I am trying to simulate running of two manufacturing lines (Line A and Line B).Their time to failure follows Weibull distribution(shape = 0.7, scale = 12 (mins)). Line A and Line B both produces at rate of 100 products/min. From real world scenario, if any of lines fails, I want to increase rate of other line (say – 120 products/min) till the time failed line has not repaired.
Challenge: With increase in rate, chances of failure increases, hence, scale parameter changes (e.g for rate of 120 products/min, scale parameter changes from 12 mins to 10 mins). I want to model this change in distribution parameter in simulation.
Example :
- Line A and Line B starts running at time 0.
- Generate random number using weibull distribution for their time to failure (TTF) – Line A : 15 mins and Line B : 20 mins.
- Line A failed at 15 mins and got repaired at 20 mins. For this 5 mins, Line B ran at increased speed.
- At t= 15 min, generate a random number using weibull (with changed parameter) to get next TTF. The process repeats till the simulation time.
Currently I am using Python Simpy to code the logic but can’t find a way to model this. Any help or reference would be very helpful. Here is my try but i am definitely missing something.
import simpy import matplotlib.pyplot as plt import numpy as np from scipy.stats import weibull_min class Machine(object): def __init__(self, env, name,scale_parameter,shape_parameter, mean_repair_time,std_repair_time,increased_rate): self.env = env self.name = name self.scale_parameter = scale_parameter self.shape_parameter = shape_parameter self.mean_repair_time = mean_repair_time self.std_repair_time = std_repair_time self.increased_rate = increased_rate self.broken = False self.processing_list = [0,] self.machine_status = 1 self.process = env.process(self.run()) # Start the failure process env.process(self.check_machines_status()) def run(self): """ Run as long as the simulation runs. """ while True: try: yield self.env.timeout(self.mean_time_to_failure()) self.processing_list.append(self.env.now) print(f'{self.env.now:.2f} {self.name} is in failure.') trial_resource.get(1) yield self.env.timeout(self.mean_time_to_repair()) print(f'{self.env.now:.2f} {self.name} is repaired.') self.processing_list.append(env.now) trial_resource.put(1) except simpy.Interrupt: self.machine_status = 0 yield self.env.timeout(self.updated_mean_time_to_failure()) print(f'{self.env.now:.2f} {self.name} is in updated failure.') #trial_resource.get(1) self.broken = True yield self.env.timeout(self.mean_time_to_repair()) print(f'{self.env.now:.2f} {self.name} is in updated repaired.') trial_resource.put(1) self.machine_status =1 def check_machines_status(self): """Periodically check the status of running machines. If any machine fails interrupt the process""" while True: print(self.env.now,trial_resource.level) print(self.name) if trial_resource.level < trial_resource.capacity and self.broken == False and self.machine_status == 1: # Only break the machine if it is currently working. self.process.interrupt() print('Machine running process interrupted %d' % env.now) yield env.timeout(1) def mean_time_to_failure(self): x = int(weibull_min.rvs(self.shape_parameter, loc=0, scale= self.scale_parameter, size=1).tolist()[0]) if x == 0: x = 1 return x def updated_mean_time_to_failure(self): correction_factor = (1-self.increased_rate)/100 x = int(weibull_min.rvs(self.shape_parameter*correction_factor, loc=0, scale= self.scale_parameter, size=1).tolist()[0]) if x == 0: x = 1 return x def mean_time_to_repair(self): x = int(np.random.lognormal(self.mean_repair_time,self.std_repair_time)) if x ==0: x =1 return x env = simpy.Environment() trial_resource = simpy.Container(env,init=3,capacity=3) machine_1 = Machine(env, 'M1', 12, 0.65, 0.51,1,10) machine_2 = Machine(env, 'M2', 14, 0.65, 0.51,1,10) machine_3 = Machine(env, 'M3', 8, 0.65, 0.51,1,10) env.run(until = 12) print(machine_1.processing_list) print(machine_2.processing_list) print(machine_3.processing_list)
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Answer
This solution can handle more then 2 machines. When a machine breaks it sends a message to all of the other machines notifying them of the break down. A machine also sends a notification when it gets fixed. Each machine tracks how many machines are broken and speeds up production if 1 or more machines is broken. Time till failure (ttf) is also sped up. when rates change, the progress of a current in progress part is factored in to calculating the new finish time. The interrupt is used to both trigger a breakdown, but to also reset when a work in progress will finish. also check out the machine shop example in the docs. I ran out of time to work on this so it may not be perfect
""" Machine shop example where machines change their production rate and break down rates in response to other machines breaking down or getting fixed If one machine breaks down, the remaining machines will speed up until all machines are fixed speeding up the production rate also speeds up the time till failure ttf rates can change in the middle of making a part Programmmer: Michael R. Gibbs """ import simpy import random class Machine(): """ Machine that makes parts. Machine breaks down at ramdom time The machine has a normal mode, and a fast mode Machine speeds up when it receives a message that another machine has broken down and slows back down when it receives messages that all broken machines are fixed env: simulation environment id: name of the machine rate: number of parts per time unit (normal mode) fast_rate: number of parts per time unit (fast mode) ttf_gen: zero param func to generate ttf (normal mode) fast_ttf_gen: zero param func to generate ttf (fast mode) """ def __init__(self, env, id, rate, fast_rate, ttf_gen, fast_ttf_gen): self.id = id self.env = env self.rate = rate self.fast_rate = fast_rate self.ttf_gen = ttf_gen self.fast_ttf_gen = fast_ttf_gen self.broken = False self.fast_mode = False self.remaining_time = 0 self.current_rate = self.rate self.mach_list = [] self.broke_cnt = 0 # start the part making, an the count down till failure self.make_parts_proc = self.env.process(self.make_parts()) self.breakdown_proc = self.env.process(self.gen_breakdown()) def make_parts(self): """ Main loop to manufacture parts interupts are used to trigger updates when rates change and when breakdowns occure """ while True: if self.remaining_time <= 0: # starting a new part print(f'{self.env.now:.2f}: mach: {self.id} has started a part') # need to store times so other methods can upate # the procesing state self.total_part_time = 1 / self.current_rate self.remaining_time = self.total_part_time while self.remaining_time > 0: # need to loop incase get inturrupted # while in the middle of making a part try: self.part_start_time = self.env.now # used to track progress yield self.env.timeout(self.remaining_time) # got here without being interupted, done with part self.remaining_time = 0 except simpy.Interrupt: # can get inturpted because processing rate changed # or a breakdown has happend # if rate changed, we are using the inturput to update # the processing timeout if self.broken: # processing is interuped, fix machine # update processing progress self.remaining_time -= (self.env.now - self.part_start_time) print(f'{self.env.now:.2f}: mach: {self.id} has broken down') # notify other machines that this machine has broke for m in self.mach_list: m.someone_broke(self) # time out for fixing yield self.env.timeout(5) # notify other machines that this machine is fixed for m in self.mach_list: m.someone_fixed(self) print(f'{self.env.now:.2f}: mach: {self.id} has been fixed') # start a new breakdown count down self.breakdown_proc = self.env.process(self.gen_breakdown()) self.broken = False print(f'{self.env.now:.2f}: mach: {self.id} has finish a part') def gen_breakdown(self): """ counts down to failure and uses a interrupt to stop processing and start repairs using class properties instead of local variables so other methods can update the countdown state of ttf """ if not self.broken: # get breakdown based on current fast mode if self.fast_mode: self.total_ttf = self.fast_ttf_gen() else: self.total_ttf = self.ttf_gen() self.remaining_ttf = self.total_ttf while self.remaining_ttf > 0: self.ttf_start = self.env.now print(f'{self.env.now:.2f}: mach: {self.id} has {self.remaining_ttf} till breakdown') try: yield self.env.timeout(self.remaining_ttf) # failure has orrured self.broken = True self.make_parts_proc.interrupt() self.remaining_ttf = 0 except simpy.Interrupt: # the state has been updated # the timeout has been interupted # so it can be restarted with new state print(f'{self.env.now:.2f}: mach: {self.id} updating ttf {self.remaining_ttf}') print(f'{self.env.now:.2f}: mach: {self.id} ttf gen exit') def someone_broke(self, mach): """ Another machine is notifing this machine that it has broken and this machine needs to change to fast mode, if not already in fast mode """ self.broke_cnt += 1 print(f'{self.env.now:.2f}: mach: {self.id} received mess that mach: {mach.id} has broke, broke cnt: {self.broke_cnt}') if not self.fast_mode: self.fast_mode = True # update the ttf based on the fast mode ttf func # keep the same progress so if we were 90% of of the # old ttf, then set things so we are still 90% of new ttf # update with the last bit of progress self.remaining_ttf -= self.env.now - self.ttf_start per_ttf_left = (self.remaining_ttf/self.total_ttf) # update based on fast ttf self.total_ttf = self.fast_ttf_gen() self.remaining_ttf = per_ttf_left * self.total_ttf if self.remaining_ttf <= 0: # special case when notification happens at same time as breakdown self.remaining_ttf = 0.001 # update the part processing state # update the last bit of processing progress self.remaining_time -= self.env.now - self.part_start_time # update state based on new processing fast rate # like ttf keep the same perenct of progress self.current_rate = self.fast_rate old_total = self.total_part_time self.total_part_time = 1 / self.current_rate per_left = self.remaining_time / old_total self.remaining_time = self.total_part_time * per_left if not self.broken: # if broken nothing to interrupt # new states will used when machine # is fixed and processing starts up again self.breakdown_proc.interrupt() self.make_parts_proc.interrupt() def someone_fixed(self, mach): """ Another machine is notifing this machine that it has been fixed and this machine needs to change to normal mode, if there are no more broken machines """ self.broke_cnt -= 1 print(f'{self.env.now:.2f}: mach: {self.id} received mess that mach: {mach.id} is fixed, broke cnt: {self.broke_cnt}') # only change if all machines are fixed and broke cnt is 0 if self.broke_cnt <= 0: self.broke_cnt = 0 if self.fast_mode: self.fast_mode = False # update the ttf based on the normal mode ttf func # keep the same progress so if we were 90% of of the # old ttf, then set things so we are still 90% of new ttf # update with the last bit of progress self.remaining_ttf -= self.env.now - self.ttf_start per_ttf_left = (self.remaining_ttf/self.total_ttf) self.total_ttf = self.ttf_gen() self.remaining_ttf = per_ttf_left * self.total_ttf if self.remaining_ttf <= 0: # special case when notifcation happens at breakdown time self.remaining_ttf = 0.001 # update state based on new processing normal rate # like ttf keep the same perenct of progress self.remaining_time -= self.env.now - self.part_start_time self.current_rate = self.rate old_total = self.total_part_time self.total_part_time = 1 / self.current_rate per_left = self.remaining_time / old_total self.remaining_time = self.total_part_time * per_left if not self.broken: # if broken nothing to interrupt # new states will be used when machine # is fixed and processing starts up again self.breakdown_proc.interrupt() self.make_parts_proc.interrupt() def set_mach_list(self, mach_list): """ set the list of machines to be notified if this machine breaks down, or is fixed """ self.mach_list = mach_list # ttf generator function # # by wrapping a dist in a lambda I # created create a 0 param function # that I can pass to the Machine class # To change the dist I just need to # update the lambda, no hard codeing # of dist func parameters in the Machine # class code ttf = lambda : random.randint(8,10) fast_ttf = lambda: random.randint(5,7) # create sim env = simpy.Environment() mach_list = [] machines_cnt = 2 # can be more then 2 for i in range(1, machines_cnt + 1): m = Machine(env, i, 5, 8, ttf, fast_ttf) mach_list.append(m) # build list of machines to notify # when a machine breaks or gets fixed for m in mach_list: # filter out the current machine # don't want to send to self other_m = mach_list.copy() other_m.remove(m) m.set_mach_list(other_m) env.run(until = 50) print("end of simulation")