Question

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.)**

Process capability index 0.9167

**b.** Suppose the process average shifts to 97.
Calculate the new process capability. **(Round your answer to
4 decimal places.)**

New process capability index 0.1667

**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 (help me find this please)

Answer #1

USL = 106+11 = 117

LSL = 106-11 = 95

Standard deviation, = 4

a) For centered process, Process capability index and ratio are equal, Cpk = Cp = (USL-LSL)/6

= (117-95)/(6*4)

= **0.9167**

b) Mean, = 97

Process capability index, Cpk = MIN((USL-)/3, (-LSL)/3)

= MIN((117-97)/(3*4), (97-95)/(3*4))

= **0.1667**

c) z value for USL = (117-97)/4 = 5

z value for LSL = (95-97)/4 = -0.5

Probability of defective output = P(z>5) + P(z<-0.5)

= (1-NORMSDIST(5)) + NORMSDIST(-0.5)

= **0.3085**

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b. Suppose the process average shifts to 97.
Calculate the new process capability. (round to 4 decimal
places)
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