Analysis of Process Capability on the Digital Control Board Batch Testing

Transcription

1 Sensors & Transducers 2014 by IFSA Publishing, S.. htt:// Analysis of Process aability on the Digital ontrol Board Batch Testing hun-jiang SHUAI Shaanxi University of Technology, School of Physics and Electronic Information Engineering, Han Zhong, Shaanxi, hina, Received: 20 December 2013 /Acceted: 28 February 2014 /Published: 31 March 2014 Abstract: This aer introduces a rocess control method and analysis rocedure. urrent data for the digital control single board was obtained with the Statistical Process ontrol method for a TD outdoor base station. The ass rate and quality of the digital single board was obtained through a roduction rocess caability analysis. The imrovements associated with the single board method have been ut forward here in order to lay a foundation for the enhancement of the quality of several indices. Indices here include the index for rocess caability and rocessing accuracy. oyright 2014 IFSA Publishing, S.. Keywords: Digital control board, Statistical rocess control, Pass rate. 1. Introduction In the rocess of roduction and rocessing, there are always some variations in the data. Examles here include the accetance number, first ass yield, and single board test time. Therefore, a roblem lies in how to gras the volatility and make a decision in a timely manner. Process control (SP) [1, 2] is a owerful tool that can kee the roduction line stable. It can also reduce quality fluctuations. According to Dr Shewhart's classification for the variations in the rocess, there are two general cases. The first is created by a common cause, which is often difficult to eliminate, but which reresents an easily reeatable and redictable general variation. The second is caused accidentally by secial reasons with significant effects. This tye is unredictable and reresents an abnormal variation which must be ruled out. These two variations become the root roblems associated with roduct occurrence quality. They have a significant statistical regularity for quality fluctuation. Through the use of control charts, many abnormalities can be found. Ultimately, by rocess control and diagnosis theory (SPD) [3, 4], the causes of these abnormalities can be found and ruled out. Using a statistical method for rocess caability analysis, [5, 7] embodies niing the roblem in the bud. It is also a modern management idea characterized by revention and control. It rovides a more accurate scientific basis that can be used to analyze and solve the roblems. This aer obtained current suly data for the digital single board [8] after a batch test by the roduction line. This was done in order to conduct a rocess caability analysis of single board roduction. It also rovided a qualified rate and the Article number P_1941 1

2 quality of digital board. This eventually laid a foundation for the imrovement of the single board, as well as a further enhancement of its quality. Therefore, this study has an imortant ractical value. It can rovide ositive guidance for imroving the overall roduction rocess. 2. Process ontrol Method 2.1 Process aability and its Index Process caability refers to the actual rocessing caacity (inherent caacity/quality assurance caacity) of a given rocess over a certain time and within a state of control (steady state). The rocess caability index (the scoe of the rocess quality requirements (tolerance) and the ratio of rocess caability) reresents the value of the rocess caability that meets the requirements of the rocess quality standard. 1) The bilateral tolerance rocess caability indices are unbiased T TU T = 6σ 6σ 2) The bilateral tolerance rocess caability indices are biased ε 2Tm x ite deviation ratio k = =, then T / 2 T there is k = ( 1 k ) T 2ε = 6s (3) Individual tolerance rocess caability indices If it is only necessary to obtain the uer limits of tolerance, then U TU μ TU X = 3σ 3σ If it is only necessary to obtain the lower limits of tolerance, then μ T = 3σ X T = 3σ Unbiased shows the consistency of rocessing (namely, the "quality" factor). The greater the the smaller the quality feature distribution values. For a stronger quality factor in the biased situation k signifies the rocess caability indices where the rocess center μ and Tm are offset, the greater the k, the smaller offset, rocess distribution center is more accurate to the secific center, which is a comrehensive result of the "quality ability" and "management" of rocess The Relationshi between the Process aability Indices and Reject Ratio 1) The relation between unbiased and reject ratio P. Suose Pu=P are the reject ratios beyond the uer and lower limits of the secification resectively. Here, the total reject ratio would be: Therefore, P = P + P = 2P U P = P( X < T ) X μ T μ = P( < ) σ σ = P( Z < 3 ) = Φ( 3 = 2 = 2Φ( 3 ) 2) The relationshi between the biased rocess caability index k, offset rate K, and the reject ratio P. When the distribution center offsets to the uer limit of the secification TU X μ TU μ PU = P[ X > TU] = P > σ σ = T T TU ( + ε) P Z 2 ε P Z 2 = > = > = σ σ T (1 k) P Z 2 = > = PZ 3 (1 K) σ > = = 1 Φ (1 K) Similarly, the rocedure may be adated to obtain: X μ T μ P = P[ X < T] = P < σ σ = T T T ( + ε ) (1 k) P Z 2 + P Z 2 = < = < = o σ = P Z < 3 (1 + K) =Φ 3 (1 + K) Therefore, the total reject ratio is: = U + ) [ 3 (1 K) ] Φ[ (1 + )] = 2 Φ K 2

3 When K becomes higher, P will be close to zero and can be omitted, so U [ 3 (1 )] = 1 Φ K The values of quality factor are shown in Table 1. Table 1. Process caability evaluation and analysis table. Value >1.33 = < <1 <0.67 Evaluation The rocess caability fully meets the requirements, but when value is too large, the tolerance requirements and rocess conditions should be analyzed to avoid the waste of equiment recision The rocess caability is adequate, which is the ideal condition The rocess caability meets the requirements, but when the value is too close to 1, there is the ossibility of error, which should be strengthened the control. The rocess caability is inadequate, and the reject ratio is almost 5% that needs to take some measures The rocess caability is severely inadequate that cannot conduct the roduction, so the rocess should be studied and adjusted 2.3. Introduction to Minitab Minitab [9-15] is statistical analysis software. It can be used for learning about statistics as well as statistical research. Statistical analysis comuter alications have the advantage of being accurate, reliable, and generally faster than comuting statistics and drawing grahs by hand. Minitab is relatively easy to use once you know a few fundamentals. For this examle, we will draw a histogram and boxlot of the temerature data and a scatterlot of the water consumtion versus the temerature. 1) To draw a histogram, select GRAPH > HISTOGRAM. 2) hoose Simle and click OK. 3) In the Grah Variables box, select 1 (Temerature). 4) lick OK. 5) omare your answer with the resulting histogram shown on the right. (Note: You can change the settings for the width of the bars in the histogram by clicking the x-axis and clicking EDITOR > EDIT X-Scale and then selecting the Binning tab). 6) To draw a boxlot, select GRAPH > BOXPOT. 7) hoose Simle under One Y and click OK. (Note: If your data is broken down into categories, choose another tye of boxlot. For examle if you were grahing GPA by Gender, you would choose With Grous to get two box lots, one for each gender). 8) In the Grah Variables, select 1 (Temerature). 9) lick OK. 10) omare your answer with the resulting boxlot shown on the right. 11) To grah a scatterlot for water consumtion based on temerature, select GRAPH > SATTERPOT. 12) hoose Simle, and lick OK. 13) In the first row, under Y, select 2 (Water onsumtion) and under X, select 1 (Temerature). 14) lick OK. 15) omare your grah with the grah shown on the right. 3. Solutions 1) Hyothesis regarding the measurement system analysis The test data is obtained during the roduction rocess according to the standardized test methods. Here, the stes are regulated by the rocess document, and the measured object (current value) is accessible. This is for ersonnel and the environment to have an influence over (based on theory and exerience inference). Therefore, it is assumed that the entire measurement system [16-21] met the requirements, was stable and reliable, and could be used as a rerequisite for later analysis. 2) Measure data. 3) Analyze data, establish the control chart, and determine the rocess caability. 4) If the rocess can be controlled, calculate the rocess caability. If it cannot be controlled, collect long-term data for the analysis of variation. 5) Draw a conclusion and ut forward directions for imrovement. 4. Practical Situations 4.1. The Block Diagram of Working urrent Test on Single Board The block diagram of working current test of single board as shown in Fig. 1. 3

4 Power suly Imid of single board by the ammeter EPD download the socket (Power suly socket) Paralle l ort Measured TBDB MU internal ccurrence From the signal source omuter X 6 (20 core socket) Interface board Jumer switch Synchronizing signal ommunication Fig. 1. Test of the measured objects Data ollection The current value of digital single board is continuous data, and test data that collects 101 ieces of single boards. Due to the switch feature of high seed digital circuit, the maximum and the minimum value of the current should be observed resectively in the normal oeration of single board (00 is defined as: at the state, the block word, AD voltage of 1.5 V, etc.) Data Analyzing and Processing Data Normality Test Note: for simlicity, only the current average Imid have been analyzed. From Fig. 2: < 0.05, here, the Imid normality test data in the grah is not straight. A solitary oint aears, suggesting this iece of board is abnormal. Through the use of histograms, the statistical characteristic value of Imid can be calculated, MEAN = 169, StDev = According to the time sequence diagram (as show in Fig. 3), it can be seen that an excetion occurred in the 77th samling oints. By watching the box figure at the same time, the overall data distribution was carried with the reliminary characteristics of normal distribution. Therefore, by neglect the outlier, and in accordance with the samling value (101-1=100), it can be calculated by the following way. According to Table 2, the equation P - VAUE = > 0.05 can be obtained. Here, the data is in a normal distribution, and can be continued for later analysis. Table 2. alculated values. Variable Imid N 100 N* 0 Mean SE Mean StDev 2.20 Minimum Q Median Q Data Stability Test Fig. 4 shows that, by dividing 100 data grous into four subsystems and observing them in chronological order, the data was not found to be eriodic within or among the subgrous. Neither was it offset or with some kind of increase/decrease trend and clustering henomenon. This means it was showing good consistency in the digital single board and stable test rocess Analyze the I-MR ontrol hart From Fig. 5 in accordance with model rules and the requirement # 1, # 2, # 3 and # 4 in the rules of the road - the data is normal. Here, the testing rocess is controlled, which means the center is stable, and the short-term variations are stable. 4

5 Fig. 2. Normality test diagram and histogram. Fig. 3. Imid Box figure and time sequence diagram. Fig. 4. Sequence diagram of acket time. 5

6 Fig. 5. I-MR ontrol chart Process aability Analysis According to the rincile of digital single board design, the factors that affect the actual changes of the ower suly current are: 1) By actual measurement, when a running light on the single board (H5) shining will bring: I = U/R = V / 1000 Ω material current of 1.5 ma current fluctuation; 2) According to digital device materials used by the digital single board, the working current is shown in Table 3. Devices EPD -4256V DSP5409 -ORE DSP5409 -PIN FASH -39VF010 RAM -Y71011 Table 3. Working current of devices. Usage quantity Working urrent (ma) onditions V H H V/100 MHz 3.3 V/100 MHz V/5 MHz V/MOS 3.3 V/outut low 3.3 V/outut low For simlicity, assume that when the digital chis were under normal oerations, the digital circuit changes (mainly the address and data line) could cause 5.0 ma in current fluctuation; 3) 23 digital chis and 164 resistors are used on the digital single board. Assume that value of current change among different boards caused by the inherent inconsistency in the device was 1.0 ma. Therefore, the current total variation would be: = 7.5 ma. Based on the measured data, and according to the 99.0 % confidence interval, it can be calculated that Imid is in a range between ~ Presumably then, the digital board average current is ma. Therefore, the uer and lower secification lines can be set as follows: ±7.5. In other words, the S = ma, US = ma. Here, the hysical meaning is: if a single current is less than the S or greater than the US, it can be concluded that abnormalities exist and that there needs to be reairs). Finally, the rocess caability analysis is shown in Fig. 6. From Fig. 6, it can be known that =1.39, k=1.39, K=7.50/2.20= onclusions 1) k>1.33 this shows good consistency of the rocess and sound quality of the current in the single board. If imrovements were to be made, the average would be decreased, and k would be increased. 2) >1 this suggests that the rocess variation is less than the width of the secification, and the roduction is relatively stable. If imrovements were to be made, the deviation would be decreased, and k would be increased. 3) The short-term quality of this batch of single boards was 3.4 sigma. By checking the Z table (normal distribution table), the yield is %, and the reject ratio is 0.67 %. 4) The SP calculation objectively reflects the digital late testing level of the roduction line. Here, the reliminary rocess caability around 4 sigma (short-term) can be obtained. 5) For the single board, the real quality of the boards can be reflected through the analysis. Due to the fact that there were no statistics calculations 6

7 before, the abnormal board surface function is normal. However, the current value is larger than normal (22 ma). This results in hidden quality trouble. When the abnormal roducts were judged to be qualified, they would then be assembled into the whole flow field. Fig. 6. Process caability analysis diagram. Acknowledgements Project: the Science and Technology Program of the Education Deartment of Shaanxi Province Government (number: 2013JK1112). References [1].. Wu, Study of statistical rocess control method and alication, Ph.D. Thesis, Shangdong University, Shangdong, [2]. Y. Q. Zhang, B. Y. Duan, T. J. i., Deloyment control method for flexible deloyable antennas based on FFT filter, Journal of Mechanical Engineering, Vol. 3, 2012, [3]. H. X. Wang, Z. D. Zhou, S. H. Hu, Guiding structure of scientific information ontology, Journal of entral South University (Science and Technology), No. 5, 2010, [4]. T. J. Zeng, X. Y. Song, R. Q. Pei, et al., Study on SP diagnosis system based on the theory of synergetic exert system, hina Mechanical Engineering, Vol. 24, 2002, [5]. K. Zhao, Z. He, M. Zhang, Multivariate rocess caability analysis based on the rincial comonent analysis method, Journal of Northwestern Polytechnical University, No. 5, 2011, [6].. Wang, Alication of Rayleigh distribution in the rocess ability analysis of tye II restriction gradually in the roduct, Statistics and Decision, Vol. 20, 2012, [7].. Niu, M. Z. Wang, Alication of imroved caability lot in analysis of multivariate rocess caability, Alication Research of omuters, No. 12, 2010, [8].. J. Shuai, DOE to Solve Problem of ow Noise on RF Board, oal Technology, No. 8, 2011, [9].. X. Gong, Y. iu, The quality analysis and control of roduction based on Minitab software, Journal of hongqing University of Technology (Natural Science), Vol. 23, Issue 2, 2013, [10].. J. Shuai, K. M. Teng, and H.-E. Jia, On the error estimates of a new oerator slitting scheme for the Navier-Stokes equations with oriolis force, Mathematical Problems in Engineering, No. 12, 2012, Article ID , 23 ages. [11].. J. Shuai, Analytic hierarchy rocess (AHP) of selecting the rogram of otical interface, Mathematics in Practice and Theory, Vol. 43, Issue 17, 2013, [12]. Suseong Park, Jaemin Kim, Won-Jee hung, O-hul Shin, Alication of resonse surface method for otimal transfer conditions of multi-layer ceramic caacitor alignment system, Journal of entral South University of Technology, No. 3, 2011, [13]. V. Pouvafar, S. A. Sadough, F. Hosseinj, M. R. Rahmani, Design of exeriments for determination of influence of different arameters on mechanical roerties of semi-solid extruded arts, Transactions of Nonferrous Metals Society of hina, Issue S3, [14] J. W. Yu, Study on bias and linearity analysis of MEMS measurement system based on Minitab, Research and Exloration in aboratory, Vol. 31, Issue 1, 2012, [15]. J. uo, D.. Song, Y. Q. Zheng, et al., The alication of quality control technique based on Minitab in the manufacture rocess, Modern Manufacturing Engineering, No. 2, 2009, , 25. [16]. Y. J. i, S.. Du, Measurement system analysis for quality control, Machine Building & Automation, No. 3, 2010,

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