Analysis of the learning curve in the modern enterprise network application _ to write papers

Papers to write net: Abstract learning curve is a producer behavior through learning and experience and improved production output characteristic function, the learning curve can be used to scientifically develop cost plan to improve operational plans, work quotas and labor planning, quality improvement, etc. This also summarizes the long-term quality cost model, the model with the cumulative long-term cost of quality production increases.

Keywords:: learning curve; curve fitting, quality control

I. Introduction
According to the National Bureau of Statistics data show that the manufacturing sector ranks the leading position of China's industry, the number of industrial enterprises in China accounted for over 90% of main business income of more than 80%, 70% of profits. China is now recognized worldwide as the "manufacturing center "improve the productivity of manufacturing enterprises to become a top priority of China's industrial Science to develop production plans, capacity expansion planning, production volume, work quotas, cost planning and quality improvement can improve production efficiency, but the traditional method, the production of the product unit time, the cost in a very long time (or within a batch are assumed to be constant, while in practice the production process, they fall as production increases and the order to be more scientifically demonstrated that dynamic changes caused by the impact of this paper, the learning curve analysis to explain the dynamic production companies operate in some of the phenomena, and to the production operation of a new approach.

Second, single-factor learning curve model
Learning curve from the World War II aircraft manufacturing, aircraft assembly operation, over time, need to invest the time will gradually reduce direct labor. 1936 White for the first time American scholars in the aviation industry magazine presented the practical effect of the learning curve, that is, on average, the assembly operation in the aircraft industry, the output doubled, about falling demand for labor time by 20% that is, no matter when the first plane with the number, the first 2N N frame with only the first frame when 80% of the production of a repeat of this in the product, with the increase in production per unit of product when used to reduce the phenomenon of a regular known as the learning effect. When using this product unit (or cost function and output relationship between the Cartesian coordinates corresponding to the curve known as the learning curve. The evolution of the learning curve has been widely used in the aviation industry and other industries in which the learning rate is not static, it varies with the product, and also with changes in the production environment is different, as shown in Figure 1 (Figure 1
It can be seen from Figure 1, the learning curve consists of two phases: a learning phase, the unit production time increases with the number of products decreased, and the other is a standard stage, this section of the learning effect is negligible. It is obvious that learning curve is a dynamic production function, the corresponding expression of a variety of functions and mathematical models.

1, White learning curve model (basic model
Yi = Y1X-b (1
Where: Yi-i-th unit of time or cost, Y1-1 units of time or cost, X-production number, count up to when the first i units, b-constants, and learning and progress rates of .

After doubling and doubling production before the cumulative ratio of the average working hours is called the learning rate, with R, ie:
R = Y2x/Yx = (2X-b / (Xb = 2-b (2
Therefore, b =- log2R (3
Therefore, b R with the decrease of learning rate increases.

2 and improve the efficiency of the initial model (Stanford type-B curve and it is the early U.S. Department of Defense developed at Stanford Research Institute, and its performance in the form of:
Yi = Y1 (X + Bb (4
Constant B for the introduction of amendments to the initial stages of production efficiency. Because of the new products into production before (or a new job before the start of production technology well prepared, or have more detailed experience to draw on, or new products and old products are close, there are many common operations, so that productivity per unit of product than the first high, then the normal curve in the middle of a certain learning curve began to slowly change can be seen that when B = 0, the model reduces to the basic model or work in the production process, due to improved equipment, tools, or access to a proprietary technology to enhance efficiency, they can use this model.

3, the ultimate efficiency model when production or work to a certain extent, the production process into the standardization phase, the actual efficiency increased slowly. To reflect this situation, the learning curve can be amended as follows:
Yi = A + KX-b (5
Where, A is the standard of work time or cost, K is a constant, determined by the nature of the work from (5-style can be seen, X → + ∞ when, Y → A, the limit can be obtained by calculating the standard unit of time or cost. The model shows that production increased to a certain extent progress is slow, so in reality the production of old products, competitive pressure, but the market price more stable, faster new product progress, unit costs fell quickly, the market price down on something else.

Third, the learning curve fitting and prediction
1, fitting procedures and methods, first to collect data from actual production, and data processing, data released from the obvious exception, and then using the least square method of fitting the data processed by regression analysis, and then return to get the learning curve, This increase can predict the next batch of production unit cost or time in practice to test its accuracy.

2, fitting case study. A production of new product development as shown in Table 1 (Table 1) This is a new product development, so using the basic learning curve model, (1 where both sides of the logarithmic, too:
㏑ Yi = ㏑ Y1-b ㏑ X (6
So P = ㏑ Yi, Q = ㏑ X, A = ㏑ Y1
Is: P = A-bQ (7
That is converted into a linear equation, using the least square method in Table 1 into Table 2 (Table 2
-B = (10ΣPQ-ΣQΣP / [10ΣQ2-(ΣQ2] =- 0.157
A = ΣP/10- (-bΣQ/10 = 1.972
Correlation coefficient:
r = (10ΣPQ-ΣQΣP / [10ΣQ2-(ΣQ2] 1 / 2 [10ΣP2-(ΣP2] 1 / 2 =- 0.9975
Shows P, Q relevance of large, high degree of curve fitting.

And because A = ㏑ Y1, the Y1 = eA = 7.185, that is to be the product of the unit production hours and the cumulative production relationship Yi = 7.185 (X-0.157.

Links to free download http://www.hi138.com Fourth, the learning curve in the modern enterprise management application
Ease the learning curve after the aviation industry found wide application, such as product design and manufacturing time estimates (cost, cost forecast, schedule prediction.

1, the cost of direct labor hours and cost projections. Set production quantities of n units, the first x units of production time for the YX, the total time required for the Tn. Do not consider learning effects, there are Y1 = Y2 = ... = Yn, then:
Tn = nY1 (8
Consider the learning effect, there are:
If the unit cost of working hours, L, S is the total of the total labor costs:
S Total = TnL = Y1Ln1-b / (1-b (10
2, the development of fixed working hours. The use of the learning curve of changes in working hours, fixed working hours after the stable production in the curve of the standard should be set phase (approaching the level of that in the short term under current conditions can not be improvements in the specific operation, should be Note the following:
(1) new products or new job, be guided by similar work in the past data, according to the basic model described above to solve the learning curve to develop up to standard working hours before the time fixed for temporary workers, to encourage staff to improve learning for traditional work, improve efficiency in accordance with the initial model (Stanford type-B curve of the application learning curve.

(2 new workers a fixed requirement difficult to achieve, it may dampen enthusiasm for work, then you can determine by Research into the learning curve, to be properly used, for example, for the period of apprenticeship or skilled workers, according to the different segments to develop a fixed percentage requirements, encourage them to quickly achieve proficiency standards.

3, improved inventory order quantities in storage operations Research has been made on the basic economic order quantity model in the model, the total storage cost of TIC for the storage costs and ordering costs, ie:
TIC = (Q / 2 · C2 · N + (D · N / Q · C1 (11
Where: Q is an order quantity, C2 for the unit cost of materials stored for one year, D is the material-year requirement, N is the number of years, C1 cost for each order according to formula (11) can get the minimum cost of ordering inventory volume, that is, economic order quantities:
Qopt = [(2DC1/C2] 1 / 2 (12
In this model, storage costs are usually the C1 C2 and subscription fees as a constant, which for short-term deposit business purchase decision is appropriate, but in fact, volume is generally not a short-term decision making behavior, it is an important strategic decision of business component should be the viewpoint of a strategic decision-making batches from the long-term business perspective, cost per order is not constant, but with the increase in the number of orders declined, so (12 is also in the economic order quantity should be declining, the total storage cost would meet with the cost of ordering quantities "learning curve" of the law. with the formula can be expressed as follows:
Sn = S1 (D · N / Qb (13
Where: S1 is the first time, ordering cost, Sn for the n-th order, the average subscription cost, b is the learning rate index, which revised the total available storage costs TIC '.

TIC '= (Q / 2 · C2 · N + (D · N / Q [S1 (D · N / Qb] (14
Namely:
TIC '= (Q / 2) · C2 · N + S1 (D · N / Q) 1 - b (15
To minimize the total storage costs must be met:
dTIC '/ dQ = 0
Have economic order quantities:
Q'opt = [2S1 (1-b (D · N1-b / (C2 · N)] 1 / (2 - b) (16
V. CONCLUSIONS
This article describes the learning curve of several models, but also for example to simulate the learning curve regression analysis, and to explore its application in the modern aspects of the enterprise, indicating the direction of its application value.

In practice, when the normal production time, there has been described in the slow learning curve changes, indicating that production is close to the standard production phase, can be high-volume production. The establishment of the production data file is the key to get the right learning curve factor, the learning curve for the enterprise business more effectively produce, scientific basis for the development of production management program and if the production process to a halt, the curve will be interrupted, need to re-establish the learning curve, and the introduction of new technology or process will be greatly improved learning rate, which can improve the learning curve, which shows the learning curve is a dynamic curve. apply a good learning curve, will help to improve business efficiency.

(Author: China University of Mining (Beijing)

Main References:
[1] QI stone. Logistics Engineering, Beijing: Higher Education Press, 2006.

[2] Li Jian, Victor, etc. learning curves and progress functions - consider the technological progress factor optimization Jiangsu: Scientific Management, 1997.

[3] Lang Chi is Quality management and its techniques and methods. Beijing: China Standard Press, 2003.

[4] Xu Li, Si-Qing Zhuo, etc. the learning curve in the economic order quantities apply. Hubei: Wuhan Electric Power University, 1998. Links to free download http://www.hi138.com