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