Question

Sam’s Long Life 75-watt light bulbs are designed to have a life of 1,135 hours with tolerances of ±215 hours. The process that makes light bulbs has a mean of 1,030 hours, with a standard deviation of 50 hours. Compute the process capability ratio and the process capability index, and comment on the overall capability of the process. (Round answers to 2 decimal places, e.g. 2.75.) Process capability ratio Process capability index While Cp = indicates the process: is or is not? capable, Cpk = indicates that: Shorter lived or long lived? bulbs will be generated.

Answer 1

Answer:

Process capability ratio, Cp = 1.43, Process capability index, Cpk = 0.73

While Cp =1.43 indicates the process is capable ,

Cpk=0.73 indicates that shorter lived bulbs will be generated

Explanation:

It is given that the bulbs are designed to have life of 1,135 hours with tolerances of ±215 hours.

Hence USL= 1135+215 = 1350 hours

LSL = 1135-215 = 920 hours

Standard deviation, = 50 hours

Mean = 1030 hours

Process capability ratio, Cp = (USL-LSL)/6 = (1350-920)/(6x50)= 1.43

When Cp is greater than 1, it means the process is capable of meeting the design specifications.

Process capability index, Cpk = min [(USL-mean)/3, (mean-LSL)/ 3]

                               =min [(1350-1030)/(3*50), (1030-920)/(3*50)]

                               = min[ 2.1333, 0.7333]

Cpk = 0.7333 = 0.73

When Cpk is 0.73 which is less than 1, it means that the process is not capable of meeting the design specifications. The process mean is off center and has shifted towards the lower specification limit. Hence shorter lived bulbs will be generated.