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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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