Question

Sos please help!!1

The design specifications require that a key dimension of a product must be between 19 and 21 cm. A process that is being used for producing this product has a mean of 20 and standard deviation (sigma) of 0.5 cm. Is this process capable of meeting the specifications? What should be the standard deviation (sigma) of the process that will meet the specifications? (20 Points)

Answer 1

Upper Specification limit = 21

Lower Specification limit = 19

Design target, Process mean = 20

Process capability index = Cpk = Min (USL - Mean) / 3*Std deviation , (Mean - LSL) / 3*Std deviation

= min {(21 - 20) / 3 * 0.05 , (20-19) / 3*0.05 } = 1/1.5 = 0.67

The process is not capable as Cpk is less than 1.33. For process to be capable Cpk must be atleast 1.33.

Let required Standard deviation be S so that process is capable

Cpk = 1.33 = (21 - 20) / 3 * S

4S = 1

S = 0.25