Quality Control Chapter 8 Control Charts for Attributes

Quality Control Chapter 8 - Control Charts for Attributes 1

Outline q Attribute q Control Charts for Nonconforming Units q Control Charts for Count of Nonconformities q A Quality Rating System 2

Learning Objectives When you have completed this chapter you should: q. Know limitations of variable control charts and the different types of attribute 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 3

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 4

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The P Chart Construction for Constant Subgroup Size 1. Select the quality characteristic(s): a) b) c) d) e) f) Single quality characteristic. Group of quality characteristics. A part. An entire product. A number of products. It can be established for performance control of an operator, work center, department, shift, plant, or corporation

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.

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

The P Chart Construction for Constant Subgroup Size 4. Calculate the trial central line and the control limits:

The P Chart Construction for Constant Subgroup Size (cont’d. ) 5. Establish the revised central line and control limits.

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.

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.

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.

The P Chart Construction for Variable Subgroup Size (cont’d. ) 3. As the subgroup size gets larger, the control limits are closer together. 4. Establish revised central line and control limits:

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 ¯P (bar) is the average proportion (fraction) nonconforming of many subgroup.

The P Chart Construction for Variable Subgroup Size (cont’d. ) • Po is the standard or reference value of the proportion (fraction) nonconforming based on the best estimate of PBar. • Φ is the population proportion (fraction) nonconforming.

The P Chart Minimizing the Effect of Variable Subgroup Size Control limits for an average subgroup size: By using an average subgroup size, one limit can be calculated and placed on the control chart.

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.

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.

The np Chart Number Nonconforming Chart (np): q The 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.

The np Chart 31

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.

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.

Control Charts for Count of Non-conformities 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.

Control Charts for Count of Non-conformities 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.

Control Charts for Count of Non-conformities 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.

Control Charts for Count of Non-conformities 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.

Control Charts for Count of Non-conformities 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

Control Charts for Count of Non-conformities C Chart construction (cont’d. ): 2. Determine the subgroup size and method: 3. Collect the data: q At least 25 subgroups. q Different sources.

Control Charts for Count of Non-conformities c-Chart Construction (cont’d. ): 4. Calculate the trial central line and the control limits:

Control Charts for Count of Non-conformities C chart construction (cont’d. ): 5. Establish the revised central line and control limits

Control Charts for Count of Non-conformities 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.

Control Charts for Count of Nonconformities/Unit Chart for Count of Nonconformities/Unit (u Chart)

Control Charts for Count of Non-conformities 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.

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.

Control Charts for Demerits/Unit 46

Control Chart Selection Quality Characteristic Variable n>1? no Attribute Defective x and MR yes n>=10? yes x and s Defect no x and R constant sample size? yes no p-chart with variable sample size constant sampling unit? p or np yes c no u