Control chart

1、 company workwork instructionsinstructions document number issuepage 1 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versions are uncontrolled except when stamped “controlled copy” in red. 1.0purpose the purpose of this specificat

2、ion is to provide the methodology for set-up and operating control charts and guideline whether a system is statistically able to meet a set of specifications or requirements. 2.0scope this document applies to all operations with responsibility for ensuring process control for processes directly aff

3、ecting product quality. 3.0document information 3.1reference documents document numberdocument title quality system manual control of quality records statistical techniques and analysis of data continuous improvement process total control methodology (tcm) statistical process control (spc) 3.2docume

4、nt classification this document is classified as “company general business information”. the information disclosed herein is the property of company, company reserves all proprietary, design, manufacturing, reproduction, use, and sales rights thereto, and to any article or process utilizing such inf

5、ormation, except to the extent that rights are expressly granted to others. 3.3acronyms, definitions the property of being in statistical control. stable process processes that are in statistical control. variation in the output of a stable process arises only from common causes. a stable process is

6、 predictable. standard deviation the scatter or spread in the sample data as defined below: statistical control the condition of a process from which all special causes of variation have been eliminated and only common causes remain. statistical control is evidenced on a control chart by the absence

7、 of points beyond the control limits and by the absence of any non-random patterns or trends. variables data measurements taken on a continuous scale. they are quantifiable and incremental in nature. variation the inevitable differences among the measurements of a process. 4.0control charts the foll

8、owing flowchart may be used to determine the appropriate control chart for each of the variables being monitored. company workwork instructionsinstructions document number issuepage 4 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed

9、versions are uncontrolled except when stamped “controlled copy” in red. no or yes no variable attribute n1 n=1 large small large small percentages / ratios defects / events large small large small yes or data from a process to be controlled wandering mean? sample size? data type? shift size? x-bar /

10、 s x-bar / r cusum ewma shift size? x (individual) mr cusum ewma shift size? p np cusum ewma using p shift size? c u cusum ewma using c,u; time between events modified cusum, ewma fit arma model; apply control charts to model residuals use ewma with control limits based on prediction error variance

11、are data autocorrelated ? variables or attributes? fit arima model; apply control charts to model residuals company workwork instructionsinstructions document number issuepage 5 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versio

12、ns are uncontrolled except when stamped “controlled copy” in red. 4.1the control chart is a graph used to analyze variation from a processes or equipment. they provide real-time feedback on the stability and predictability of processes and equipment. by comparing current data to historically determi

13、ned lines, one can make conclusions about whether the process is stable or is being affected by special causes of variation. note on terminology: if a process is stable over time, it is said to be in-control. if it is unstable, it is said to be out-of-control. the terms (stable, in-control, and unst

14、able, out-of-control) are used interchangeably in spc literature and applications. (figure 1) illustrates a typical control chart. . . u uc cl l l lc cl l c cl l t ti imme e v va ar ri ia ab bl le e s su ummmma ar ry y s st ta at ti is st ti ic c a a c co on nt tr ro ol l c ch ha ar rt t (figure 1.

15、example of control chart) 4.2control charts are trend charts that are used to monitor and control processes or equipment. they provide real-time feedback on the stability and predictability of processes and equipment. each point on the chart is an outcome of a subgroup summary statistic of the proce

16、ss measurements, such as a mean, a range or a standard deviation, or an individual value, plotted at some given point of time. thus, the control chart plots the trend of the particular summary statistic over time. the horizontal axis of a control chart is a time variable, such as hour, shift, day or

17、 week. company workwork instructionsinstructions document number issuepage 6 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versions are uncontrolled except when stamped “controlled copy” in red. 4.3control limits and center line t

18、he features of a control chart that distinguish it from a basic trend chart are the presence of statistically based control limits and a center line. these features allow for the objective evaluation of the stability of a process. 4.3.1 the center line (cl) the center line of a control chart (denote

19、d by cl in figure 1) is the mean value of the summary statistic when the process is stable (i.e., in-control). note: in general, the center line is not the target of the process variable. 4.3.2 control limits (ucl and lcl) upper and lower control limits (ucl and lcl, respectively in figure 1) are co

20、nstructed so that a high percentage of the time (e.g., 99.73%) the process summary statistic will fall within the control limits, if the process is stable (i.e., in- control). note: control limits are not specification limits. the state of the process determines the control limits, which will change

21、 based upon elimination of causes of variability and/or process changes (including procedural or equipment changes). if the control limits are constructed correctly, and the process remains stable, it is very unlikely that a value of the summary statistic will fall outside these limits. if there has

22、 been a change in the process, equipment or data collection procedures, a point falling outside of the control limits is a signal that some corrective action is required. 5.0how to make control charts control charts exist to distinguish special cause variation from common cause variation, so that th

23、e process perturbations that generated the special cause variation can be effectively diagnosed and eliminated from the process. company workwork instructionsinstructions document number issuepage 7 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from s

24、erver. printed versions are uncontrolled except when stamped “controlled copy” in red. the control chart limits must be calculated appropriately to optimize the performance of the control system. limits that are too wide for the process data will fail to detect special cause variation, and result in

25、 missed opportunities to improve the process. limits those are too tight for the process data will mistakenly identify an inordinate amount of common cause variation as special cause, thwarting effective trouble shooting of the process. note: the use of the shewhart formulas for some processes can l

26、ead to incorrect control limits, thus resulting in false signals of out-of-control events, or an inability to detect actual out-of-control conditions. 5.1determine new control limits and/or change in existing limits 5.1.1 a new control chart will need limits calculated before it can be put to use in

27、 the manufacturing area. it is important to determine the appropriate control limits for each control chart. incorrect control limits will allow for data points to be in control when the process is out of control, or for data points to be out of control when the process is in control. 5.1.2 listed b

28、elow are reasons that control limits need to be changed: recalculation and revision control of control limit should be performed in spc system. periodic recalculation which should be performed in spc system automatically, is based on set-up criteria of scheduled recalculation and should be reviewed

29、and approved by the pertinent process engineer or spc responsible engineer. for process change or equipment, the recalculation and acceptance of new control limit should be performed by the pertinent process engineer. 5.1.2.1 process change 5.1.2.2 scheduled recalculation (recalculation per 30 subgr

30、oups) company workwork instructionsinstructions document number issuepage 8 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versions are uncontrolled except when stamped “controlled copy” in red. 5.1.2.3 equipment: - new piece of eq

31、uipment from existing equipment set - equipment modification - equipment move or re-qualification - identified and accepted equipment wear 5.1.3 extract data over proper timeframe and reference. there must be adequate data to encompass the natural variation of the process. 5.1.3.1 30 plot points is

32、a rule of thumb (rot) that, historically, delineates the progression from a small sample to a large sample. a plot point is the point to be plotted on the chart. it may represent an individual data point or the summary statistic for a subgroup of data points. 5.1.3.2 in reality, 30 plot points rarel

33、y encompasses the natural variation of a process. for instance, some operations can generate 30 plot points in two days, while batches of material in the same operations are changed once a month. if limits are calculated on the two-days-worth of data, it is probable that those limits will not encomp

34、ass the monthly material change, ensuring that the limits need to be recalculated once every month. conversely, some operations may take days to complete. waiting several months to institute process control is probably not prudent for these operations. 5.1.4 determine whether change or not control l

35、imits 5.1.4.1 if the range of control limit (current or new) is tighter than below 30% of spec limit, and each control limit must be parted from each spec limit as 20% of spec range, then additional change is not needed. 5.1.4.2 if new control range is tighter than current control range as over 20%,

36、 new control limit should be changed. if below 20%, change is not needed. company workwork instructionsinstructions document number issuepage 9 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versions are uncontrolled except when st

37、amped “controlled copy” in red. 5.1.4.3 if new control range is wider than current control range as below 20%, change is not needed. if over 20%, the process of interest is probably too unstable to implement control charts upon, and should be reviewed by spc responsible engineer. 5.1.4.4 if new cont

38、rol limit is shifted from current control limit as below 20%, new control limit can be accepted. if over 20%, the process of interest is probably too unstable to implement control charts upon, and should be reviewed by spc responsible engineer. 5.1.5 assess the control chart with limits and /or new

39、limits 5.1.5.1 if no points are out of control, continue. 5.1.5.2 if less than 10% of the plot points are out of control based upon the newly- calculated control limits, cull the out-of-control plot points from the reference dataset, recalculate the limits, reattach them to the chart, and reassess t

40、he new limits. 5.1.5.3 if 10% or greater of the plot points are out of control based upon the newly- calculated control limits, the process of interest is probably too unstable to implement control charts upon, and shall follow continuous improvement procedure. note： company follow quarterly review

41、control limit 5.2 data type 5.2.1 variable data variables type data consist of continuous (i.e. quantitative) type data. such data are measured on a continuous scale, where all values on this scale are possible outcomes of a measurement. the actual observed outcome is limited only by the discriminat

42、ion capability of the measuring tool. examples of variables data include measurements of length, thickness, temperature, resistance, voltage, time, etc., as measured in such continuous scales as millimeters, degrees, ohms, etc. company workwork instructionsinstructions document number issuepage 10 o

43、f 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versions are uncontrolled except when stamped “controlled copy” in red. 5.2.2 attribute data attribute data include categorical data (e.g., good or bad, machines 1, 2, or 3), count data

44、 (e.g., number of defects, particles added, number of failed wire bonds) and percentages or proportions (e.g. fraction defective, yields). attribute data are measured on a discrete rather than a continuous scale. that is, only certain outcomes are possible. 5.3 control charts by data type there are

45、two types of data collected in the manufacturing line; variables data and attribute data. the type of control chart used depends upon the data type being monitored. 5.3.1 variable control charts variable control charts are used to monitor either the summary statistics or individual data points that

46、measure the location (e.g., the mean) and the variability of the process data. examples of variable control charts include: - individual x / moving range charts - x-bar chart - r chart (range chart) - s chart (standard deviation chart) - multivariate chart - cusum chart - ewma chart note: it is stro

47、ngly recommended that variables data always is monitored using a combination of a location chart (e.g. a mean chart) and a variability chart (e.g. a range chart). 5.3.2 attribute control charts attribute control charts are used to monitor attribute type data. common summary statistics include counts

48、, average counts and percentages or proportions. company workwork instructionsinstructions document number issuepage 11 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versions are uncontrolled except when stamped “controlled copy”

49、in red. examples of attribute control charts include: - c charts - u charts - p charts - np charts 5.4 calculate limits and/or new limits limits for variable charts will be calculated using the grand mean and the standard deviation of all the subgroup summary statistic values from the reference data

50、set. (appendix ae : x-bar chart, r chart, s chart, individual x chart, mr chart) limits for attribute charts will be calculated using the median plus 1.5 times the inter- quartile range. (appendix fg : p chart, c chart) 6.0 analysis of control charts control charts are said to be statistically in co

51、ntrol if the following conditions are encountered. all points lie within the control limits most are near the central line. the point grouping does not form any non-random pattern. 6.1 criteria for a controlled state - all points lie within the control limits - most are near the central line, - the

52、point grouping does not form any nonrandom pattern 6.2 criteria for an abnormal state - some points are outside the control limits - all points are within the control limits, but they form patterns. 6.3 control chart zones control chart zones display a typical x-bar chart, with three zones a, b, and

53、 c on either side of the center line. company workwork instructionsinstructions document number issuepage 12 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versions are uncontrolled except when stamped “controlled copy” in red. ucl

54、 cl lcl x-bar a b c c b a c co on nt tr ro ol l c ch ha ar rt t z zo on ne es s the zones are defined by equally dividing the area between the control limits in sixths, where zone a is the farthest from the center line and zone c is nearest to the center line. 6.4 establish a response plan 6.4.1 det

55、ermine the appropriate out-of-control (ooc) rules (shewhart tests) to be used with each control chart, utilizing at least test 1 as a minimum. 6.4.2 out-of-control-action-plans (ocaps) specify defined and repeatable responses to an out-of-control condition as defined by the control rules. an ocap fo

56、r this chart should provide directions to the operator on how to proceed to identify and correct the cause of the out-of-control event. no control chart should be implemented without an accompanying ocap. 6.5 establish a review mechanism 6.5.1 document events, including out-of-control conditions, co

57、rrective actions taken, changes to process or equipment, and maintenance performed. 6.5.2 establish a regular review of all control charts to determine if any action is necessary, such as control limits adjustment, data collection frequency, etc. note： companywh follow quarterly review 6.5.3 the ins

58、tability index may be used to determine if the control limits need adjustment. company workwork instructionsinstructions document number issuepage 13 of 26 title : control chart electronic versions are uncontrolled except when accessed directly from server. printed versions are uncontrolled except w

59、hen stamped “controlled copy” in red. 6.6shewhart tests that indicates non-random patterns: no.definitiondescriptionpurposeexample 1 one point beyond zone a (control limit) the points show beyond the control limit. (unstable) detects a shift in the mean, an increase in the standard deviation, or a s

60、ingle aberration in the process. for interpreting test 1, the r chart can be used to rule out increase in variation. 2 9 points in a row in a single (upper or lower) side of zone c or beyond most points appear quite close together, upper or lower side of center line. detects a shift in the process m