## output_analysis.confidence_interval_method()


Determine the minimum number of simulation replications required to achieve


Usage

``` python
output_analysis.confidence_interval_method(
    replications,
    alpha=0.05,
    desired_precision=0.1,
    min_rep=5,
    decimal_places=2
)
```


a target precision in the confidence interval of one or several performance metrics.

This function applies the **confidence interval method**: it identifies the smallest replication count where the relative half-width of the confidence interval is less than the specified `desired_precision` for each metric.


## Parameters


`replications: (`  
`    pd.Series`  
`    | pd.DataFrame`  
`    | Sequence[float]`  
`    | Sequence[Sequence[float]]`  
`    | dict[str, Sequence[float]]`  
`)`    
Replication results for one or more performance metrics. Accepted formats:

- `pd.Series` or 1D list/numpy array → single metric
- `pd.DataFrame` → multiple metrics in columns
- `dict[str, list/array/Series]` → {metric_name: replications}
- list of lists / numpy arrays / Series → multiple metrics unnamed Each inner sequence/Series/numpy array must contain numeric replication results in the order they were generated.

`alpha: float | None = ``0.05`  
Significance level for confidence interval calculations (CI level = 100 \* (1 - alpha) %).

`desired_precision: float | None = ``0.1`  
Target CI half-width precision (i.e. percentage deviation of the confidence interval from the mean).

`min_rep: int | None = ``5`  
Minimum number of replications to consider before evaluating precision. Helps avoid unstable early results.

`decimal_places: int | None = ``2`  
Number of decimal places to round values in the returned results table.


## Returns


`- Single-metric input → tuple ``(n_reps, results_df)`  

`- Multi-metric input → dict:`  
`{metric_name: (n_reps, results_df)}`

`Where`  
n_reps : int The smallest number of replications achieving the desired precision. Returns -1 if precision is never reached. results_df : pandas.DataFrame Summary statistics at each replication: "Mean", "Cumulative Mean", "Standard Deviation", "Lower Interval", "Upper Interval", "% deviation"


## Warns


`UserWarning`  
Issued per metric if the desired precision is never reached.