Question

Problem 6s.42 18 Question Help Linda Boardman, Inc., an equipment manufacturer in Boston, has submitted a sample cutoff valve to improve your manufacturing process. Your process engineering department has conducted experiments and found that the valve has a mean (1) of 12.00 and a standard deviation () of 0.05. Your desired performance is p = 12.00 +3 standard deviations, where o = 0.045. (round your response to three decimal For the given information, the process capability index (Ca)= places)

Answer 1

Mean = 12.00

Standard deviation (SD) = 0.05

Desired performance is 12 +/- 3 standard deviation where $\sigma$ = 0.045

So , Upper specification limit (USL) = 12 + 3$\sigma$ = 12 + (3 × 0.045) = 12 + 0.135 = 12.135

Lower specification limit (LSL) = 12 - 3$\sigma$ = 12-(3 × 0.045) = 12-0.135 = 11.865

Cpl = (Mean - LSL) / (3 x SD) = (12.00-11.865)/(3x0.05) = 0.135/0.15 = 0.900

Cpu = (USL - Mean) / (3 x SD) = (12.135-12.00)/(3x0.05) = 0.135/0.15 = 0.900

Process capability index (Cpk) = Minimum of (Cpu, Cpl)

= Minimum of (0.900 , 0.900)

= 0.900