CSP sampling plan连续抽样方案

CSP, the multi-level continuous sampling plan, offers some important advantages to the quality management team when they decide which sampling plan is better to the company. In fact, this idea is not a fresh one but described by H.F. Dodge in 1943. When production is continuous, the procedure of inspection lots according to the lot-by-lot acceptance sampling plan (n; Ac, Re) is somewhat artificial. Moreover, where the conveyor line is used, it mostly led to unduly waste or efficiency lower down. 1943年美国统计学家道奇提出了这个方案，与之对应的美国军用标准是MIL-STD-1235。可能大家对分批次的抽样方案（样本量；可接受，拒收）更熟悉，但对于连续性生产的工序来说，每一批次的积累过程更容易导致成本上升和效率浪费。
CSP sampling plan offers some important advantages. Firstly, it is not necessary to accumulate a lot before making a decision, so the production team can deliver products more rapidly. Less storage space is occupied as well as the quality performance can meet customer expectation, both the producer and the customer save on the inspection cost. On the other hand, as soon as the quality gets worse than the AOQL, the rate of inspection increases accordingly. In this way, there is a more effective chance of detecting root causes of defects soon after they occur than the lot accumulated. 生产过程常常出现这样的问题：待检产品需要堆积成整一摞才可以开始抽检，储存空间越来越不够用，等抽检中发现缺陷时生产早已结束，要去找原因只有查记录了，诸多问题难于得到根本解决。当以上问题变成大问题时，CSP抽样方案可能是更好的选择。最重要的是，当工序的品质水平下降时，检查比率会迅速提高甚至完全做全检，速度放慢，产量减少，所有的人都开始关注了。
The basic procedure of CSP-1 is defined as followings，流程如下:
a. at the outset, inspection 100% consecutively until i units in succession are found clear of defects, and then
b. inspect a fraction f, selecting individual sample from the flow of product.
c. If defective found, revert immediately to 100% inspection of succeeding units until again i units in succession are found clear of defects.

One day I got a call from my customer there is 100,000 pieces products need to find an adequate sampling plan to ensure both customer satisfied quality level (AQL 0.65) and most urgent lead time of delivery. I proposed the sampling plan as: CSP-1 sampling plan, i=170, f=1/10, AOQL=0.65. Figure-1 is the AOQ curve, and figure-2 is the procedure.


If the process is excellent, the actual sampling size is only about 10%. On the contrary, the worst case is 100% inspection. The sampling plan is a challenge to both customer and producer. The pressure of the challenge pushed the engineering team reviewed and optimized the whole procedure seriously. With all effort input, the result is so incredible and we saved great cost from less inspection time and manpower located. The defect rate in customer side is only 0.3% (in 6 months). 在工序品质优秀的情况下，实际的抽样比率只有10%，反之则可能全检。所以，选择CSP抽样方案，就意味着选择了挑战。挑战的压力需要我们付出更多，而回报是成本的降低，质量的优异。
The primary measure of effectiveness of CSP sampling plan is AOQ function, or, more specifically, the AOQL. Then, what is AOQL？ It is Average Out-going Quality Limit. The accepted lots will certain approximately the percent defective submitted, although they will be slightly improved by reverting to 100% inspection or screening. Thus, at any given level of incoming quality p greater than 0, there is some lower level of Average Outgoing Quality (AOQ). And the worst case is AOQL. 选择CSP抽样方案的首要之表示AOQ。它的定义是：经过检验后产品的平均质量。根据p (%) 所提交产品的合格百分数）的不同，我们可以计算出AOQ的函数曲线，正如图一所示，当p=0.012时，出现AOQ的最大值，即AOQL=0.647 (%)。

However, CSP-1 is just the most elemental one of CSP sampling plan family. It can be adopted widely and easily. Successfully experience is, from the date we implemented CSP-1, the quality performance was improved significantly while quality cost was decreasing. We can make the process flow more rapid as well as less storage space and resource input. In one word, quality innovation pushes us to improve continuously.
实际上，CSP抽样方案是个系列，而CSP-1只是其中最基本也是最常用的一个。以往成功的经验告诉我们，适当的抽样方案在提高品质水平的同时降低了品质成本，生产流程更加顺畅，存货空间和资源投入更小。所以，品质的创新推动持续的改善。