Relibilitydataplotweibull.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reliability Data Plot for Weibull Distribution Using Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " * In Relibility, we can Test to see if a common distribution will be useful a model by using a reliability data plot. \n",
    " * This will help us visualize if the distribution of the data will fit the model\n",
    " * When plotting failure data in reliability we use exponential, weibull, normal and lognormal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *In an experiment Twenty test devices are stressed to investigate dielectric breakdown strength. The test was concluded at 600 hours at which time 18 units had failed. The data is shown in Table below.* "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>event</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.69</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.94</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.12</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.79</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.28</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>9.31</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9.95</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12.90</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>12.93</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>21.33</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>64.56</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>69.66</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>108.38</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>124.88</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>157.02</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>190.19</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>250.55</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>552.87</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>600.00</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>600.00</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      time  event\n",
       "0     0.69      1\n",
       "1     0.94      1\n",
       "2     1.12      1\n",
       "3     6.79      1\n",
       "4     9.28      1\n",
       "5     9.31      1\n",
       "6     9.95      1\n",
       "7    12.90      1\n",
       "8    12.93      1\n",
       "9    21.33      1\n",
       "10   64.56      1\n",
       "11   69.66      1\n",
       "12  108.38      1\n",
       "13  124.88      1\n",
       "14  157.02      1\n",
       "15  190.19      1\n",
       "16  250.55      1\n",
       "17  552.87      1\n",
       "18  600.00      0\n",
       "19  600.00      0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Basic libriaries to be used for the experiment\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "from lifelines import WeibullFitter\n",
    "from lifelines.plotting import plot_lifetimes\n",
    "\n",
    "dat=pd.read_csv('Desktop/data1.csv') # reading the data\n",
    "display(dat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *In reliability censored data indicates that a failure did not occur. If you observe the event column in the table, the last 2 entries are 0. The reason because those devices did not fail during the test (lifetime distribution) of the experiment after 600 hours of runtime.*\n",
    "\n",
    "### *The life plot below will give a careful illustration of the experiment runtime*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    " # lifelines plot of the dataset to show failed and survived equipment\n",
    "#df=dat.sample(25)  # random sampling of data\n",
    "plt.figure(figsize=[12,7])\n",
    "plot_lifetimes(dat['time'])\n",
    "plt.axvline(x=552.87, color='b')  # creating a vertical line to indicate last failure point.\n",
    "plt.title('Equipment failure plot')\n",
    "plt.xlabel('time in hours')\n",
    "plt.ylabel('equipment')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *Next we would use ordinary least square regression to create a probability plot. Also weibull distribution will be used to model the results to visualize if its a reasonable fit for the data.*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r=(dat['event'].cumsum()) # summing failure events to get failure rate\n",
    "ft=round((r-0.3)/(20+0.4),2) # failure rate\n",
    "dat['ft']=ft # add ft to the data\n",
    "\n",
    "# ordinary least square regression\n",
    "xx=np.log(dat['time'])\n",
    "xxc=sm.add_constant(xx) # add constant to the intercept\n",
    "yy=np.log(-np.log(1-dat['ft']))\n",
    "lmres=sm.OLS(yy,xxc).fit()\n",
    "plt.scatter(xx,yy,label='Obs')\n",
    "plt.plot(xx,lmres.predict(xxc) ,label='Weibul model')\n",
    "plt.title('Weibull probability plot')\n",
    "plt.xlabel('ln(time)') # log of time\n",
    "plt.ylabel('ln(-ln(1-Ft))') # weibull estimate\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *From the plot we can see that the data is clustered along the slope line which means weibull distribution will be a good fit to model the experiment.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *Lets estimate the parameters of the distribution from the graph: the shape factor 𝛽 and characteristic life 𝛼.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>ft</td>        <th>  R-squared:         </th> <td>   0.930</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.927</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   240.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 14 Jul 2023</td> <th>  Prob (F-statistic):</th> <td>7.33e-12</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:15:28</td>     <th>  Log-Likelihood:    </th> <td> -3.9666</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    20</td>      <th>  AIC:               </th> <td>   11.93</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    18</td>      <th>  BIC:               </th> <td>   13.92</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -2.3865</td> <td>    0.135</td> <td>  -17.659</td> <td> 0.000</td> <td>   -2.670</td> <td>   -2.103</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>time</th>  <td>    0.5181</td> <td>    0.033</td> <td>   15.514</td> <td> 0.000</td> <td>    0.448</td> <td>    0.588</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.979</td> <th>  Durbin-Watson:     </th> <td>   0.950</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.007</td> <th>  Jarque-Bera (JB):  </th> <td>   8.114</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.029</td> <th>  Prob(JB):          </th> <td>  0.0173</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.345</td> <th>  Cond. No.          </th> <td>    8.22</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                     ft   R-squared:                       0.930\n",
       "Model:                            OLS   Adj. R-squared:                  0.927\n",
       "Method:                 Least Squares   F-statistic:                     240.7\n",
       "Date:                Fri, 14 Jul 2023   Prob (F-statistic):           7.33e-12\n",
       "Time:                        15:15:28   Log-Likelihood:                -3.9666\n",
       "No. Observations:                  20   AIC:                             11.93\n",
       "Df Residuals:                      18   BIC:                             13.92\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -2.3865      0.135    -17.659      0.000      -2.670      -2.103\n",
       "time           0.5181      0.033     15.514      0.000       0.448       0.588\n",
       "==============================================================================\n",
       "Omnibus:                        9.979   Durbin-Watson:                   0.950\n",
       "Prob(Omnibus):                  0.007   Jarque-Bera (JB):                8.114\n",
       "Skew:                          -1.029   Prob(JB):                       0.0173\n",
       "Kurtosis:                       5.345   Cond. No.                         8.22\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lmres.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha: 100.09026262965247\n",
      "beta: 1.9300826015807049\n"
     ]
    }
   ],
   "source": [
    "print('alpha:', np.exp(-(lmres.params.const/lmres.params.time)))\n",
    "print('beta:', 1/lmres.params.time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *Lets model the survival analysis of the equipment in the experiment using weibull distribution*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *Because weibull function in lifelines does not account for censored data, we would drop the last 2 rows of the data from the experiment because they are censored data.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>event</th>\n",
       "      <th>ft</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.69</td>\n",
       "      <td>1</td>\n",
       "      <td>0.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.94</td>\n",
       "      <td>1</td>\n",
       "      <td>0.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.12</td>\n",
       "      <td>1</td>\n",
       "      <td>0.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.79</td>\n",
       "      <td>1</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.28</td>\n",
       "      <td>1</td>\n",
       "      <td>0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>9.31</td>\n",
       "      <td>1</td>\n",
       "      <td>0.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9.95</td>\n",
       "      <td>1</td>\n",
       "      <td>0.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12.90</td>\n",
       "      <td>1</td>\n",
       "      <td>0.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>12.93</td>\n",
       "      <td>1</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>21.33</td>\n",
       "      <td>1</td>\n",
       "      <td>0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>64.56</td>\n",
       "      <td>1</td>\n",
       "      <td>0.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>69.66</td>\n",
       "      <td>1</td>\n",
       "      <td>0.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>108.38</td>\n",
       "      <td>1</td>\n",
       "      <td>0.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>124.88</td>\n",
       "      <td>1</td>\n",
       "      <td>0.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>157.02</td>\n",
       "      <td>1</td>\n",
       "      <td>0.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>190.19</td>\n",
       "      <td>1</td>\n",
       "      <td>0.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>250.55</td>\n",
       "      <td>1</td>\n",
       "      <td>0.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>552.87</td>\n",
       "      <td>1</td>\n",
       "      <td>0.87</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      time  event    ft\n",
       "0     0.69      1  0.03\n",
       "1     0.94      1  0.08\n",
       "2     1.12      1  0.13\n",
       "3     6.79      1  0.18\n",
       "4     9.28      1  0.23\n",
       "5     9.31      1  0.28\n",
       "6     9.95      1  0.33\n",
       "7    12.90      1  0.38\n",
       "8    12.93      1  0.43\n",
       "9    21.33      1  0.48\n",
       "10   64.56      1  0.52\n",
       "11   69.66      1  0.57\n",
       "12  108.38      1  0.62\n",
       "13  124.88      1  0.67\n",
       "14  157.02      1  0.72\n",
       "15  190.19      1  0.77\n",
       "16  250.55      1  0.82\n",
       "17  552.87      1  0.87"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dat.shape\n",
    "dat2=dat.drop([18,19])\n",
    "display(dat2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# survival plot of the experiment\n",
    "wft=WeibullFitter()\n",
    "wft.fit(dat2['time'],dat2['event'])\n",
    "wft.survival_function_.plot()\n",
    "plt.title('weibull survival curve')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('Survival Prob')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# hazard rate for the experiment\n",
    "wft.hazard_.plot()\n",
    "plt.title('weibull hazard curve')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('hazard rate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>se(coef)</th>\n",
       "      <th>coef lower 95%</th>\n",
       "      <th>coef upper 95%</th>\n",
       "      <th>cmp to</th>\n",
       "      <th>z</th>\n",
       "      <th>p</th>\n",
       "      <th>-log2(p)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lambda_</th>\n",
       "      <td>59.360496</td>\n",
       "      <td>24.641757</td>\n",
       "      <td>11.063539</td>\n",
       "      <td>107.657453</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.368358</td>\n",
       "      <td>0.017867</td>\n",
       "      <td>5.806538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rho_</th>\n",
       "      <td>0.600018</td>\n",
       "      <td>0.110733</td>\n",
       "      <td>0.382985</td>\n",
       "      <td>0.817050</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-3.612135</td>\n",
       "      <td>0.000304</td>\n",
       "      <td>11.685128</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              coef   se(coef)  coef lower 95%  coef upper 95%  cmp to  \\\n",
       "lambda_  59.360496  24.641757       11.063539      107.657453     1.0   \n",
       "rho_      0.600018   0.110733        0.382985        0.817050     1.0   \n",
       "\n",
       "                z         p   -log2(p)  \n",
       "lambda_  2.368358  0.017867   5.806538  \n",
       "rho_    -3.612135  0.000304  11.685128  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(wft.summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *You will notice that lambda and rho are different from the earlier result when we used OLS regression. This is because we did not account for censored data in the experiment. If we run this function and include censored data, our result will be much more similar. See below*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>se(coef)</th>\n",
       "      <th>coef lower 95%</th>\n",
       "      <th>coef upper 95%</th>\n",
       "      <th>cmp to</th>\n",
       "      <th>z</th>\n",
       "      <th>p</th>\n",
       "      <th>-log2(p)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lambda_</th>\n",
       "      <td>99.683183</td>\n",
       "      <td>47.436745</td>\n",
       "      <td>6.708871</td>\n",
       "      <td>192.657496</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.080311</td>\n",
       "      <td>3.749702e-02</td>\n",
       "      <td>4.737080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rho_</th>\n",
       "      <td>0.506242</td>\n",
       "      <td>0.096236</td>\n",
       "      <td>0.317623</td>\n",
       "      <td>0.694862</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-5.130692</td>\n",
       "      <td>2.886784e-07</td>\n",
       "      <td>21.724034</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              coef   se(coef)  coef lower 95%  coef upper 95%  cmp to  \\\n",
       "lambda_  99.683183  47.436745        6.708871      192.657496     1.0   \n",
       "rho_      0.506242   0.096236        0.317623        0.694862     1.0   \n",
       "\n",
       "                z             p   -log2(p)  \n",
       "lambda_  2.080311  3.749702e-02   4.737080  \n",
       "rho_    -5.130692  2.886784e-07  21.724034  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wft.fit(dat['time'],dat['event'])  # censored data included\n",
    "display(wft.summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *Earlier result when we used OLS regression.: the shape factor 𝛽 and characteristic life 𝛼.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha: 100.09026262965247\n",
      "beta: 1.9300826015807049\n"
     ]
    }
   ],
   "source": [
    "print('alpha:', np.exp(-(lmres.params.const/lmres.params.time)))\n",
    "print('beta:', 1/lmres.params.time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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