A barbecue sauce producer sells their product in a 20-ounce bottle. Their current process mean is 19.9 ounces with a standard deviation of 0.33 ounces. If their tolerance limits are set at 20 ounces plus or minus 1 ounce, what is the process capability index/ratio of the bottle filling process?
Answer:
We have, Mean µ = 19.90 ounces
Standard deviation σ = 0.33 ounces
Upper specification limit, USL = 20 ounces + 1 ounces = 21 ounces
Lower specification limit, LSL = 20 ounces - 1 ounces = 19 ounces
The process capability index,
Cp = (USL –LSL)/6σ = (21 -19) /6*0.33 = 1.01
Cpk= Min [(Mean – LSL)/3 *σ, (USL – Mean)/3* σ]
= min [(19.90 – 19)/ 3* 0.33, (21 – 19.90)/ 3 * 0.33]
= min [(0.909, 1.11] = 0.909
Cpk =0.909 (less than 1)
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