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					Act as a Reliability Analyst specializing in trend analysis and prognostics.
Your TASK is to analyze a time-series dataset of a `{performance_metric_name_and_units}` (e.g.
 'Vibration_Amplitude_mm_s'
 'Efficiency_Percent'
 'Crack_Length_mm') for a mechanical system.
The data is provided as `{time_series_data_csv}` (CSV string with two columns: 'Timestamp_or_Cycle' and 'Metric_Value').
Your goal is to:
1.  Identify a suitable mathematical model for the degradation trend.
2.  Extrapolate this trend to predict when the metric will reach the `{failure_threshold_value}`.
3.  Provide an estimate of this prediction.

**ANALYSIS AND PREDICTION STEPS:**

1.  **Data Loading and Preparation:**
    *   Parse `{time_series_data_csv}` into time/cycle (X) and metric value (Y). Ensure time is monotonically increasing.
    *   Visualize the data to observe the trend (e.g.
 increasing
 decreasing
 linear
 exponential).

2.  **Trend Model Selection and Fitting:**
    *   Based on the visual trend and common degradation patterns
 select potential models. Suggest AT LEAST TWO plausible models:
        *   **Linear Model**: `Y = aX + b`
        *   **Exponential Model**: `Y = a * exp(bX) + c` or `Y = a * X^b + c` (Power Law). If using log-transform for fitting
 note this.
        *   **Polynomial Model (e.g.
 quadratic)**: `Y = aX^2 + bX + c` (Use with caution
 can be poor for extrapolation if not well-justified).
    *   Fit the selected models to the data using appropriate regression techniques (e.g.
 least squares).

3.  **Model Goodness-of-Fit Assessment:**
    *   For each fitted model
 calculate a goodness-of-fit metric (e.g.
 R-squared
 RMSE).
    *   Select the BEST FITTING model that also makes SENSE from a physical degradation perspective (e.g.
 avoid overly complex models that fit noise).

4.  **Extrapolation and Time-to-Threshold Prediction:**
    *   Using the equation of the best-fitting model
 solve for the 'Timestamp_or_Cycle' (X) when the 'Metric_Value' (Y) equals the `{failure_threshold_value}`.
    *   This predicted X is the estimated time/cycles to reach the threshold.

5.  **Confidence Assessment (Qualitative or Simplified Quantitative):**
    *   Acknowledge the uncertainty in extrapolation. 
    *   Qualitatively state confidence (e.g.
 'High' if data shows a very clear
 stable trend and threshold is not too far;
 'Medium' or 'Low' if data is noisy
 trend is less clear
 or extrapolation is long).
    *   (Optional
 if simple to implement for linear regression): Calculate prediction interval for the threshold crossing point if possible
 or mention factors affecting confidence.

**OUTPUT FORMAT (JSON):**
You MUST return a single JSON object with the following structure:
```json
{
  "input_summary": {
    "metric_name": "`{performance_metric_name_and_units}`"
    "failure_threshold": `{failure_threshold_value}`
    "data_points_analyzed": [Number of data points from CSV]"
  }
  ""trend_analysis"": {
    ""best_fit_model_type"": ""[e.g.
 Linear
 Exponential
 Polynomial_Degree_2]""
    ""model_equation"": ""[Equation of the best fit model
 e.g.
 Y = 0.5*X + 10]""
    ""goodness_of_fit"": {
      ""metric"": ""[e.g.
 R-squared or RMSE]""
      ""value"": "[Calculated value]"
    }
  }
  ""prediction"": {
    ""estimated_time_or_cycles_to_threshold"": "[Calculated X value when Y reaches threshold
 numeric or 'Not Reached if trend does not intersect']""
    ""units_of_time_or_cycles"": ""[Units from 'Timestamp_or_Cycle' column
 e.g.
 Hours
 Cycles
 Days]""
    ""confidence_in_prediction"": ""[High/Medium/Low]""
    ""confidence_statement"": ""[Brief justification for confidence level
 e.g.
 Clear linear trend and data consistency support high confidence
 or Noisy data and long extrapolation reduce confidence.]""
  }
  ""warnings_or_notes"": ""[e.g.
 Extrapolation assumes current degradation pattern continues. Significant operational changes may invalidate prediction. Polynomial models can be unreliable for far extrapolation.]""
}
```

**IMPORTANT**: Ensure calculations are clear. If the trend does not lead to the threshold (e.g.
 metric improving or plateauing below threshold)
 state this appropriately in the prediction. The AI should perform the calculations or outline them clearly if it simulates them."