adjusted file with gemini

rel.ipynb

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+```python
+# Cell 1: Install the reliability library (if not already installed)
+# You only need to run this cell once.
+# !pip install reliability
+```
+
+```python
+# Cell 2: Import necessary libraries
+import pandas as pd
+from reliability.Fitters import Fit_Weibull_2P
+from reliability.Distributions import Weibull_Distribution
+import numpy as np
+from math import gamma
+import matplotlib.pyplot as plt # Often useful for custom plotting
+```
+
+```python
+# Cell 3: Generate Sample Data (Simulated for demonstration)
+# In a real scenario, you would load your own data.
+# 'data' represents the observed failure times
+# 'censored' is a boolean array: True if censored, False if failed
+
+# Example 1: Some failures, some right-censored data
+data_1 = [90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240]
+censored_1 = [False, False, False, False, False, False, False, False, True, True, True, True, True, True, True, True] # Last 8 are censored
+
+# Example 2: More failures, fewer censors (uncomment to use this data)
+# data_2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]
+# censored_2 = [False, False, False, False, False, False, False, False, False, False, True, True, True, True, True]
+
+# Choose which dataset to use
+data = data_1
+censored = censored_1
+
+print("Sample Data:")
+print(f"Observed Times: {data}")
+print(f"Censored Status (True if censored): {censored}")
+```
+
+```python
+# Cell 4: Fit Weibull Distribution to Data
+# The Fit_Weibull_2P function handles censored data automatically
+print("--- Fitting Weibull Distribution ---")
+weibull_fit = Fit_Weibull_2P(failures=np.array(data), right_censored=np.array(censored), show_probability_plot=True, print_results=True)
+
+# The fit_weibull_2P object now contains the fitted parameters (alpha and beta)
+alpha = weibull_fit.alpha
+beta = weibull_fit.beta
+
+print(f"\nFitted Weibull Parameters:")
+print(f"Shape parameter (beta): {beta:.4f}")
+print(f"Scale parameter (alpha): {alpha:.4f}")
+```
+
+```python
+# Cell 5: Calculate Mean Time To Failure (MTTF) for the fitted Weibull distribution
+# MTTF for a Weibull distribution is given by: alpha * gamma(1 + 1/beta)
+# where gamma is the Gamma function.
+
+mttf = alpha * gamma(1 + 1/beta)
+print(f"Calculated Mean Time To Failure (MTTF) for the fitted Weibull distribution: {mttf:.2f}")
+```
+
+```python
+# Cell 6: Plotting the PDF, CDF, and Reliability Function
+# Create a Weibull distribution object with the fitted parameters
+weibull_dist = Weibull_Distribution(alpha=alpha, beta=beta)
+
+plt.figure(figsize=(12, 8))
+
+# Plot PDF
+plt.subplot(3, 1, 1) # 3 rows, 1 column, 1st plot
+weibull_dist.PDF(dashes=True, label='Weibull PDF', plot_type='plt', show_plot=False)
+plt.title('Weibull Probability Density Function')
+plt.xlabel('Time')
+plt.ylabel('Probability Density')
+plt.legend()
+plt.grid(True)
+
+# Plot CDF
+plt.subplot(3, 1, 2) # 3 rows, 1 column, 2nd plot
+weibull_dist.CDF(dashes=True, label='Weibull CDF', plot_type='plt', show_plot=False)
+plt.title('Weibull Cumulative Distribution Function')
+plt.xlabel('Time')
+plt.ylabel('Cumulative Probability')
+plt.legend()
+plt.grid(True)
+
+
+# Plot Reliability Function (Survival Function)
+plt.subplot(3, 1, 3) # 3 rows, 1 column, 3rd plot
+weibull_dist.SF(dashes=True, label='Weibull Reliability Function (SF)', plot_type='plt', show_plot=False)
+plt.title('Weibull Reliability (Survival) Function')
+plt.xlabel('Time')
+plt.ylabel('Reliability')
+plt.legend()
+plt.grid(True)
+
+
+plt.tight_layout()
+plt.show() # Display all plots
+```
+
+```python
+# Cell 7: Extracting other useful information (e.g., B10 life, reliability at time)
+
+# B10 life is the time at which 10% of the population has failed (90% reliability)
+b10_life = weibull_dist.b_n(n=10)
+print(f"B10 Life (time at which 10% have failed): {b10_life:.2f}")
+
+# Example: Reliability at a specific time (e.g., 150 units of time)
+time_point = 150
+reliability_at_time = weibull_dist.SF(t=time_point)
+print(f"Reliability at {time_point} units of time: {reliability_at_time:.4f}")
+
+# Example: Time at a specific reliability (e.g., 70% reliability)
+target_reliability = 0.70
+time_at_reliability = weibull_dist.quantile(q=1 - target_reliability) # Quantile takes probability of failure (1-Reliability)
+print(f"Time at {target_reliability*100}% reliability: {time_at_reliability:.2f}")
+```
+
+When you run this in a Jupyter Notebook, the probability plot from `Fit_Weibull_2P` will appear directly below the cell where it's called, and the PDF, CDF, and Reliability plots will appear below Cell 6. The text outputs will appear in their respective cells.