In the process of producing engine valves, the valves are subjected to a first g

Question

In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 74% of the valves meet the specification, 19% are reground, and 7% are scrapped. Furthermore, assume that of those valves that are reground, 90% meet the specification, and 10% are scrapped.

a. Given that a valve is scrapped, what is the probability that it was ground twice?

b. Given that a valve meets the specification (after either the first or second grind), what is the probability that it was ground twice?

c. Given that a valve meets the specification, what is the probability that it was ground only once?

Explanation / Answer

The three questions would be calculated as follows: -

a) 7% initially scrapped + [19%*10%]=7+1.9=8.9%

1.9 (grounded twice)/8.9 (scrapped)=0.2135 or 21.35%

b) 74% meet specification (initial run) + [19%*90%]=74+17.1=91.1%

17.1 (grounded twice)/91.1=0.1877 or 18.77%

c) 74/91.1=0.8123 or 81.23%

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