Question

Your firm bottles water in plastic bottles labeled for 16.9 ounces. The specifications are 16.75 ounces to 17.05 ounces. Your filling process has an average fill of 16.90 ounces with a standard deviation of 0.04 ounces. Which of the following statements are TRUE? 1 The Cp calculation indicates that the process is capable. II The Cpk calculation is less than the Cp calculation. lll The process is centered, so the Cp calculation should be used. Tonly Dll only bill only I and III II and III

Answer 1

Cp and Cpk measure how consistent our data is around our average performance. The ‘k’ stands for ‘centralizing factor.’ This takes into consideration the fact that our data may not be centered. Cpk tells us what a process is capable of doing in the future, assuming it remains in statistical control.

In the problem, the average fill is within the specifications defined.

Cpk = Min(Cpl,Cpu)

Cpl = (Process Mean – LSL)/(3*Standard Deviation) = (16.9 - 16.75) / (3 x 0.04) = 0.15 / 0.12 = 1.25

Cpu = (USL – Process Mean)/(3*Standard Deviation) = (17.05 - 16.9) / (3 x 0.04) = 0.15 / 0.12 = 1.25

Hence, Cpk = 1.25

Cp = (USL - LSL) / (6 x Standard Deviation) = (17.05 - 16.75) / (6 x 0.04) = 0.3 / 0.24 = 1.25(Means that the process is capable)

This makes the 1st statement correct and 2nd statement incorrect as both Cp & Cpk have same calculation.

From the above calculations, it is also found that the average lies exactly between the specified limits. And hence, the process is centered. When a process is centered we always use Cp calculations, which makes the 3rd statement also correct.

Ans: l and lll