Design specifications require that a key dimension on a product measure 100 ± 16
ID: 460601 • Letter: D
Question
Design specifications require that a key dimension on a product measure 100 ± 16 units. A process being considered for producing this product has a standard deviation of six 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.)
b. Suppose the process average shifts to 93. Calculate the new process capability. (Round your answer to 4 decimal places.)
c. 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.)
Explanation / Answer
= (116-84)/6*6
= 0.88
Thus, according to process capability ratio of 0.88, the process is not capable of meeting the specification limit.
2. Process average shift to 93
Process capability index = minimum (average-LSL/3*sigma, USL-average/3* sigma)
= Minimum ((93-84)/3*6, (116-93)/3*6)
= Minimum (0.5, 1.27)
= 0.5
Thus, according to process capability index of 0.5, the process is not capable of meeting the specification limit.
3. Left tail is (84-93)/6 = -1.5 which correspond to probability of 0.0668
Right Tail is (116-93)/6 = 3.8333 which correspond to probability of 1.0000 approximately
Probability above USL is 1- 1.0000 = 0
Therefore, 0.068 is the probability of defective output after process change.
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