Sam’s Long Life 75-watt light bulbs are designed to have a life of 1,130 hours with tolerances of ±200 hours. The process that makes light bulbs has a mean of 1,010 hours, with a standard deviation of 54 hours. Compute the process capability ratio and the process.

Life of bulb = 1130 ± 200 hours

Lower specification level (LSL) = 1130 - 200

Lower specification level (LSL) = 930 hours

Upper specification level (USL) = 1130 + 200

Upper specification level (USL) = 1330 hours

S.D. of the process (σ) = 54 hours

Process mean (µ) = 1010 hours

Process capability = (USL – LSL)/6σ

Process capability = (1330 - 930)/(6*54)

Process capability =   400/324

Process capability = 1.2346

Process capability index = Minimum [(USL – µ)/3σ, (µ – LSL)/3σ]

= Minimum [(1330 - 1010)/(3*54), (1010 - 930)/(3*54)]

= Minimum [320/162], (80/162)

= Minimum[1.98, 0.49]

Process capability index = 0.429. The process capability > 1. Conclusion is that the process is capable.

Also, Process capability index =1.98. The process capability index < 1 and mean is towards lower specification limit, the bulbs produced will be of shorter life.

Process capability = 1.2346 (>1) indicates the process is capable, Process Capability = 0.49 (<1) indicates that shorter lived bulbs will be generated.