Problem 3: Your company produces wheel rims for heavy-duty industrial vehicles.

Question

Problem 3: Your company produces wheel rims for heavy-duty industrial vehicles. Each rim should weigh exactly 550 lbs. Weights as low as 544 lbs. and as high as 552 lbs. are acceptable. In 2017, the average weight of a wheel rim was 549 lbs. with a standard deviation of 0.75 lbs. What are the 3 standard deviation Cpk statistics for the upper and lower specification limits? What do these values tell you? The CEO intends to launch a new quality initiative which implies the use of six sigma-level quality when evaluating the process. How would this change your results?

Explanation / Answer

Upper Specification Limit (USL) = 552 lbs.
Lower Specification Limit (LSL) = 544 lbs.

Cpk = Min{(USL - Mean)/3, (Mean - LSL)/3} = Min{(552 - 549)/3*0.75, (549 - 544)/3*0.75}
or, Cpk = Min{1.333, 2.222} = 1.333

The two values suggests that -

The minimum value suggests that the sigma level of this process is 3 x 1.333 = 4. In other words, it is a 4 process.

For 6 quality level, the Cpk value will improve from 1.333 to 2.0.

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