Quality Control Charts for Attributes Besterfield Quality Control

Outline q Attribute q Control Charts for Nonconforming Units q Control Charts for Count of Nonconformities q A Quality Rating System Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

The P Chart q The P Chart is used for Fraction nonconforming is the ratio of the number of nonconforming items in a population to the total number of items in that population. q Recall: A quality characteristic follows a binomial distribution if: 1. All trials are independent. 2. Each outcome is either a “success” or “failure”. 3. The probability of success on any trial is given as p. The probability of a failure is ( 1 -p). 4. The probability of a success is constant. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

$The P Chart Formula: q The fraction nonconforming, p, is usually small, say, 0.$

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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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 X bar and R chart: They are more sensitive to variation. 6. Determine acceptance criteria of a product before shipment to the customer. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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 © 2009 Pearson Education, Upper Saddle River, NJ 07458. Besterfield: Quality Control, 8 ed. . th All rights reserved

The P Chart 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

The P Chart 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 Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

The P Chart 4. Calculate the trial central line and the control limits: Besterfield:

Example : P chart with constant sample size A production manager at a tire manufacturing plant has inspected the number of defective tires in twenty random samples with twenty observations each. Following are the number of defective tires found in each sample: 3/20 Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

P-Chart with variable sample size Three Approaches for Control Charts with Variable Sample Size 1. Variable Width Control Limits 2. Control Limits Based on Average Sample Size 3. Standardized Control Chart Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

P-Chart with variable sample size, cont. Variable Width Control Limits Determine control limits for each individual sample that are based on the specific sample size. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

Example Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle

Solution: Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle

Control Limits Based on an Average Sample Size o Control charts based on the average sample size results in an approximate set of control limits. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

The Standardized Control Chart o The points plotted are in terms of standard deviation units. The standardized control chart has the follow properties: n Centerline at 0 n UCL = 3 Besterfield: Quality Control, 8 th ed. . LCL = -3 © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River,

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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

$The np Chart Number Nonconforming Chart (np): q If the fraction nonconforming po is$

The np Chart Number Nonconforming Chart (np): q If the fraction nonconforming po is unknown, then it must be determine by collecting data, calculating trial control limits, and obtaining the best estimate of po. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

The np Chart Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education,

Example Sample number Lot size (n) Number of rejects 1 200 23 2 200 15 3 200 17 4 200 15 5 200 41 6 200 0 7 200 25 8 200 31 9 200 29 10 200 0 11 200 8 12 200 16 Totals 2400 Besterfield: Quality Control, 8 th ed. . 220 © 2009 Pearson Education, Upper Saddle River, NJ 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 Count of nonconformities (c) chart. q Count of nonconformities per unit (u) chart. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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 and the standard deviation is the square root of the mean. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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 X bar and R chart. 6. Determine acceptance criteria of a product before shipment to the customer. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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 Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 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: Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

Control Charts for Count of Nonconformities/Unit Chart for Count of Nonconformities/Unit (u Chart) Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

U-Chart with variable sample size o U-chart with variable sample size is computed as p-chart, the same three methods are used. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

Control Chart Selection Quality Characteristic Variable Attribute Defective n>1? no x yes n>=10? Defect no yes x and s Besterfield: Quality Control, 8 th ed. . x and R constant sample size? yes no p-chart with variable sample size constant sampling unit? p or np yes no c u © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

Differences Each has its own advantages and disadvantages o Attributes data is easy to collect and several characteristics may be collected per unit. o Variables data can be more informative since specific information about the process mean and variance is obtained directly. o Variables control charts provide an indication of impending trouble (corrective action may be taken before any defectives are produced). o Attributes control charts will not react unless the process has already changed (more nonconforming items may be produced. Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved

Class Questions o What are the differences between p, np, c and u charts? (use, type, used distribution, …. . ) Which one is used more? ? What are the differences between variable and attribute charts? Besterfield: Quality Control, 8 th ed. . © 2009 Pearson Education, Upper Saddle River, NJ 07458. All rights reserved