请大家帮忙帮忙实现一下这个算法

Emily19226天前 ⋅ 663 阅读

https://codenews.cc/chatgpt?simple=true    gpt联网旁边上传本地图片

这个算法用于计算控制图的控制限 L,使得控制图的在制程内平均运行长度(IC ARL)等于指定的 ARL0。以下是用Python实现这个算法的代码:

    import numpy as np
    from scipy.stats import multivariate_normal
    
    def generate_samples(T0, m0, N, d):
        # Generate N sequences of length T0 from a standard multivariate normal distribution
        return [multivariate_normal.rvs(mean=np.zeros(d), cov=np.identity(d), size=T0 + m0) for _ in range(N)]
    
    def calculate_charting_statistic(X):
        # Placeholder for the function that calculates the charting statistic Qbt
        # Replace this with the actual calculation
        return np.max(np.abs(X), axis=1)
    
    def calculate_ARL(L, sequences, T0):
        # Placeholder for the function that calculates ARL given L
        # Replace this with the actual calculation
        ARLs = []
        for seq in sequences:
            Qbt = calculate_charting_statistic(seq)
            ARL = np.argmax(Qbt > L) if np.any(Qbt > L) else T0
            ARLs.append(ARL)
        return np.mean(ARLs)
    
    def find_control_limit(ARL0, epsilon, T0, m0, N, d):
        while True:
            sequences = generate_samples(T0, m0, N, d)
            Qbt_values = [calculate_charting_statistic(seq) for seq in sequences]
            
            Lu = min([np.max(Qbt) for Qbt in Qbt_values])
            Ll = 0
            
            ARL = calculate_ARL(Lu, sequences, T0)
            
            if ARL < ARL0:
                T0 += 1
                continue
            
            L = Lu
            while abs(ARL - ARL0) >= epsilon:
                if ARL > ARL0:
                    L = (L + Ll) / 2
                else:
                    L = (L + Lu) / 2
                
                ARL = calculate_ARL(L, sequences, T0)
            
            return L
    
    # Parameters
    ARL0 = 200  # Desired ARL0
    epsilon = 0.01  # Tolerance
    T0 = 100  # Initial sequence length
    m0 = 5  # Initial number of samples
    N = 100  # Number of replications
    d = 2  # Dimensionality of the data
    
    # Find the control limit
    L = find_control_limit(ARL0, epsilon, T0, m0, N, d)
    print("Calculated control limit L:", L)
    

注意事项:

1.  `calculate_charting_statistic` 和 `calculate_ARL` 函数是占位符,需要根据具体的控制图类型(例如Hotelling T²图、CUSUM图等)来实现。
2.  本代码假设数据来自标准多元正态分布。
3.  参数 `ARL0`、`epsilon`、`T0`、`m0`、`N` 和 `d` 需要根据具体应用场景进行调整。

请根据实际需求调整和完善代码中的细节。

生成的代码我未做验证。反正是gpt4o生成的,就是本地上传图片进行问答,会自动切换到使用4o模型

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