Question

B) Crunchy Potato Chip plant sells packaged chips with a printed net weight of 825 grams. Their packaging specification limits are +/- 8 grams of this published fill weight. Currently the process is running at a mean of 822 grams with a standard deviation of 1.59 grams. The firm requires a process capability ration of at least 1.33 to be deemed "capable." Is the process capable? Is an adjustment needed?

Answer 1

Given that,

USL = 825+8 = 833

LSL = 825-8 = 817

Process mean, m = 822

Process SD, s = 1.59

Process capability index, Cpk = MIN(Cpu, Cpl)

Cpu = (USL-m)/3s = (833-822)/(3*1.59) = 2.31

Cpl = (m-LSL)/3s = (822-817)/(3*1.59) = 1.05

Cpk = MIN(2.31, 1.05) = 1.06

Process capability ratio, Cp = (USL-LSL)/6s = (833-817)/(6*1.59) = 1.68

We see that Cpk is less than 1.33, but Cp is greater than 1.33 . Therefore, currently process is not capable of producing as per specifications, because it is not centered. However it needs adjustment. After adjustment of the mean, process has potential to become capable of producing within the specifications.