Slide 1: Adamson University Graduate School CHAPTER 7
ATTRIBUTE CONTROL CHARTS Selections Introduction
Types of Attribute Control Charts
The p Chart for Constant Subgroup Sizes The p Chart for Variable Subgroup Sizes
The np Chart
Count Charts c Charts
Limitations of Attribute Control Chart PART 1 PART 2 PART 3 MNE 624
Total Quality Management Chapter Objectives : Chapter Objectives To discuss when to use the different types of attribute control chart
To construct the different types of attribute Control Charts: p Chart, np Chart, c Chart and µ Chart
To analyze and interpret attribute control charts
To discuss the limitations of attribute control charts Slide 3: Introduction ATTRIBUTE
The term attribute, as used in quality, refers to those quality characteristics that conform to specifications or do not conform to specifications. Attributes are used: Where measurements are not possible - - for example, visually inspected items such as color, missing parts, scratches, and damage. Where measurements can be made but are not made because of time, cost, or need. PART 1 Two basic types of attribute control charts: : Two basic types of attribute control charts: Classification Charts
Count Charts Classification Charts
deal with either the fraction of items or the number of items in a series of subgroups that have a particular characteristics p Chart
used to control the fraction of items with the characteristics. 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 characteristics and is used only with constant subgroup sizes. Slide 5: Count Charts
deal with the number of times a particular characteristic appears in so me given area of opportunity. c Chart
used to control the number of times a particular characteristic appears in a constant area of opportunity. µ Chart
serves the same basic function as a c chart, but is used when the area of opportunity changes from subgroup to subgroup. Construction of a p Chart : Construction of a p Chart Conditions for Use : Conditions for Use Each unit must be classifiable as either possessing or not possessing the characteristic of interest.
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 interest is assumed to be independent of whether any other unit possesses the characteristic. The objectives of nonconforming charts are to: : The objectives of nonconforming charts are to: Determine the average quality level.
Bring to the attention of management any changes in the average.
Improve the product quality.
Evaluate the quality performance of operating and management personnel.
Suggest place to use X and R charts.
Determine acceptance criteria of a product before shipment to the customer. End of part 1 Slide 9: p Chart for Constant Subgroup Size
Constant subgroup size implies that the same number of items is sampled and then classified for each subgroup on the chart. We use discrete countable characteristic of output to construct a p Chart. THE CENTER LINE AND CONTROL LIMIT WHERE: p - Centerline
UCL ( p ) - Upper Control Limit
LCL ( p ) - Lower Control Limit
n - Constant Subgroup Size PART 2 Construction of a p Chart : Construction of a p Chart Fig.7.3 Minitab p Chart for Fraction of Cracked Tiles Slide 11: Fig.7.4 Minitab Revised p Chart for Fraction of Cracked Tiles Iterative Re evaluations : Iterative Re evaluations It is possible that by changing the process, removing points that were out of control and recomputing the control limits and points that initially exhibited only common variation will now indicate lack of control. If and when this happens, the system must again re evaluate to eliminate the newly special cause of variation. Analysis of the process will continue to iterate in this manner until there are no longer appears to be lack of control. At some point a decision must be made to stop analysing the original data and collect new data. There is no explicit rule the point at which this should be done; only knowledge and experience with the process can dictate when to stop analysing previous data and begin collecting and analysing new data. SUBGROUP SIZE As general rule, Control Charts based on classification count data should have sizes large enough. Subgroup sizes should remain the same for all subgroups but occasionally circumstances require variation in subgroup size. Whether the subgroup size for p Chart varies or remain constant, the larger the subgroup size, the narrower the control limits will be. p Chart for Variable Subgroup Size : p Chart for Variable Subgroup Size Fig. 7.6 Minitab p Chart for Vehicles with Exact Change Slide 14: Fig. 7.5 Number of Vehicles using Exact Change, Transponders, or Tokens Fig. 7.7 Minitab Revised Control Chart for Vehicles with Exact Change Slide 15: np Chart Traditionally np charts are use only when subgroup size are constant. Data collected for an np chart will be a series of integer, each representing the number of nonconforming (or conforming) item in its subgroup. Fig. 7.8 Minitab p Chart for Cracked Tiles End of part 2 Slide 16: In industrial statistics, the c-chart is a type of control chart used to monitor "count"-type data, typically total number of nonconformities per unit. It is also occasionally used to monitor the total number of events occurring in a given unit of time. c Chart Examples of processes suitable for monitoring with a c-chart include:
Monitoring the number of voids per inspection unit in injection molding or casting processes
Monitoring the number of discrete components that must be re-soldered per printed circuit board
Monitoring the number of product returns per day From Wikipedia PART 3 The number of events in an area of opportunity is denoted by c, the count for each area of opportunity. The sequence of successive c values, taken over time, is used to construct the control chart. : The number of events in an area of opportunity is denoted by c, the count for each area of 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 The standard error is the square root of the mean. Adding and subtracting three times the standard error from the Centerline, c , yields the upper and lower control limits. Thus Counts, Control Limits, and Zones : As we have already seen with p charts and np charts, when a process is in a state of control, only very rarely will points fall beyond the control limits. Therefore, when a point does fall outside the control limits, we will consider it an indication of a lack of control and take appropriate action. When the lower limit is calculated to be negative, we will use 0 uses as the lower control limit because, just as with p charts and np charts, negative numbers of events (such as – 3 defects on a radio) are meaningless. Counts, Control Limits, and Zones Sample Problem
Consider a firm that has decided to use a c chart to help keep track 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. This value is c, the centerline. Slide 19: Given : c = 40.2 Actual counts occurring in an area of opportunity will always be whole numbers. Thus a count of 59 is within the control limits, while a count of 60 is beyond the UCL. The A,B and C zone boundaries are constructed at one and two standard errors from the centerline, respectively. The zone boundaries are: Because the actual counts are whole numbers, the observations would fall into zones as follows: 59.2 The zones each contain a reasonable number of whole numbers and are close enough in size to workable. But consider the problem that would have been encountered if the process average had been C = 2.4. Here we would get : The zones each contain a reasonable number of whole numbers and are close enough in size to workable. But consider the problem that would have been encountered if the process average had been C = 2.4. Here we would get As before, because the counts are whole numbers, the observations will fall into zones as follows: Furthermore, keep in mind that when the average count is small, larger and larger areas of opportunity will b needed to detect imperfections. This will occur as a natural consequence of improved quality through the use of control charts. Construction of a c Chart: An Example : Construction of a c Chart: An Example Consider the output of a paper mill: the product appears at the end of a web and is rolled onto a spool called a reel. Every reel is examined for blemishes, which are imperfections. Each reel is an area of opportunity. Result of these inspections produces the data in table below (table 1.1). In this example the average number of imperfections per reel is Centerline (c) = c = 150/25 = 6.00 Standard Error = c = 6.00 = 2.45
UCL (c) = 6.00 + 3 (2.45) = 13.35
LCL (c) = 6.00 – 3 (2.45) = -1.35 (use 0.0) Slide 22: Fig. 1.1 Minitab c Chart for Blemishes When average counts are small, data appearing as counts will tend to be symmetric. This may lead to over adjustment (false alarms) or under-adjustment (too little sensitivity). False alarms are indications that the process is exhibiting special variation when no special variation can be found. Most often, these indications will be points on the control chart that are just beyond the upper control limit. False alarms, in and themselves can destabilize a stable process.
In some cases, control limits calculated using the Equations 1.1 and 1.2 may not provide sufficient sensitivity to an indication of a special source of variation. This can result in a loss of opportunity for process improvement. Small Average Counts Fixed Control Limits : Fixed Control Limits To avoid both of these problems, we may use a set of fixed control limits for c chart. These fixed control limits are sometimes called probability control limits and provide an excellent and economical rule for separating special and common variations when average counts are less than 20. Therefore, for this application of the c Chart the control limits should properly have come from the Table 1.2. As 6.00 is in the 5.59 to 6.23 range, the values for the lower and upper control limits respectively are 0.5 and 13.5. These values have been used top draw by hand because Minitab does not incorporate fixed probability limits. Slide 24: The µ Chart is similar to the c Chart in that it is a control chart for the count of number of events, such as number of conformities over a given area of opportunity. The fundamental difference lies in the fact that during construction of a c chart, the area of opportunity remains constant from observation to observation, while this is not a requirement for the µ Chart. Instead, the µ Chart considers the numbers of events (such as blemishes or other defects) as a fraction of the total size of the area of opportunity in which these events were possible, thus circumventing the problem of having different area of opportunity for different observations. Examples of processes suitable for monitoring with a µ-chart include:
Monitoring the number of nonconformities per lot of raw material received where the lot size varies
Monitoring the number of new infections in a hospital per day
Monitoring the number of accidents for delivery trucks per day µ Chart Slide 25: The characteristic used for the control chart, μ, is the ratio of the number of events to the area of opportunity in which the events may occur. For observation ₁, we call the number of events (such as imperfections) the observed c₁, and the area of opportunity a₁. Thus, µ₁ is the ratio µ₁ = c₁ / a₁ Equation 1.1 The average of all the µ₁ values, µ, provides a centerline for the control chart Centerline (u) = µ = ∑c₁ / ∑a₁ Equation 1.2 Standard Error = µ / a₁ Since the area of opportunity varies from subgroup to subgroup, so does the standard error. This results in control limits that vary from subgroup to subgroup: Construction of a µ Chart : An Example : Construction of a µ Chart : An Example Here is an example of the u chart template in the QI Macros for Excel. Just type data into the yellow input area and the chart will be drawn to the right. You can also cut and paste data from another spreadsheet into the template. Slide 27: Consider the case of the manufacture of a certain grade of plastic. The plastic is produced in rolls, with samples taken five times daily. Because of the nature of the process, the square footage of each sample varies from inspection lot to inspection lot. Table 3.1 Defects in Rolls of plastic Centerline (u)
= Average Number of defects /100 sq.ft.
= u = 120/47.90 = 2.51 Slide 28: As process improve and defects or defectives become rarer, the number of units that must be examined to find one or more of these events increases. Table 4.1Control Limits for Defects in Rolls of Plastic Fig. 4.1 Minitab u Chart for Number of Defectives in Rolls of Plastic Attribute control charts are limited in terms of the level of process improvement, they enable. Another disadvantage of using attribute control charts is that if special variation from several different sources is present, it is difficult to identify and isolate the special sources individually. Limitations of Attribute Control Charts Slide 29: End of part 3 Thank You!☺ PRESENTORS
JOSEILYN “jo” ANG
ROBERTO “obet” LIZARDO
JONAS “nash” JASARENO