Question

SEL makes Fiber optic cables. The mean for the length of the fiber optic cables is 30 feet. SEL wants the USL to be 2.0 standard deviations above the mean, and the LSL to be 1.5 standard deviations below the mean. If it costs $2.50 to fix any fiber optic cable that is out of spec and SEL produces 20,000 fiber optic cables per year, what is the expected annual cost to fix these fiber optic cables? (in intermediate steps, keep 4 decimals)

Answer 1

Let us use the normal distribution to find out the percentage of observations falling outside the UCL and LCL

In the above normal distribution, we need to find out the percentage of observations outside the UCL and LCL. This is found out by finding the area of the shaded grey portion.

From the z table, P(z < -1.5) = 0.0668

P(z > 2) = 1 - 0.9772 = 0.0228

Hence, percentage of observations outside the control limits are (0.0668 + 0.0228)*100% = 8.96%

Hence, Number of items to be fixed = 8.96% of 20000 = 1792

Annual Cost to fix 1792 cables = 1792 * 2.5 = $4,480