Solve the following mathematical problems:

Consider an example from a maintenance shop. The inter-arrival times of tools at that shop are exponential with an average time of 10 minutes. The length of the service time is assumed to be exponentially distributed, with mean minutes. Estimate the fraction of the day that an operator will be idle.

dsuc.created: 2 years ago | dsuc.updated: 1 year ago

dsuc.updated: 1 year ago

এটি মূলত Cost accounting এর অংক। এই অংকের সমাধানের ক্ষেত্রে আমরা একটি সূত্র ব্যবহার করব যার মাধ্যমে একজন Operator এর Ideal time বের করা সম্ভব হবে।

Average arrival time of tools is 10 minutes

∴ Average arrival rate $a_{r} = \frac{60}{10} = 6 p e r h o u r s$

Again, average service time is 6 minutes

∴ Average service rate $S_{r} = \frac{60}{6} = 10 p e r h o u r s$

∴ Average idle time $= \frac{a_{r}}{S_{r} (S_{r} - a_{r})} = \frac{6}{10 (10 - 6)} = \frac{6}{10 \times 4} = \frac{3}{20} h o u r s$

$a n s . A v e r a g e i d l e t i m e i s \frac{3}{20} h o u r s$

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