Question

A barbecue sauce producer sells their product in a 20-ounce bottle. Their current process mean is 19.60 ounces with a standard deviation of 0.3 ounces. If their tolerance limits are set at 20 ounces plus or minus 1 ounce, what is the process capability index of the bottle filling process? Group of answer choices

.89

1.11

.67

1

Answer 1

Answer) 0.67

Given that,

Mean = 19.6 ounces

Standard Deviation = 0.3 ounces

Tolerance limits = 20  ± 1

Therefore, on the basis of tolerance limits,

USL = 20 + 1 = 21

LSL = 20 - 1 = 19

Process Capability Index, Cpk = Min (((USL - Mean) / (3 x Standard Deviation)) , (Mean - LSL) / (3 x Standard Deviation)))

= Min (((21 - 19.6) / (3 x 0.3)) , (19.6 - 19) / (3 x 0.3)))

= Min ((1.4 / 0.9) , (0.6 / 0.9))

= Min (1.555 , 0.666)

= 0.666

= 0.67 (rounding off to nearest two decimal places)

Cpk = 0.67

Therefore, Process Capability Index of the bottle filling process, Cpk is 0.67