A barbecue sauce producer makes their product in an 80-ounce bottle for a specialty store. Their historical process mean has been 80.1 ounces and their tolerance limits are set at 80 ounces plus or minus 1 ounce. What does their process standard deviation need to be in order to sustain a process capability index of 1.5?
A)0.10
B)0.15
C)0.20
D)0.25

Question

Quizplus · Accepted Answer

We first need to calculate the process capability index (Cpk) using the formula:

Cpk = min((USL - mean)/(3 x standard deviation), (mean - LSL)/(3 x standard deviation))

where USL is the upper specification limit (80 + 1 = 81), LSL is the lower specification limit (80 - 1 = 79), and mean is the historical process mean (80.1).

Substituting these values and rearranging the formula to solve for standard deviation, we get:

standard deviation = min((81 - 80.1)/(3 x Cpk), (80.1 - 79)/(3 x Cpk))

Since we want a Cpk of 1.5, we can plug this into the formula and solve for the standard deviation:

standard deviation = min((81 - 80.1)/(3 x 1.5), (80.1 - 79)/(3 x 1.5))

standard deviation = min(0.0333, 0.0333)

standard deviation = 0.0333

Rounding to two decimal places, we get a standard deviation of 0.20. Therefore, the answer is C.

A Barbecue Sauce Producer Makes Their Product in an 80-Ounce