Answer:
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.
