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Excel神技能:评估学习曲线,预测生产成本

  • 2026-04-03 20:42:45
Excel神技能:评估学习曲线,预测生产成本
所谓熟能生巧，对一个生产型组织来说也不例外。随着公司产品产量的增加，它会学习如何更高效地制造产品。那么，该如何建模“累计产量”与“生产单位产品所需时间”之间的关系呢？
1936年，俄亥俄州代顿市的莱特-帕特森空军基首次提出 “学习曲线” 这一概念。他们经过研究发现，每当飞机的累计产量翻倍时，制造每架飞机所需的时间就会下降约15%。
维基百科提供了更多行业的学习曲线评估值：
  • 航空航天业：85%
  • 造船业：80%–85%
  • 复杂机床：75%–85%
  • 重复性电子制造和机械加工：90%–95%
  • 原材料：93%–96%
它的含义是：每当累计产量翻倍时，生产单位产品所需的时间（或成本）将缩减至原先的百分之多少，百分比越低，代表学习效应越显著（即进步越快）。例如，造船业的 80% 意味着产量翻倍后，工时减少了 20%；而原材料的 93% 则意味着进步空间较小，工时仅减少了 7%。
如果你是制造业的分析师，那么评估你公司生产某个产品的学习曲线，然后将其与行业平均水平进行对比，将是一个非常有价值的数据诊断。我们以一家生产传真机的公司为例，介绍如何评估学习曲线，并预测生产成本将如何降低。
如上图，我们收集了传真机公司1982年-1988年间的实际产量（C列）以及每年的单台生产成本（E列）。例如1983年的产量是70000台，单台生产成本是3416元。
计算累计产量：由于学习曲线旨在根据累计产量数据来预测生产单位产品所需的成本或时间，因此我们需要计算截至每年年底的累计产量, 在D4输入 =SUM($C$4:C4)，往下填充到D10, 计算出截至每一年的累计产量。
创建散点图：选中D3:E10, 插入选项卡---散点图，在创建出的散点图数据点上点击右键，选择添加趋势线；趋势线选项选择乘幂；勾选显示公式和显示R平方值。
得出预测公式如下：
生产传真机的成本 = 65,259 × (累计产量)^-0.2533
请注意，大多数数据点都紧贴拟合的幂曲线，且 R 平方值接近 1，这表明幂曲线与数据的拟合度非常好。
将公式 =65259*D4^-0.2533 从F4填充到F10，可以计算出每年生产的传真机的预测成本。请注意，符号^用于表示幂运算，例如^2就是平方。
预测1989年的情况：由于我们采集的实际数据只到1988年，所以我们对1989年的情况进行预测，我们假设1989年生产了 1,000,000 台传真机，在 D11 单元格计算出 1989 年的总累计产量为2,744,000后，在F列将预测公式复制到 F11，从而预测 1989 年生产的传真机成本为 1,527元。
评估学习曲线：这需要预测累计产量翻倍的情况下的学习率，在D12 单元格中输入1988年累计产量的两倍，并将 F10 中的预测公式复制到 F12，你会发现：当累计产量翻倍时，预测成本降至之前数值的 83.8%。因此，当前的这条曲线被称为“84% 学习曲线”。
这意味着每当产量翻倍，制造传真机所需的人工成本就会下降 16.2%。
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  1. CONNECT:[ UseTime:0.000492s ] mysql:host=127.0.0.1;port=3306;dbname=h_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000694s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000284s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000273s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000646s ]
  6. SELECT * FROM `set` [ RunTime:0.000255s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000709s ]
  8. SELECT * FROM `article` WHERE `id` = 472611 LIMIT 1 [ RunTime:0.013019s ]
  9. UPDATE `article` SET `lasttime` = 1775507600 WHERE `id` = 472611 [ RunTime:0.004798s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000301s ]
  11. SELECT * FROM `article` WHERE `id` < 472611 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000507s ]
  12. SELECT * FROM `article` WHERE `id` > 472611 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.004983s ]
  13. SELECT * FROM `article` WHERE `id` < 472611 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.005814s ]
  14. SELECT * FROM `article` WHERE `id` < 472611 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.019510s ]
  15. SELECT * FROM `article` WHERE `id` < 472611 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.023810s ]
0.156555s