A Cutting Tool Has a Lifetime That Is Normally Distributed

question 32

Essay

A cutting tool has a lifetime that is normally distributed with an average life of 400 hours and a standard deviation of 50 hours.Present policy is preventive maintenance which requires changing all cutting tools at the end of each month.Current operations are two shifts per day and 7 working hours per shift.At 20 days per month,each cutting tool is in use 280 hours per month.(All cutting tools that fail are simply shut down until the end of the month sweep).The variable costs of replacement under the current policy are $8 per tool plus installation labor of $6 per tool.There are 40 tools in use.
-What is the estimated annual cost of replacements under the current policy?

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Definitions:

Muscle Spindles

Sensory receptors within the belly of a muscle that primarily detect changes in the length of the muscle and send signals to the central nervous system.

Superficial Pain

Pain that occurs on the skin or surface tissues, typically sharp but not deep-seated.

Visceral Pain

Pain arising from the internal organs, often described as a deep squeeze, pressure, or ache.

Mechanoreceptors

Sensory receptors sensitive to mechanical pressures or changes, involved in sensations such as touch, pressure, and sound.