Question

A metal-cutting operation has a target value of 20 and consistently averages 19.8 with a standard deviation of 0.5. The design engineers have established an upper specification limit of 22 and a lower specification limit of 18. What is the process capability index? A) 1.20 B) 1.33 C) 1.46 D) 1.66 12. Following Q11, what is the process capability ratio? A) 1.33 B) 1.50 C) 1.66 D) 2.00

Answer 1

Answer:

process capability  index =  Cpl ( lower ) = 1.20 ( A )

The process capability ratio = 1.33

Explanation:

Target value = 20

mean = 19.8

standard deviation = 0.5

upper specification limit = 22

lower specification limit = 18

The process capability index =

Cpu = $\frac{22- 18}{6(0.5)}$   = 4 / 3 = 1.33

Cpk ( upper ) = (22 - mean ) / 3 * std

                      = ( 22 - 19.8 ) / ( 3 * 0.5 ) = 2.2 / 1.5 = 1.47

Cpl ( lower ) = ( mean - 18 ) / ( 3 * 0.5 ) = ( 19.8 - 18 ) / 1.5

                    = 1.8 / 1.5 =  1.2

hence the process capability index is Capability index with the minimum value which is Cpl ( lower ) = 1.20 ( A )

The process capability ratio = 1.33 refer to Cpu equation