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Quality Control

Quality Control. Control Charts for Attributes. Outline. Attribute Control Charts for Nonconforming Units Control Charts for Count of Nonconformities A Quality Rating System. Attribute.

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Quality Control

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  1. Quality Control Control Charts for Attributes

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

  3. Attribute • The term Attribute refers to those quality characteristics that conform to specifications or do not conform to specifications. • Attribute are used: • Where measurements are not possible. • Where measurements can be made but are not made because of time, cost, or need.

  4. Attribute • Defect is appropriate for use when evaluation is in terms of usage. • Nonconformity is appropriate for conformance to specifications. • The term Nonconforming Unit is used to describe a unit of product or service containing at least one nonconformity.

  5. Attribute • 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. • Limitations of variable control charts: These charts cannot be used for quality characteristics which are attributes.

  6. Attribute Types of Attribute Charts: • Nonconforming Units (based on the Binomial distribution): p chart, np chart. • Nonconformities (based on the Poisson distribution): c chart, u chart.

  7. The P Chart • 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. • 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.

  8. The P Chart Formula: • The fraction nonconforming, p, is usually small, say, 0.10 or less. • Because the fraction nonconforming is very small, the subgroup sizes must be quite large to produce a meaningful chart.

  9. The P Chart • It can be used to control one quality characteristic, as is done with X bar and R chart, • Or to control a group of quality characteristics of the same type or of the same part, • Or to control the entire product. • It can be established to measure the quality produced by a work center, by a department, by a shift, or by an entire plant.

  10. The P Chart • It is frequently used to report the performance of an operator, group of operators, or management as a means of evaluating their quality performance. • The subgroup size of the P chart can be either variable or constant.

  11. The P Chart Objectives of the P Chart: • Determine the average quality level: This information provides the process capability in terms of attributes. • Bring to the attention of management any changes in the average. • Improve the product quality: Ideas for quality improvement.

  12. The P Chart Objectives of the P Chart cont’d: • Evaluate the quality performance of operating and management personnel. • Suggest places to use X bar and R chart: They are more sensitive to variation. • Determine acceptance criteria of a product before shipment to the customer.

  13. The P Chart P-Chart Construction for Constant Subgroup Size • Select the quality characteristic(s): • 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

  14. The P Chart • Determine the subgroup size and method: • The size of the subgroup is a function of the proportion nonconforming. • A minimum size of 50 is suggested as a starting point.

  15. The P Chart • Collect the data: • At least 25 subgroups. • Different sources (Check sheet). • For each subgroup the proportion nonconforming is calculated by the formula P = np/n

  16. The P Chart • Calculate the trial central line and the control limits:

  17. 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

  18. P-Chart with variable sample size Three Approaches for Control Charts with Variable Sample Size • Variable Width Control Limits • Control Limits Based on Average Sample Size • Standardized Control Chart

  19. 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.

  20. Example

  21. Solution:

  22. Control Limits Based on an Average Sample Size • Control charts based on the average sample size results in an approximate set of control limits.

  23. Solution

  24. The Standardized Control Chart • The points plotted are in terms of standard deviation units. The standardized control chart has the follow properties: • Centerline at 0 • UCL = 3 LCL = -3

  25. The P Chart • The P Chart is most effective if it is posted where operating and quality personnel can view it. • 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.

  26. The P Chart • 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. • P-chart is based on the binomial distribution.

  27. The np Chart Number Nonconforming Chart (np): • The np chart is easier for operating personnel to understand than the p chart. • The limitation that this chart has is that the subgroup size needs to be constant.

  28. The np Chart Number Nonconforming Chart (np): • 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.

  29. The np Chart

  30. Example

  31. Solution

  32. Control Charts for Count of Non-conformities • The nonconformities chart controls the count of nonconformities within the product or service. • Count of nonconformities (c) chart. • Count of nonconformities per unit (u) chart.

  33. Control Charts for Count of Non-conformities • Since these charts are based on the Poisson distribution, two conditions must be met: • The average count of nonconformities must be much less than the total possible count of nonconformities. • The occurrences are independent and the standard deviation is the square root of the mean.

  34. Control Charts for Count of Non-conformities Objectives: • Determine the average quality level: This information gives the initial process capability. • Bring to the attention of management any changes in the average. • Improve the product quality: Ideas for quality improvement.

  35. Control Charts for Count of Non-conformities Objectives cont’d.: • Evaluate the quality performance of operating and management personnel. • Suggest places to use X bar and R chart. • Determine acceptance criteria of a product before shipment to the customer.

  36. Control Charts for Count of Non-conformities C Chart construction: • Select the quality characteristic(s): • 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

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

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

  39. Control Charts for Count of Non-conformities/Unit Chart for Count of Nonconformities/Unit (u Chart)

  40. U-Chart with variable sample size • U-chart with variable sample size is computed as p-chart, the same three methods are used.

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

  42. Differences Each has its own advantages and disadvantages • Attributes data is easy to collect and several characteristics may be collected per unit. • Variables data can be more informative since specific information about the process mean and variance is obtained directly. • Variables control charts provide an indication of impending trouble (corrective action may be taken before any defectives are produced). • Attributes control charts will not react unless the process has already changed (more nonconforming items may be produced.

  43. Class Questions • 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?

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