Question

The upper and lower specifications for a service are 11.5 min. and 9.0 min., respectively. The process average is 9.50 min. If 6-sigma process capability is desired:

(a) what should the process mean be? (Provide your answer rounded to 2 decimal places.)

(b) what should the process standard deviation be? (Provide your answer rounded to 4 decimal places.)

Answer 1

Here, Given Data, Upper Specification Limit or USL = 11.5 Minutes Lower Specification Limit or LSL = 9.0 Minutes Current Process Mean = 9.50 Minutes, As 6 Sigma Process Capability is Desired, Thus, Process Capability Cp has to be 2, Cp = 2 = (USL-LSL)/(6* Standard Deviation), Or, (11.5-9.0)/( 6* Standard Deviation) = 2 Or, Standard Deviation = 2.5/12 = 0.2083 Minutes Lower Bound for the Process Capability Index or Cpl has to be 2 Cpl = 2 = (Process Mean – LSL)/3*Standard Deviation, Or, (Process Mean – 9.0)/3*0.2083=2, Or, Process Mean = 9.0 + 1.25 = 10.25 Minutes Upper Bound for the Process Capability Index or Cpu has to be 2 or (USL – Process Mean)/3*Standard Deviation= 2, (11.5 – Process Mean)/(3*0.2083) = 2, Or, Process Mean = 11.5 – 1.25 = 10.25 Minutes, Answer for a) Hence, Process Mean Should be 10.25 Minutes, Answer for b) Hence, Process standard Deviation should be 0.2083 Minutes