(87, 94, 8, TRUE) = 0.1908

P(Dimention is outside spec) = 0.00202 + 0.1908 = 0.1928

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