Assume that the probability of producing a nonconforming item in certain process

Question

Assume that the probability of producing a nonconforming item in certain process is P = 5%. If an inspector is placed at the end of the inspection line, all the nonconforming items can be detected and removed. However, the inspector is paid 40 QAR per hour. The inspector can inspect units in the process at the rate of 30 unit per hour. If NO INSPECTOR is used and nonconforming products are allowed to pass to the customer, there is a cost of 15 QAR per unit to be replaced later on. SHOULD AN INSPECTOR BE HIRED?

Explanation / Answer

in 1 hour

30 units are processed

if inspector is hired - total cost in 1 hour = 40

if inspector is not hired

then expected noncorforming item in 1 hour = 0.05 * 30 = 1.5 {as p =5 % = 0.05}

cost of replacement = 15 * 1.5 = 22.5 QAR

since 40 > 22.5 , inspector should not be hired

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