Question

Tyler Apiaries sells bees and beekeeping supplies. Bees​ (including a​ queen) are shipped in special packages according to weight. Suppose Tyler changes its processes so that the average package weight is 1.9​kg, with a new standard deviation of0.14 kg. Tyler markets the packages of bees as weighing 1.8 ​kg, and the lower and upper tolerance limits are 1.1 kg and 2.5 ​kg, respectively. Calculate the process capability index for the weight of the bee packages. Is Tyler able to meet the tolerance​ limits?

Answer 1

Answer: 0.143

Explanation:

Given the following :

Average package weight(m) = 1.9kg

Standard deviation(sd) = 1.4kg

Upper Tolerance Limit (UTL) = 2.5kg

Lower Tolerance limit (LTL) = 1.1kg

Cpk = min[( average weight -Lower Tolerance Limit / 3 (standard deviation) , (UTL- average weight / 3(Standard Deviation)]

Cpk = min[( 1.9 - 1.1 / 3 (1.4)) , (2.5 - 1.9 / 3(1.4))]

Cpk = min[(0.8 / 4.2), (0.6 / 4.2)]

Cpk = min[0.190, 0.143])

Hence,

Process capability index = 0.143