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 to 4 decimal places)

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

C) What is the probability of defective output after the process shift? (Round z values to 2 decimal places, round answer to 4 decimal places)

Answer 1

Upper specification limit, USL = 106+11 = 117

Lower specification limit, LSL = 106-11 = 95

Standard deviation, s = 4

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a)

Since, the process is centered wrt specifications, Cpk = Cp

Process capability index, Cpk = Cp = (USL-LSL)/6s

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

= 0.9167

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b)

Process average, xbar = 97

Cpu = (USL-Xbar)/3s = (117-97)/(3*4) = 1.6667

Cpl = (Xbar-LSL)/3s = (97-95)/(3*4) = 0.1667

Cpk = Minimum of Cpu and Cpl = 0.1667

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c)

for USL, z value = (USL-Xbar)/s = (117-97)/4 = 5, P(z) = NORMSDIST(5) = 1

Probability of output greater than USL = 1 - P(z) = 1-1 = 0

for LSL, z value = (LSL-Xbar)/s = (95-97)/4 = -0.5, P(z) = NORMSDIST(-0.5) = 0.3085

Probability of output smaller than LSL = P(z) = 0.3085

Probability of defective output after the process shift = Probability of output greater than USL + Probability of output smaller than LSL

= 0 + 0.3085

= 0.3085

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