質(zhì)量管理 Quality Management_ Attribute Control Charts

1、Chapter 7Attribute Control ChartsSectionsLearning ObjectivesIntroductionTypes of Attribute Control ChartsClassification ChartsThe p Chart for Constant Subgroup SizesThe p Chart for Variable Subgroup SizesThe np ChartCount Chartsc Chartsu ChartsIntroductionAttribute data are data based on counts, or

2、the number of times we observe a particular event. The events may be:the number of nonconforming items;the fraction of nonconforming items;the number of defects;or any other distinct occurrence that is operationally defined. Attribute data may include such classifications as: defective or conforming

3、;go or no-go;acceptable or not acceptable;or number of defects per unit. Types of Attribute Control ChartsThere are two basic types of attribute control charts: classification chartscount charts.Types of Attribute Control ChartsClassification Charts Classification charts deal with either the fractio

4、n of items or the number of items in a series of subgroups that have a particular characteristic. p Chart. The p chart is used to control the fraction of items with the characteristic. Subgroup sizes in a p chart may remain constant or may vary. A p chart might be used to control defective versus co

5、nforming, go versus no-go, or acceptable versus not acceptable. np Chart. The np chart serves the same function as the p chart except that it is used to control the number rather than the fraction of items with the characteristic and is used only with constant subgroup sizes.Count ChartsCount charts

6、 deal with the number of times a particular characteristic appears in some given area of opportunity. An area of opportunity can be:a radio;a crate of radios;a hospital room;an airline reservation;a roll of paper;a section of a roll of paper;a time period;a geographical region;a stretch of highway;o

7、r, any delineated observable region in which one or more events may be observed.Count Chartsc Chart. A c chart is used to control the number of times a particular characteristic appears in a constant area of opportunity. A constant area of opportunity is one in which each subgroup used in constructi

8、ng the control chart provides the same area or number of places in which the characteristic of interest may occur. For example:defects per air conditioner;accidents per workweek in a factory;and, deaths per week in a city.The area of opportunity is the subgroup, whether it be the air conditioner, th

9、e factory workweek, or the week in the city.u Chart. A u chart serves the same basic function as a c chart, but it is used when the area of opportunity changes from subgroup to subgroup. For example, we may examine:varying square footage of paper selected from rolls for blemishes;or, carloads of lum

10、ber for damage when the contents of the rail cars varies.Classification ChartsConditions for UseWhen each unit can be classified as either conforming or nonconforming (or having some characteristic of interest or not), a classification chart is appropriate. Samples of n items are periodically select

11、ed from process output. For these n distinct units comprising a subgroup:Each unit must be classifiable as either possessing or not possessing the characteristic of interest. For example, each unit in a subgroup might be classified as either defective or non-defective, or conforming or nonconforming

12、. The number of units possessing the characteristic of interest is called the count, X.The probability that a unit possesses the characteristic of interest is assumed to be stable from unit to unit.Within a given area of opportunity, the probability that a given unit possesses the characteristic of

13、interest is assumed to be independent of whether any other unit possesses the characteristic.For data satisfying these conditions, we may use a p chart or np chart.When Not to Use p Charts or np ChartsIt is important that the denominator in the fraction being charted is the proper area of opportunit

14、y. If it is not, then the data are not truly a proportion but a ratio. For example, the fraction of defectives found on the second shift will be a useful proportion only if it is computed by dividing the number of defectives found on the second shift by the proper area of opportunity, the number of

15、units produced on the second shift.Control charting output from combined different processes will result in irrational subgroups or subgroups that will not enable us to identify process problems. Little if anything can be learned from such charts, and the net effect may be a masking of special cause

16、s of variation.The Deming CyclePlanThe process to be studied using the control chart must be named a flowcharted.The purpose of the chart must be determined.The characteristic to be charted must be selected and operationally defined.The manner, size, and frequency of subgroup selection must be estab

17、lished.The type of chart (i.e., p chart or np chart) must be established.If subgroup sizes will vary from subgroup to subgroup, it must be decided whether new control limits will be computed for each subgroup or whether one of the approximate methods (to be discussed later in this chapter) will be u

18、sed.Forms for recording and constructing the control chart must be established.DoData must be recorded either manually onto control chart paper or electronically onto a Minitab worksheet, see Appendix 7 for instructions on using Minitab to create attributes control charts.The fraction of items with

19、the characteristic of interest must be calculated for each of the subgroups, either manually or electronically by Minitab.The average value must be calculated, either manually or electronically by Minitab.The control limits and zone boundaries must be calculated and plotted onto the control chart, e

20、ither manually or electronically by Minitab.The data points must be entered on the control chart, either manually or electronically by Minitab.StudyThe control chart must be examined for indications of a lack of control, either manually or electronically using the “Test option in Minitab.All aspects

21、 of the control chart must be reviewed periodically and appropriate changes made when required.ActActions must be undertaken to bring the process under control by eliminating any special causes of variation.Actions must be undertaken to reduce the causes of common variation for the purpose of never-

22、ending improvement of the process.Specifications must be reviewed in relation to the capability of the process.The purpose of the control chart must be reconsidered by returning to the Plan stage.The p-chart for Constant Subgroup SizesThe Centerline and Control LimitsConstruction of a p-chartAn Exam

23、pleAs an illustration, consider the case of an importer of decorative ceramic tiles. Some tiles are cracked or broken before or during transit, rendering them useless scrap. The fraction of cracked or broken tiles is naturally of concern to the firm. Each day a sample of 100 tiles is drawn from the

24、total of all tiles received from each tile vendor.Centerline (p) = 183/3000 = 0.061For a stable process, the probability that any subgroup fraction will be outside the three-sigma limits is small. Also, if the process is stable, the probability is small that the data will demonstrate any other indic

25、ations of the presence of special causes of variation. But if the process is not in a state of statistical control, the control chart provides an economical basis upon which to search for and identify indications of this lack of control.For this p-chart - or, in fact, for any of the attribute contro

26、l charts - the exact probabilities that a stable process will generate points indicating a lack of control are impossible to calculate because even a stable process exhibits variation in its mean, dispersion, and shape. Nevertheless, the exact value of these probabilities is not too important for or

27、dinary applications; what is important is the fact that they are small. Therefore, if a point does lie beyond the upper or lower control limits, we will infer that it indicates a lack of control. Additionally, for p-charts, the six other rules for out-of-control points described in Chapter 6 can all

28、 be applied. In order to do so, we need to compute the boundaries for the A, B, and C zones.7.4.2 Construction of a p-chartBoundary between upper zones B and C In our example this value is 0.061 + 0.024 = 0.085 Boundary between lower zones B and C In our example this value is 0.061 - 0.024 = 0.037.B

29、oundary between upper zones A and BBoundary between lower zones A and B Examining the chart, we find a process that is out of control. On day 1, the mean fraction value is above the upper control limit. The sample mean for day 14 is also above the upper control limit, another indication of lack of c

30、ontrol. None of the other rules presented in Chapter 6 appears to be violated.Further study reveals that on both day 1 and day 14 the regular delivery truck operator was absent because of illness. Another employee loaded and drove the delivery truck on those days. That individual had never been inst

31、ructed in the proper care of the product, which requires special handling and treatment. To solve this problem and eliminate this special cause of variation, management created and implemented a training program using the regular drivers experience for three other employees. Any one of these three e

32、mployees can now properly fill in and perform satisfactorily. Thus the system has been changed to eliminate this special cause of variation.After the process has been changed so that special causes of variation have been removed, the out-of-control points are removed from the data. The points are re

33、moved from the control chart, and the graph merely skips over them.Removing these points also changes the process average and standard error. Therefore the centerline, control limits, and zone boundaries must be recalculated.The new centerline and control limits are:= 154/2800 = 0.055Boundary betwee

34、n upper zones B and C = Boundary between lower zones B and C = Boundary between upper zones A and B = Boundary between lower zones A and B = The process now appears to be stable and in a state of statistical control. Management may now look for ways to reduce the overall process average of the numbe

35、r of cracked or broken tiles to raise the usable number of tiles per shipment and effectively increase the process output.Iterative ReevaluationsIt is possible - and not at all uncommon - that by changing the process, removing points that were out of control, and re-computing the control limits and

36、zone boundaries, points that initially exhibited only common variation will now indicate a lack of control. If and when this happens, the system must again be reevaluated to eliminate the newly revealed special causes of variation.Subgroup Size When constructing a p-chart, the subgroup size is much

37、larger than that required for variables control charts. This is because the sample size must be large enough that some nonconforming items are likely to be included in the subgroup. If, for example, a process produces 1.0 percent defectives, sample subgroups of size 10 will only occasionally contain

38、 a nonconforming item. As a general rule of thumb, control charts based on classification count data should have sample sizes large enough so that the average count per subgroup is at least 2.00. This allows the A, B, and C zones to be wide enough to provide a reasonable working region into which da

39、ta points may fall for analysis. This is true for both the p-chart and the np-chart, which we discuss later in this chapter.Subgroup FrequencyEvery process goes through physical cycles, such as shifts and ordering sequences. p-chart and np-chart calculations must be based on a sufficient number of s

40、ubgroups to encompass all of the cycles of a process to include all possible sources of variation. Subgroup data should be collected at a frequency greater than the frequency at which the process can change. This frequency is determined by a process expert.Number of SubgroupsAs a rule of thumb, the

41、number of subgroups should be at least 25 for p-charts and np-charts.The p-Chart for Variable Subgroup SizesSometimes subgroups vary in size. This makes the construction of a manual p-chart somewhat more tedious, although circumstances may make this situation unavoidable. Common among these is when

42、data initially collected for some purpose other than the creation of a control chart are later used to construct a control chart.The standard error, , varies inversely with the sample size. That is, as the sample size increases, the standard error decreases, and vice versa. Control limits and zone b

43、oundaries are calculated based on the standard error. Consequently, as the sample size changes so will the control limits and the zone boundaries.Using Average Subgroup Size: An ExampleConsider, for example, the case of a highway toll barrier with two types of toll collection mechanisms: automatic a

44、nd manned. The automatic lanes require exact change or a transponder while the manned lanes do not. The fraction of vehicles arriving with exact change or a transponder is examined using a control chart for a series of rush hour intervals on consecutive weekdays. As the number of vehicles passing th

45、rough the toll barrier varies, the control limits change day-to-day. One-hour periods (7:30 to 8:30 am) for 20 consecutive weekdays yield the data shown.Using Average Subgroup Size: An ExampleCenterline(p) = = 2569/6421=0.400We can also calculate the UCL, LCL, and zone boundariesfor the first data p

46、oint,Boundary between lower zones A and B =Boundary between lower zones B and C =Boundary between upper zones A and B =Boundary between upper zones B and C = Using Average Subgroup Size: An ExampleThe np-ChartClassification data can sometimes be more easily understood if the data appear as counts ra

47、ther than fractions. This is especially true when using attribute control charts to introduce control charting and encountering reluctance by some members of the affected community to deal with fractions rather than whole numbers, such as the number of defects.The quantity np is the number of units

48、in the subgroup with some particular characteristic, such as the number of nonconforming units. Traditionally, np-charts are used only when subgroup sizes are constant. As the information used is the same as for p-charts with constant subgroup sizes, these two charts are interchangeable.Constructing

49、 the np-ChartConstructing the np-ChartCenterline (np) = 7.6.1 Constructing the np-ChartBoundary between upper zones B and C = Boundary between lower zones B and C = The upper boundary between zones B and C for this example is given by and the lower boundary between zones B and C is given byBoundary

50、between upper zones A and B = Boundary between lower zones A and B = The results for this example are:Count ChartsA defective item is a nonconforming unit. It must be discarded, reworked, returned, sold, scrapped, or downgraded. It is unusable for its intended purpose in its present form. A defect,

51、on the other hand, is an imperfection of some type that is undesirable, although it does not necessarily render the entire good or service unusable. One or more defects may not make an entire good or service defective. For example, we would not scrap or discard a computer, a washing machine, or an a

52、ir conditioner because of a small scratch in the paint.Conditions for UseIf we are to use the c-charts or u-charts, the events we are studying must be describable as discrete events; these events must occur randomly within some well-defined area of opportunity; they should be relatively rare; and th

53、ey should be independent of each other. Exact conformance to these conditions is not always easy to verify. Usually, it is not too difficult to tell whether the events are discrete and whether there is some well-defined area of opportunity. But whether the events are relatively rare is somewhat subj

54、ective and requires process knowledge and experience. The issue of independence is generally revealed by the control chart. That is, if the events are not random and independent, they will tend to form the identifiable patterns.c-ChartsAreas of opportunity that are constant in size are easier to man

55、age than those that vary, in much the same way as constant subgroup sizes in a p-chart are easier to manage than those that vary. Constant areas of opportunity might be such things as:one unit of a particular model of a TV set;a particular type of hospital room;one printed circuit board;one purchase

56、 order;one aircraft canopy;five square feet of paper board;five linear feet of wire. When all conditions for an area of opportunity chart are met, and when the subgroup sizes remain constant, a c-chart is used.The number of events in an area of opportunity is denoted by c, the count for each area of

57、 opportunity. The sequence of successive c values, taken over time, is used to construct the control chart.The centerline for the chart is the average number of events observed. It is calculated as:Counts, Control Limits, and ZonesConsider a firm that has decided to use a c-chart to help keep track

58、of the number of telephone requests received daily for information on a given product. Each day represents an area of opportunity. Over a 30-day period, 1,206 requests are received, or an average of 40.2 per day.A count of 59 is within the control limits, while a count of 60 is beyond the UCL.Counts

59、, Control Limits, and ZonesBoundary between lower zones B and C = Boundary between lower zones A and B = Boundary between upper zones A and B = Boundary between upper zones B and C =Because the actual counts are whole numbers, the observation would fall into zones as follows:The zones each contain a

60、 reasonable number of whole numbers and are close enough in size to be workable. Counts, Control Limits, and ZonesConsider the problem that would have been encountered if the process average had been = 2.4. Here we would get:Boundary between lower zones B and C = Boundary between lower zones A and B