Problem 13-5 Design specifications require that a key dimension on a product mea
ID: 460945 • Letter: P
Question
Problem 13-5
Design specifications require that a key dimension on a product measure 101 ± 8 units. A process being considered for producing this product has a standard deviation of five units.
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.)
Suppose the process average shifts to 98. Calculate the new process capability. (Round your answer to 4 decimal places.)
What is the probability of defective output after the process shift? (Use Excel's NORMSDIST() function to find the correct probability for your computed Z-value.Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Design specifications require that a key dimension on a product measure 101 ± 8 units. A process being considered for producing this product has a standard deviation of five units.
Explanation / Answer
a) Process Capability= (Upper Specification-Lower Specification)/6*Stddev=(109-93)/(6*5)=16/30=0.533
b) New Process Capability= Min(mean-lower spec)/3*stddev, (Upper Spec-Mean)/3*std dev)
=Min((98-93)/(3*5),(108-98)/(3*5))=Min(5/15,10/15)=5/15=0.33
c) z=(lower spec-mean)/std dev=(93-98)/5=-1.00
Normsdist(-1)=0.1586
probability of defective output=15.86%