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NOTES: REJECT AND REWORK MODELS IN INDUSTRY Max Newbold: May 2004 INTRODUCTION The writer has, from observing industry, defined five different reject and rework models. The importance of these models is how they affect manufacturing lead-time and cost. Any factor that causes random changes to lead-time in manufacturing will affect the level of uncertainty. This in turn will affect competitive factors of on time delivery and delivery reliability. MODEL TYPES Of the five models listed below the most disruptive to a manufacturing system can be model number five. This is due to the systems sensitivity to changes in yield. It is this model that will be discussed more fully. Diagrams of all five models are shown in the appendix. 1. Rejected items are scrapped (Model No.1) 2. The reject item can be allocated to a different part number (Model No.2) 3. Reject items are reworked as an integral part of the production line (Model No.3) 4. Rejected items are repaired off line and returned to the line after the point of rejection (Model No.4) 5. Rejected items are repaired off line but returned to the process where the item was rejected or before the point of rejection (Model No 5) SUMMARY OF IMPACT The method of handling defective product within the manufacturing system is dependent on the ability of the product/part to be repaired. Where the part is scrapped or redefined as a different product then the following needs to be considered. Rejects from a continuous process are unlikely to greatly disrupt the flow or require large buffers so long as the yield remains above 90% between processes and the system can support the overall effect of the rolled yield. In batch production the effect of rejects can result in over or under supplies as the yield varies, creating additional uncertainty in the system. If the batch size changes to reflect any yield change, then the time in the system will also alter, again creating uncertainty. Where product is reclassified the level of disruption is dependent on whether the batches are treated as independent identities and move through the system independently. If the batches are not allowed to reform either by storing until the optimum batch size is achieved or dynamically through a “look ahead” policy, then lead-time will become unpredictable. In the case where rework is allowed, then working off line, so long as labour is available to meet changes in the quality level, little disruption to the flow will occur. A similar result is obtained where all products are moved to an inspection rework area. The system, where due to limited resources, the product must reenter the line at the point it was rejected is the most sensitive to changes in the first pass yield. Under these conditions the capacity of the system will quickly deteriorate as the yield reduces. If batching is required, then the management must consider the approach taken on the smaller rework batches. MODEL NUMBER FIVE Continuous Systems This model is common in the mining industry, where ore is crushed and screened. Over sized particles are sent back around through the crusher as shown in model five. The equilibrium position is defined when the input to the system equals the output of the system. In the mineral processing industry the particle size is considered to be a continuous function, with a normal distribution. A closer algorithm can be found in a communication’s text (Gunther 1998 The Practical Performance Analyst: Performance–by–Design Techniques for Distribution Systems McGraw – Hill) where the flow of messages is considered to be discrete objects entering the system. The feed back models for calls that can not be serviced in the first attempt are cycled back into the system. This is defined in a text by Gunther (1998) as 1 = + pn1 . This approach assumes that the value of “p n” is independent of the new arrivals, which cannot be assumed to be true for manufacturing. In manufacturing an item is rejected because of a specific defect and once this has been corrected its chance of failure differs from that of a new arrival. Thus the probability of failure of an item is dependent on the number of cycles that the item has been through the system. Modifying Guther’s formula to make the failure rate dependent on the external arrivals and the times the item has cycled the formula is: 1 = + pn This formula would hold true if and only if on the second pass through the system the item passes or is rejected. From the flow shown in appendix 2, this would make X equal to one. Each pass will have its own probability of failure; thus the formula can be expressed as follows. 1 = + pn1+ pn1pn2 + pn1pn2pn3 +… + pn1…pnn 1 =(1 + pn1+ pn1pn2 + pn1pn2pn3 +… + pn1…pnn) When the system is operating at capacity, the above formula can be simplified by dividing both sides by 1. 1 =U(1 + p1+ p1p2 + p1p2p3 +… + p1…pn) U = 1/(1 + p1+ p1p2 + p1p2p3 +… + p1…pn) (System Capacity) When the number of recycles through the system is limited and a further failure results in the item being scrapped, both passed and scrapped items leave the system allowing equation 20 to be truncated. If only three repairs are allowed, as shown in figure number five the capacity of the system would be: U = 1/(1 + p1+ p1p2 + p1p2p3) While the capacity decreases the overall final yield of the system increases. Let k1 be the first pass yield, k2 the second pass and kN the yield of the Nth pass. The final yield (kF) of the system is found by: k F = k1 + k2 p1+ k3p1p2 + k4p1p2p3 +… + k(N-1)p1…pn If it assumed that the distribution of faults on the product follows a Poisson distribution and only one defect is picked up on each examination. This type of situation is found in the testing of PCA boards at incircuit testing where the test program will stop on finding the first fault and the number of faults per board can be approximated by to a Poisson distribution. Base on the above assumption the probability that a board will pass the first time it is presented to the tester is e -u , thus the boards returning for a second passes is (1- e-z ) The proportion of boards failing on the second pass is the number of boards with 2 or more faults divided by the number of boards with 1 or more faults. Boards with one or more faults: (1- e-z ) Boards with 2 or more faults: (1- e-z - [z2 e-z /2!] ) Thus pn2 is (1- e-z - [z2 e-z /2!] ) / (1- e-z ) The calculation is repeated for each board with 3, 4 to n defects, using the probability of j defects divided by the probability of the sum of (j-1 to n) defects minus 1. The behaviour of this system is that that an apparent high yield is achieved when the product is allowed to recycle through the operation. As the defects increase from to (z + z) the final yield will be only be affected marginally affected even with large movements, but the capacity falls away even with small changes in z and follows a similar path to that of the first pass yield. The affect of this behaviour is shown in the graph below Ist Pass Yield vs Final Yield and Capacity 120% Final Yield 100% % 80% Effective Capacity 60% 40% 1st Pass Yield 20% 0% 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 Defects/unit The data used in the construction of the graph was: S = 0.25 hrs = 100 units per hr D = 40 units per hr. Q = Initial batch size entering the system = Calculated on values of 0.4 and 0.2 defects per unit Batch System When the process is batch or lot manufactured the impact will be dependent on: 1. The ability to allow the batch to be split between passed and recycled product 2. Can the recycled material wait until the next batch is processed? However since the batch sizes are altered the manufacturing lead-time will vary causing internal uncertainty. Appendix One : Differing Models MODEL NO. ONE Rejects Scrapped MODEL NO. TWO Rejects Reclassified Input Flow Flow = Input Flow Flow = Reject Found Reject Found Scrap Flow = 1 Output Flow Flow = - 1 MODEL NO. THREE Repair In-line Input Flow Flow = Output Flow A Flow = - 1 MODEL NO. FOUR Repair Off-line Input Flow Flow = Inspection and Repair Output Flow Flow = Output Flow B Flow =1 Repair Flow Flow = 1 Output Flow Flow = Appendix Two: Rework model five MODEL NO.5 Returned to the Point of Rejection Input Flow I Process Rework Output Flow FLOW DIAGRAM : REWORK TEST CYCLE Pass No p n YES C>X NO Process Rework 1 Internal External 5 Scrap