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            

Answer 1

Answer A:-UTL= 102 +15=117 units

LTL = 102 -15 = 87 units

Process capability index   = Min [(UTL- X bar )/3*Std Deviation , (X bar -LTL )/3* Std Deviation

Process capability index   =Min[(117 -102)/3*8    ,(102-87)/3*8]

Process capability index   =Min[0.625 ,0.625]

Process capability index   =0.625

Answer B:- If the process average shifts to 94 then

Process capability index   = Min [(UTL- X bar )/3*Std Deviation , (X bar -LTL )/3* Std Deviation

Process capability index   =Min[(117 -94)/3*8    ,(94-87)/3*8]

Process capability index   =Min[0.958 ,0.292]

Process capability index   =0.292

Answer C:- Let us assume the normal distribution,

The left tail [prob (x<87)]

Z=(87-94)/8=-0.875

For z= -0.875, probability is 0.190787

The right tail [prob (x>117)] = 1-[prob (x<117)]

Z=(117-94)/8 =2.875

For z= 2.875, probability is 0.00202

Thus total probability = 0.190787+0.00202

Probability of defective output = 0.192807