Quality Improvement Chapter 9 Control Charts for Attributes

Quality Improvement Chapter 9 - Control Charts for Attributes Power. Point presentation to accompany Besterfield, Quality Improvement, 9 e

Outline q Attribute q Control Charts for Nonconforming Units q Control Charts for Count of Nonconformities q A Quality Rating System Quality Improvement, 9 e Dale H. Besterfield 2 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Learning Objectives When you have completed this chapter you should: q Know limitations of variable control charts and the different types of attibute charts. q Know the objectives of the p chart group and the applicable distribution. q Be able to construct a: q Fraction defective chart- fixed subgroup size q Fraction defective chart-variable subgroup size q Percent defective chart q Number defective chart Quality Improvement, 9 e Dale H. Besterfield 3 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Learning Objectives cont’d. When you have completed this chapter you should: q Know how to minimize the effect of variable subgroup size. q Know the applications of the c chart group, the applicable distribution and two conditions. q Be able to construct a c chart and a u chart and know the difference between them. q Know the three classes of defect severity Quality Improvement, 9 e Dale H. Besterfield 4 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Attribute q The term Attribute refers to those quality characteristics that conform to specifications or do not conform to specifications. q Attribute are used: 1. Where measurements are not possible. 2. Where measurements can be made but are not made because of time, cost, or need. Quality Improvement, 9 e Dale H. Besterfield 5 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Attribute q A nonconformity is a departure of a quality characteristic from its intended level or state that occurs with a severity sufficient to cause an associated product or service not to meet a specification requirement. q Defect is concerned with satisfying intended normal, or reasonably foreseeable, usage requirement. Quality Improvement, 9 e Dale H. Besterfield 6 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Attribute q Defect is appropriate for use when evaluation is in terms of usage. q Nonconformity is appropriate for conformance to specifications. q The term Nonconforming Unit is used to describe a unit of product or service containing at least one nonconformity. Quality Improvement, 9 e Dale H. Besterfield 7 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Attribute q Defective is analogous to defect and is appropriate for use when unit of product or service is evaluated in terms of usage rather than conformance to specifications. q Limitations of variable control charts: These charts cannot be used for quality characteristics which are attributes. Quality Improvement, 9 e Dale H. Besterfield 8 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Attribute Types of Attribute Charts: 1. Nonconforming Units (based on the Binomial distribution): p chart, np chart. 2. Nonconformities (based on the Poisson distribution): c chart, u chart. Quality Improvement, 9 e Dale H. Besterfield 9 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart q The P Chart is used for data that consist of the proportion of the number of occurrences of an event to the total number of occurrences. q It is used in quality to report the fraction or percent nonconforming in a product, quality characteristic, or group of quality characteristics. Quality Improvement, 9 e Dale H. Besterfield 10 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Formula: q The fraction nonconforming, p, is usually small, say, 0. 10 or less. q Because the fraction nonconforming is very small, the subgroup sizes must be quite large to produce a meaningful chart. Quality Improvement, 9 e Dale H. Besterfield 11 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart q It can be used to control one quality characteristic, as is done with X bar and R chart, q Or to control a group of quality characteristics of the same type or of the same part, q Or to control the entire product. q It can be established to measure the quality produced by a work center, by a department, by a shift, or by an entire plant. Quality Improvement, 9 e Dale H. Besterfield 12 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart q It is frequently used to report the performance of an operator, group of operators, or management as a means of evaluating their quality performance. q The subgroup size of the P chart can be either variable or constant. Quality Improvement, 9 e Dale H. Besterfield 13 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Objectives of the P Chart: 1. Determine the average quality level: This information provides the process capability in terms of attributes. 2. Bring to the attention of management any changes in the average. 3. Improve the product quality: Ideas for quality improvement. Quality Improvement, 9 e Dale H. Besterfield 14 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Objectives of the P Chart cont’d: 4. Evaluate the quality performance of operating and management personnel. 5. Suggest places to use Xbar and R chart: They are more sensitive to variation. 6. Determine acceptance criteria of a product before shipment to the customer. Quality Improvement, 9 e Dale H. Besterfield 15 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart P-Chart Construction for Constant Subgroup Size 1. Select the quality characteristic(s): a) Single quality characteristic. b) Group of quality characteristics. c) A part. d) An entire product. e) A number of products. f) It can be established for performance control of an operator, work center, department, shift, plant, or corporation Quality Improvement, 9 e Dale H. Besterfield 16 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Construction for Constant Subgroup Size cont’d. 2. Determine the subgroup size and method: q The size of the subgroup is a function of the proportion nonconforming. q A minimum size of 50 is suggested as a starting point. Quality Improvement, 9 e Dale H. Besterfield 17 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Construction for Constant Subgroup Size cont’d. 3. Collect the data: q At least 25 subgroups. q Different sources (Check sheet). q For each subgroup the proportion nonconforming is calculated by the formula P = np/n Quality Improvement, 9 e Dale H. Besterfield 18 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Construction for Constant Subgroup Size 4. Calculate the trial central line and the control limits: Quality Improvement, 9 e Dale H. Besterfield 19 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -2 A p Chart to Illustrate the Trial Central Line and Control Limits Using the Data from Table 9 -1 Quality Improvement, 9 e Dale H. Besterfield 20 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Construction for Constant Subgroup Size cont’d. 5. Establish the revised central line and control limits. Quality Improvement, 9 e Dale H. Besterfield 21 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -3 Continuing Use of the p Chart for Representative Values of the Proportion Nonconforming, p Quality Improvement, 9 e Dale H. Besterfield 22 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart q The P Chart is most effective if it is posted where operating and quality personnel can view it. q The control limits are usually three standard deviations from the central value. Therefore, approximately 99% of the plotted points, P, will fall between the upper and lower control limits. Quality Improvement, 9 e Dale H. Besterfield 23 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart q A P Chart will also indicate long-range trends in quality, which will help to evaluate changes in personnel, methods, equipment, tooling, materials, and inspection techniques. q P-chart is based on the binomial distribution. Quality Improvement, 9 e Dale H. Besterfield 24 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -4 Various Techniques for Presenting p -Chart Information Quality Improvement, 9 e Dale H. Besterfield 25 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Construction for Variable Subgroup Size 1. Collect the data. 2. Determine the trial central line and control limits: Since the subgroup size changes each day, limits must be calculated for each day. Quality Improvement, 9 e Dale H. Besterfield 26 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -5 Preliminary Data, Central Line, and Trial Control Limits Quality Improvement, 9 e Dale H. Besterfield 27 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Construction for Variable Subgroup Size cont’d. 2. As the subgroup size gets larger, the control limits are closer together. 3. Establish revised central line and control limits: Quality Improvement, 9 e Dale H. Besterfield 28 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Construction for Variable Subgroup Size cont’d. q If Po is known, the process of data collection and trial control limits is not necessary. q P is the proportion (fraction) nonconforming in a single subgroup. q Pbar is the average proportion (fraction) nonconforming of many subgroups. Quality Improvement, 9 e Dale H. Besterfield 29 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Construction for Variable Subgroup Size cont’d. o Po is the standard or reference value of the proportion (fraction) nonconforming based on the best estimate of PBar. o Φ is the population proportion (fraction) nonconforming. Quality Improvement, 9 e Dale H. Besterfield 30 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Minimizing the Effect of Variable Subgroup Size 1. Control limits for an average subgroup size: By using an average subgroup size, one limit can be calculated and placed on the control chart. Quality Improvement, 9 e Dale H. Besterfield 31 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -7 Chart for May Data Illustrating Use of an Average Subgroup Size Quality Improvement, 9 e Dale H. Besterfield 32 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Minimizing the Effect of Variable Subgroup Size cont’d. Case I: This case occurs when a point (subgroup fraction nonconforming) falls inside the limits and its subgroup size is smaller than the average subgroup size. Case II: This case occurs when a point (subgroup fraction nonconforming) falls inside the average limits and its subgroup size is larger than the average subgroup size. Quality Improvement, 9 e Dale H. Besterfield 33 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The P Chart Minimizing the Effect of Variable Subgroup Size cont’d. Case III: This case occurs when a point (subgroup fraction nonconforming) falls outside the limits and its subgroup size is larger than the average subgroup size. Case IV: This case occurs when a point (subgroup fraction nonconforming) falls outside limits and its subgroup size is less than the average subgroup size. Quality Improvement, 9 e Dale H. Besterfield 34 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -8 p Chart Illustrating Central Line and Control Limits for Different Subgroup Sizes Quality Improvement, 9 e Dale H. Besterfield 35 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

The np Chart Number Nonconforming Chart (np): np chart is easier for operating personnel to understand than the p chart. q The limitation that this chart has is that the subgroup size needs to be constant. Quality Improvement, 9 e Dale H. Besterfield 36 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The np Chart Quality Improvement, 9 e Dale H. Besterfield 37 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

The np Chart Number Nonconforming Chart (np): q If the fraction nonconforming po is unknown, then it must be determined by collecting data, calculating trial control limits, and obtaining the best estimate of po. Quality Improvement, 9 e Dale H. Besterfield 38 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -9 Number Nonconforming Chart ( np Chart) Quality Improvement, 9 e Dale H. Besterfield 39 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Process Capability q For an attribute this process is much simpler. q The process capability is the central line of the control chart. q Management is responsible for the capability. q When the plotted point is outside the control limit, operating personnel are usually responsible. Quality Improvement, 9 e Dale H. Besterfield 40 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -10 Process Capability Explanation and Responsibility Quality Improvement, 9 e Dale H. Besterfield 41 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities q The nonconformities chart controls the count of nonconformities within the product or service. q An item is classified as a nonconforming unit whether it has one or many nonconformities. q Count of nonconformities (c) chart. q Count of nonconformities per unit (u) chart. Quality Improvement, 9 e Dale H. Besterfield 42 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities q Since these charts are based on the Poisson distribution, two conditions must be met: 1. The average count of nonconformities must be much less than the total possible count of nonconformities. 2. The occurrences are independent. Quality Improvement, 9 e Dale H. Besterfield 43 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities Objectives: 1. Determine the average quality level: This information gives the initial process capability. 2. Bring to the attention of management any changes in the average. 3. Improve the product quality: Ideas for quality improvement. Quality Improvement, 9 e Dale H. Besterfield 44 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities Objectives cont’d. : 4. Evaluate the quality performance of operating and management personnel. 5. Suggest places to use Xbar and R chart. 6. Determine acceptance criteria of a product before shipment to the customer. Quality Improvement, 9 e Dale H. Besterfield 45 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities C Chart construction: 1. Select the quality characteristic(s): a) Single quality characteristic. b) Group of quality characteristics. c) A part. d) An entire product. e) A number of products. f) It can be established for performance control of an: operator, work center, department, shift, plant, or corporation Quality Improvement, 9 e Dale H. Besterfield 46 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities C Chart construction cont’d: 2. Determine the subgroup size and method: 3. Collect the data: q At least 25 subgroups. q Different sources. Quality Improvement, 9 e Dale H. Besterfield 47 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities c-Chart Construction cont’d: 4. Calculate the trial central line and the control limits: Quality Improvement, 9 e Dale H. Besterfield 48 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -11 Control Chart for Count of Nonconformities ( c Chart), Using Preliminary Data Quality Improvement, 9 e Dale H. Besterfield 49 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities 5. Establish the revised central line and control limits Quality Improvement, 9 e Dale H. Besterfield 50 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Quality Improvement, 9 e Dale H. Besterfield 51 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities C chart construction cont’d: 6. Achieve the objectives: The reason for the control chart is to achieve one or more of the previously stated objectives. Quality Improvement, 9 e Dale H. Besterfield 52 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities/Unit Chart for Count of Nonconformities/Unit (u Chart) Quality Improvement, 9 e Dale H. Besterfield 53 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

FIGURE 9 -13 u Chart for Errors on Waybills Quality Improvement, 9 e Dale H. Besterfield 54 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Charts for Count of Nonconformities Chart for Count of Nonconformities/Unit (u Chart) q Scale selected is continuous for the u chart. For the c chart is discrete. q Subgroup size for the u chart can vary. For the c chart is 1. q The u chart is limited in that we do not know the location of the nonconformities. Quality Improvement, 9 e Dale H. Besterfield 55 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

A Quality Rating System Nonconformity Classification: 1. Critical nonconformities: Unsafe conditions for individuals using, maintaining, or depending upon the product. 2. Major nonconformities: Result in failure or reduce materially the usability of the product for its intended purpose. 3. Minor nonconformities: Reduce materially the usability of the product for its intended purpose. Quality Improvement, 9 e Dale H. Besterfield 56 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Control Chart Selection Quality Characteristic Variable Attribute Defective n>1? no x and MR yes n>=10? yes x and s Quality Improvement, 9 e Dale H. Besterfield Defect no x and R constant sample size? yes no p-chart with variable sample size Sampling Unit one p or np yes no c u 59 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Computer Program o EXCEL/Minitab program files on the website will solve for: n n p chart np chart c chart U chart Quality Improvement, 9 e Dale H. Besterfield 60 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Homework o 5, 7, 16 b, 23 Quality Improvement, 9 e Dale H. Besterfield 61 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved