Recently, Max’s hired you as a process engineer. Your first assignment is to stu

Question

Recently, Max’s hired you as a process engineer. Your first assignment is to study routine tool wear on the company’s stamping machine.In particular,you will be studying tool- wear patterns for the tools used to create knife blades. In the stamping process,the tooling wears slightly during each stroke ofthe press as the punch shears through the mate- rial. As the tool wears, the part features become smaller. Although the knife has specifications of undersized parts must be scrapped.During their use,tools can be resharpened to enable them to produce parts within speci- fication.To reduce manufacturing costs and simplify machine scheduling,it is critical to pull the tool and perform mainte- nance only when absolutely necessary.It is very important for scheduling, costing, and quality purposes that the average number of strokes,or tool run length,be determined.Know- ing the average number of strokes that can be performed by a tool enables routine maintenance to be scheduled. It is the plant manager’s philosophy that tool maintenance be scheduled proactively.When a tool is pulled unexpectedly, the tool maintenance area may not have time to work on it immediately.Presses without tools don’t run,and if they are not running, they are not making money. As the process engineer studying tool wear,you must develop a prediction for when the tool should be pulled and resharpened. The following information is available from the tool maintenance department. The average number of strokes for a tool is 45,000. The standard deviation is 2,500 strokes. A total of 25 mm can be ground off a punch before it is no longer useful. Each regrind to sharpen a punch removes 1 mm of punch life (25 total regrinds per tool). The cost to regrind is 2 hours of press downtime to remove and reinsert tool,at $300/hour 5 hours of tool maintenance time,at $65/hour 5 hours of downtime while press is not being used,at $300/hour Average wait time for unplanned tool regrind is 15 hours at $300/hour. Because of the large number of strokes per tool regrind, this is considered to be a continuous distribution. The normal curve probability distribution is applicable. Your first assignment as process engineer is to develop a prediction routine for tool wear.As mentioned previously, the plant manager’s chief concern is ensuring planned tool regrinds. Early wearout—and thus an unplanned tool pull—can be caused by a variety of factors, including changes in the hardness of the material being punched,lack of lubrication,the hardness of the tool steel,and the width of the gap between the punch and the die. Key part dimensions are monitored using and R charts. These charts reveal when the tool needs to be reground in order to preserve part quality. When a tool wears out earlier than expected, the tool room may not have time to work on the tool immediately. While waiting for the tool to be reground,the press and its operators will be idle.The plant manager would prefer that tools be pulled early in their wearout phase to avoid the chance of an unexpected tool pull.He would like to pull the tool for regrind at 40,000 strokes. What is the chance that the tool will be pulled for regrind before 40,000 strokes?

Explanation / Answer

As mentioned in the question, normal curve probability distribution is applicable, consider

mu= 45000

sigma=2500

then we have to calculate the probability of tool being pulled for regrind before 40,000 strokes

i.e. probability for strokes < mu-2sigma

=> p = 0.02275 or 2.275%

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