Question

1. Sam’s Long Life 75-watt light bulbs are designed to have a life of 1,125 hours with tolerance of ± 210 hours. A recent representative sample from the process that makes these light bulbs revealed a mean of 1,050 hours, with a standard deviation of 55 hours. Compute

1. Compute the process capability ratio and the process capability index, and comment on the overall capability of the process
2. Explain to what extent the process for producing Sam’s Long Life 75-watt light bulbs would have to be improved to achieve 6-sigma quality.

Answer 1

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Specification: life of bulb = 1125 ± 210 hours

Lower specification level (LSL) = 1125 - 210 = 915 hours

Upper specification level (USL) = 1125 + 210 = 1335 hours

Standard deviation of the process = σ = 55 hours

Process mean = µ = 1050 hours

Process capability = (USL – LSL)/6σ = (1335 – 915)/(6 x 55) = 0.785

Process capability = 0.79

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

= Minimum [(1335 – 1050)/(3*55), (1050 – 915)/(3*55)] = Minimum[1.73, 0.82]

Process capability index =0.82

The process capability is lesser than 1, thus the process is incapable.

Since the process capability index is less than 1 and mean is towards lower specification limit, the bulbs produced will be of shorter life.

While Cp = 0.79 (<1) indicates the process is incapable, Cpk = 0.82 (<1) indicates that shorter lived bulbs will be generated.

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