chapter_2/reliability_problem_compare.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Bearing Life(Hours)\n",
    "bearing_life = [1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900]\n",
    "# Bearing Life(Hours) - Probability\n",
    "bearing_probabilities = [0.10, 0.14, 0.24, 0.14, 0.12, 0.10, 0.06, 0.05, 0.03, 0.02]\n",
    "\n",
    "# calculate cumulative probabilities\n",
    "cumulative_probabilities = [bearing_probabilities[0]]\n",
    "for i in range(1, len(bearing_probabilities)):\n",
    "    cumulative_probabilities.append(cumulative_probabilities[i-1] + bearing_probabilities[i])\n",
    "\n",
    "# generate random digit assignments\n",
    "bearing_random_digits = []\n",
    "count = 0\n",
    "for i in range(len(bearing_probabilities)):\n",
    "    bearing_random_digits.append([])\n",
    "    for j in range(int(bearing_probabilities[i]*100)): \n",
    "        bearing_random_digits[i].append(count)\n",
    "        count += 1\n",
    "        \n",
    "\n",
    "# for i in range(len(cumulative_probabilities)):\n",
    "#     print(f\"{cumulative_probabilities[i]:.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "# delay Life(minutes)\n",
    "delay_life = [4 , 6 , 8]\n",
    "# delay Life(minutes) - Probability\n",
    "delay_probabilities = [0.3 , 0.6 , 0.1]\n",
    "\n",
    "# calculate cumulative probabilities\n",
    "cumulative_probabilities = [delay_probabilities[0]]\n",
    "for i in range(1, len(delay_probabilities)):\n",
    "    cumulative_probabilities.append(cumulative_probabilities[i-1] + delay_probabilities[i])\n",
    "\n",
    "# generate random digit assignments\n",
    "delay_random_digits = []\n",
    "count = 0\n",
    "for i in range(len(delay_probabilities)):\n",
    "    delay_random_digits.append([])\n",
    "    for j in range(int(delay_probabilities[i]*10)): \n",
    "        delay_random_digits[i].append(count)\n",
    "        count += 1\n",
    "\n",
    "\n",
    "\n",
    "# for i in range(len(cumulative_probabilities)):\n",
    "#     print(f\"{cumulative_probabilities[i]:.2f}\")\n",
    "\n",
    "# delay_random_digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "# for bearing 1\n",
    "total_hours_of_operation = 30000\n",
    "total_clock_hour = 0\n",
    "total_change = 0    # how many bearing have to change\n",
    "bearing_1 = []\n",
    "bearing_1_delay = []\n",
    "\n",
    "while total_hours_of_operation > total_clock_hour:\n",
    "    total_change += 1\n",
    "    bearing_random_num = random.randint(0 , 99)\n",
    "    delay_random_num = random.randint(0 , 9)\n",
    "    current_clock = 0\n",
    "    current_delay = 0\n",
    "\n",
    "    # find bearing clock from generated random num\n",
    "    for i in range(len(bearing_random_digits)):\n",
    "        if bearing_random_num in bearing_random_digits[i]:\n",
    "            current_clock = bearing_life[i]\n",
    "            break\n",
    "\n",
    "    bearing_1.append(current_clock)\n",
    "    total_clock_hour += current_clock\n",
    "\n",
    "\n",
    "    # find delay from generated random num \n",
    "    for i in range(len(delay_random_digits)):\n",
    "        if delay_random_num in delay_random_digits[i]:\n",
    "            current_delay = delay_life[i]\n",
    "            break\n",
    "\n",
    "    bearing_1_delay.append(current_delay)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "# for bearing 2\n",
    "total_hours_of_operation = 30000\n",
    "total_clock_hour = 0\n",
    "bearing_2 = []\n",
    "bearing_2_delay = []\n",
    "\n",
    "while total_hours_of_operation > total_clock_hour:\n",
    "    total_change += 1\n",
    "    bearing_random_num = random.randint(0 , 99)\n",
    "    delay_random_num = random.randint(0 , 9)\n",
    "    current_clock = 0\n",
    "    current_delay = 0\n",
    "\n",
    "    # find bearing clock from generated random num\n",
    "    for i in range(len(bearing_random_digits)):\n",
    "        if bearing_random_num in bearing_random_digits[i]:\n",
    "            current_clock = bearing_life[i]\n",
    "            break\n",
    "\n",
    "    bearing_2.append(current_clock)\n",
    "    total_clock_hour += current_clock\n",
    "\n",
    "\n",
    "    # find delay from generated random num \n",
    "    for i in range(len(delay_random_digits)):\n",
    "        if delay_random_num in delay_random_digits[i]:\n",
    "            current_delay = delay_life[i]\n",
    "            break\n",
    "\n",
    "    bearing_2_delay.append(current_delay)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "# for bearing 3\n",
    "total_hours_of_operation = 30000\n",
    "total_clock_hour = 0\n",
    "bearing_3 = []\n",
    "bearing_3_delay = []\n",
    "\n",
    "while total_hours_of_operation > total_clock_hour:\n",
    "    total_change += 1\n",
    "    bearing_random_num = random.randint(0 , 99)\n",
    "    delay_random_num = random.randint(0 , 9)\n",
    "    current_clock = 0\n",
    "    current_delay = 0\n",
    "\n",
    "    # find bearing clock from generated random num\n",
    "    for i in range(len(bearing_random_digits)):\n",
    "        if bearing_random_num in bearing_random_digits[i]:\n",
    "            current_clock = bearing_life[i]\n",
    "            break\n",
    "\n",
    "    bearing_3.append(current_clock)\n",
    "    total_clock_hour += current_clock\n",
    "\n",
    "\n",
    "    # find delay from generated random num \n",
    "    for i in range(len(delay_random_digits)):\n",
    "        if delay_random_num in delay_random_digits[i]:\n",
    "            current_delay = delay_life[i]\n",
    "            break\n",
    "\n",
    "    bearing_3_delay.append(current_delay)\n",
    "\n",
    "\n",
    "\n",
    "# print(bearing_1)\n",
    "# print(bearing_2)\n",
    "# print(bearing_3)\n",
    "# print(\"\\n\")\n",
    "# print(bearing_1_delay)\n",
    "# print(bearing_2_delay)\n",
    "# print(bearing_3_delay)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "maxlen = max( len(bearing_2) , len(bearing_1) , len(bearing_3)  )\n",
    "two_down = 0\n",
    "three_down = 0\n",
    "try:\n",
    "    for i in range(maxlen):\n",
    "        if (bearing_1[i] == bearing_2[i] == bearing_3[i]):\n",
    "            three_down += 1\n",
    "            max_delay = max(bearing_3_delay[i] , bearing_2_delay[i] , bearing_1_delay[i])\n",
    "            if bearing_3_delay[i] != max_delay:\n",
    "                bearing_3_delay[i] = 0\n",
    "            if bearing_2_delay[i] != max_delay:\n",
    "                bearing_2_delay[i] = 0\n",
    "            if bearing_1_delay[i] != max_delay:\n",
    "                bearing_1_delay[i] = 0\n",
    "        elif bearing_1[i] == bearing_2[i]:\n",
    "            two_down += 1\n",
    "            if bearing_1_delay[i] < bearing_2_delay[i]:\n",
    "                bearing_1_delay[i] = 0\n",
    "            else:\n",
    "                bearing_2_delay[i] = 0\n",
    "        elif bearing_3[i] == bearing_2[i]:\n",
    "            two_down += 1\n",
    "            if bearing_3_delay[i] < bearing_2_delay[i]:\n",
    "                bearing_3_delay[i] = 0\n",
    "            else:\n",
    "                bearing_2_delay[i] = 0\n",
    "        elif bearing_1[i] == bearing_3[i]:\n",
    "            two_down += 1\n",
    "            if bearing_1_delay[i] < bearing_3_delay[i]:\n",
    "                bearing_1_delay[i] = 0\n",
    "            else:\n",
    "                bearing_3_delay[i] = 0\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "except:\n",
    "    pass\n",
    "\n",
    "\n",
    "# print(two_down , three_down)\n",
    "# print(\"\\n\")\n",
    "# print(bearing_1)\n",
    "# print(bearing_2)\n",
    "# print(bearing_3)\n",
    "# print(\"\\n\")\n",
    "# print(bearing_1_delay)\n",
    "# print(bearing_2_delay)\n",
    "# print(bearing_3_delay)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total repairman delay time = 346 minutes\n",
      "Time spent in bearing replacement = 1300 minutes\n",
      "Total downtime = 1646 minutes\n",
      "Cost of downtime = Rs. 8230\n",
      "Cost of repairman = Rs. 541.6666666666666\n",
      "\n",
      "\n",
      "Total bearing replaced = 68\n",
      "Cost of bearing = Rs. 1360\n",
      "\n",
      "\n",
      "Total estimated cost = Rs. 10131.666666666666\n"
     ]
    }
   ],
   "source": [
    "# 20 minutes to change one bearing\n",
    "# Downtime of the machining center costs Rs. 5 per minute\n",
    "# direct on job cost of the repairman is Rs. 25 per hour \n",
    "# at a time cost of one bearing is Rs. 20.\n",
    "# at a time cost of two bearing is Rs. 30.\n",
    "# at a time cost of three bearing is Rs. 40.\n",
    "\n",
    "one_bearing_change_time_minutes = 20\n",
    "two_bearing_change_time_minutes = 30\n",
    "three_bearing_change_time_minutes = 40\n",
    "cost_of_downtime_per_minutes = 5\n",
    "cost_of_repairman_per_hour = 25\n",
    "cost_of_one_bearing = 20\n",
    "\n",
    "total_repairman_delay_time = sum(bearing_1_delay) + sum(bearing_2_delay) + sum(bearing_3_delay)\n",
    "print(\"Total repairman delay time =\" , total_repairman_delay_time , \"minutes\")\n",
    "time_spent_in_bearing_replacement = (total_change * one_bearing_change_time_minutes) - (two_down * (two_bearing_change_time_minutes - one_bearing_change_time_minutes)) - (three_down * (three_bearing_change_time_minutes - one_bearing_change_time_minutes))\n",
    "print(\"Time spent in bearing replacement =\", time_spent_in_bearing_replacement , \"minutes\")\n",
    "total_downtime = total_repairman_delay_time + time_spent_in_bearing_replacement\n",
    "print(\"Total downtime =\" , total_downtime , \"minutes\")\n",
    "\n",
    "cost_of_downtime = cost_of_downtime_per_minutes*total_downtime\n",
    "print(\"Cost of downtime = Rs.\",  cost_of_downtime)\n",
    "cost_of_repairman = time_spent_in_bearing_replacement*cost_of_repairman_per_hour/60\n",
    "print(\"Cost of repairman = Rs.\",  cost_of_repairman)\n",
    "\n",
    "print(\"\\n\")\n",
    "print(\"Total bearing replaced =\", total_change)\n",
    "cost_of_bearing = cost_of_one_bearing*total_change\n",
    "print(\"Cost of bearing = Rs.\",  cost_of_bearing)\n",
    "\n",
    "print(\"\\n\")\n",
    "total_estimated_cost_old_policy = cost_of_repairman+cost_of_bearing+cost_of_downtime\n",
    "print(\"Total estimated cost = Rs.\",  total_estimated_cost_old_policy)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For new policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "# for bearing 1 , 2 , 3\n",
    "total_hours_of_operation = 30000\n",
    "total_clock_hour = 0\n",
    "total_delay_minutes = 0\n",
    "total_change = 0    # how many bearing have to change\n",
    "\n",
    "while total_hours_of_operation > total_clock_hour:\n",
    "    total_change += 1\n",
    "    bearing_random_num_1 = random.randint(0 , 99)\n",
    "    bearing_random_num_2 = random.randint(0 , 99)\n",
    "    bearing_random_num_3 = random.randint(0 , 99)\n",
    "    delay_random_num = random.randint(0 , 9)\n",
    "    current_clock = 0\n",
    "    current_delay = 0\n",
    "\n",
    "    # find bearing 1 clock from generated random num\n",
    "    for i in range(len(bearing_random_digits)):\n",
    "        if bearing_random_num_1 in bearing_random_digits[i]:\n",
    "            current_clock = bearing_life[i]\n",
    "            break\n",
    "    \n",
    "    # find bearing 2 clock from generated random num\n",
    "    for i in range(len(bearing_random_digits)):\n",
    "        if bearing_random_num_2 in bearing_random_digits[i]:\n",
    "            current_clock = min(bearing_life[i] , current_clock)\n",
    "            break\n",
    "\n",
    "    # find bearing 3 clock from generated random num\n",
    "    for i in range(len(bearing_random_digits)):\n",
    "        if bearing_random_num_3 in bearing_random_digits[i]:\n",
    "            current_clock = min(bearing_life[i] , current_clock)\n",
    "            break\n",
    "\n",
    "\n",
    "    total_clock_hour += current_clock\n",
    "\n",
    "\n",
    "    # find delay from generated random num \n",
    "    for i in range(len(delay_random_digits)):\n",
    "        if delay_random_num in delay_random_digits[i]:\n",
    "            current_delay = delay_life[j]\n",
    "            break\n",
    "\n",
    "\n",
    "    total_delay_minutes += current_delay\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total repairman delay time = 108 minutes\n",
      "Time spent in bearing replacement = 1080 minutes\n",
      "Total downtime = 1188 minutes\n",
      "Cost of downtime = Rs. 5940\n",
      "Cost of repairman = Rs. 450.0\n",
      "\n",
      "\n",
      "Total bearing replaced = 81\n",
      "Cost of bearing = Rs. 1620\n",
      "\n",
      "\n",
      "Total estimated cost = Rs. 8010.0\n"
     ]
    }
   ],
   "source": [
    "# 20 minutes to change one bearing\n",
    "# Downtime of the machining center costs Rs. 5 per minute\n",
    "# direct on job cost of the repairman is Rs. 25 per hour \n",
    "# cost of a bearing is Rs. 20.\n",
    "\n",
    "three_bearing_change_time_minutes = 40\n",
    "cost_of_downtime_per_minutes = 5\n",
    "cost_of_repairman_per_hour = 25\n",
    "cost_of_one_bearing = 20\n",
    "\n",
    "print(\"Total repairman delay time =\" , total_delay_minutes , \"minutes\")\n",
    "print(\"Time spent in bearing replacement =\", total_change*three_bearing_change_time_minutes , \"minutes\")\n",
    "print(\"Total downtime =\" , total_delay_minutes+(total_change*three_bearing_change_time_minutes) , \"minutes\")\n",
    "\n",
    "cost_of_downtime = cost_of_downtime_per_minutes*(total_delay_minutes+(total_change*three_bearing_change_time_minutes))\n",
    "print(\"Cost of downtime = Rs.\",  cost_of_downtime)\n",
    "cost_of_repairman = total_change*three_bearing_change_time_minutes*cost_of_repairman_per_hour/60\n",
    "print(\"Cost of repairman = Rs.\",  cost_of_repairman)\n",
    "\n",
    "print(\"\\n\")\n",
    "print(\"Total bearing replaced =\", total_change*3)\n",
    "cost_of_bearing = cost_of_one_bearing*total_change*3\n",
    "print(\"Cost of bearing = Rs.\",  cost_of_bearing)\n",
    "\n",
    "print(\"\\n\")\n",
    "total_estimated_cost_new_policy = cost_of_repairman+cost_of_bearing+cost_of_downtime\n",
    "print(\"Total estimated cost = Rs.\",  total_estimated_cost_new_policy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saves = 20.94094423424905 %\n"
     ]
    }
   ],
   "source": [
    "print(\"Saves =\" ,(total_estimated_cost_old_policy - total_estimated_cost_new_policy) / total_estimated_cost_old_policy * 100 , \"%\")"
   ]
  }
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