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# Statistical process control ppt @ bec doms

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Statistical process control ppt @ bec doms

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• Points which might be emphasized include: - Statistical process control measures the performance of a process, it does not help to identify a particular specimen produced as being “good” or “bad,” in or out of tolerance. - Statistical process control requires the collection and analysis of data - therefore it is not helpful when total production consists of a small number of units - While statistical process control can not help identify a “good” or “bad” unit, it can enable one to decide whether or not to accept an entire production lot. If a sample of a production lot contains more than a specified number of defective items, statistical process control can give us a basis for rejecting the entire lot. The issue of rejecting a lot which was actually good can be raised here, but is probably better left to later.
• This slide provides a framework for differentiating between “Process Control” and “Acceptance Sampling,” and “Variables” and “Attributes.” One might also raise the distinction between producer (process control) and customer (acceptance sampling). The next several slides deal with these distinctions.
• Students should understand both the concepts of natural and assignable variation, and the nature of the efforts required to deal with them.
• Once the categories are outlined, students may be asked to provide examples of items for which variable or attribute inspection might be appropriate. They might also be asked to provide examples of products for which both characteristics might be important at different stages of the production process.
• This slide introduces the difference between “natural” and “assignable” causes. The next several slides expand the discussion and introduce some of the statistical issues.
• This slide helps introduce different process outputs. It can also be used to illustrate natural and assignable variation.
• It may be useful to spend some time explicitly discussing the difference between the sampling distribution of the means and the mean of the process population.
• An example of a control chart. .
• The next three slides can be used in a discussion of the theoretical basis for statistical process control.
• This slide simply introduces the various types of control charts.
• This slide introduces the statistical control process. It may be helpful here to walk students through an example or two of the process. The first walk through should probably be for a manufacturing process. The next several slides present information about the various types of process control slides:
• The following slide provides much of the data from Table S6.1.
• Ask the students to imagine a product, and consider what problem might cause each of the graph configurations illustrated.
• Here again it is useful to stress that acceptance sampling relates to the aggregate, not the individual unit. You might also discuss the decision as to whether one should take only a single sample, or whether multiple samples are required.
• You can use this and the next several slides to begin a discussion of the “quality” of the acceptance sampling plans. You will find additional slides on “consumer’s” and “producer’s” risk to pursue the issue in a more formal manner in subsequent slides.
• Once the students understand the definition of these terms, have them consider how one would go about choosing values for AQL and LTPD.
• This slide introduces the concept of “producer’s” risk and “consumer’s” risk. The following slide explores these concepts graphically.
• This slide presents the OC curve for two possible acceptance sampling plans.
• It is probably important to stress that AOQ is the average percent defective , not the average percent acceptable.
• This may be a good time to stress that an overall goal of statistical process control is to “do it better,” i.e., improve over time.
• ### Statistical process control ppt @ bec doms

1. 1. Statistical Process Control
2. 2. Outline <ul><li>STATISTICAL PROCESS CONTROL (SPC) </li></ul><ul><ul><li>Control Charts for Variables </li></ul></ul><ul><ul><li>The Central Limit Theorem </li></ul></ul><ul><ul><li>Setting Mean Chart Limits </li></ul></ul><ul><ul><li>Setting Range Chart Limits ( R -Charts) </li></ul></ul><ul><ul><li>Using Mean and Range Charts </li></ul></ul><ul><ul><li>Control Charts for Attributes </li></ul></ul><ul><ul><li>Managerial Issues and Control Charts </li></ul></ul>
3. 3. Outline <ul><li>PROCESS CAPABILITY </li></ul><ul><ul><li>Process Capability Ratio (C p ) </li></ul></ul><ul><ul><li>Process Capability Index (C pk </li></ul></ul><ul><li>ACCEPTANCE SAMPLING </li></ul><ul><ul><li>Operating Characteristic (OC) Curves </li></ul></ul><ul><ul><li>Average Outgoing Quality </li></ul></ul>
4. 4. <ul><li>When you complete this chapter, you should be able to Identify or Define : </li></ul><ul><ul><li>Natural and assignable causes of variation </li></ul></ul><ul><ul><li>Central limit theorem </li></ul></ul><ul><ul><li>Attribute and variable inspection </li></ul></ul><ul><ul><li>Process control </li></ul></ul><ul><ul><li>LCL and UCL </li></ul></ul><ul><ul><li>p-charts and C-charts </li></ul></ul>Learning Objectives
5. 5. <ul><li>When you complete this chapter, you should be able to Identify or Define : </li></ul><ul><ul><li>Acceptance sampling </li></ul></ul><ul><ul><li>OC curve </li></ul></ul><ul><ul><li>AQL and LTPD </li></ul></ul><ul><ul><li>AOQ </li></ul></ul><ul><ul><li>Producer’s and consumer’s risk </li></ul></ul>Learning Objectives - Continued
6. 6. Learning Objectives - Continued <ul><li>When you complete this chapter, you should be able to Describe or explain : </li></ul><ul><ul><li>The role of statistical quality control </li></ul></ul>
7. 7. <ul><li>Measures performance of a process </li></ul><ul><li>Uses mathematics (i.e., statistics) </li></ul><ul><li>Involves collecting, organizing, & interpreting data </li></ul><ul><li>Objective: provide statistical signal when assignable causes of variation are present </li></ul><ul><li>Used to </li></ul><ul><ul><li>Control the process as products are produced </li></ul></ul><ul><ul><li>Inspect samples of finished products </li></ul></ul>Statistical Quality Control (SPC)
8. 8. Types of Statistical Quality Control Statistical Quality Control Process Control Acceptance Sampling Variables Charts Attributes Charts
9. 9. Natural and Assignable Variation
10. 10. <ul><li>Characteristics for which you focus on defects </li></ul><ul><li>Classify products as either ‘good’ or ‘bad’, or count # defects </li></ul><ul><ul><li>e.g., radio works or not </li></ul></ul><ul><li>Categorical or discrete random variables </li></ul>Quality Characteristics Characteristics that you measure, e.g., weight, length May be in whole or in fractional numbers Continuous random variables Attributes Variables
11. 11. <ul><li>Statistical technique used to ensure process is making product to standard </li></ul><ul><li>All process are subject to variability </li></ul><ul><ul><li>Natural causes : Random variations </li></ul></ul><ul><ul><li>Assignable causes : Correctable problems </li></ul></ul><ul><ul><ul><li>Machine wear, unskilled workers, poor material </li></ul></ul></ul><ul><li>Objective: Identify assignable causes </li></ul><ul><li>Uses process control charts </li></ul>Statistical Process Control (SPC)
12. 12. Process Control: Three Types of Process Outputs Frequency Lower control limit Size (Weight, length, speed, etc. ) Upper control limit ( b) In statistical control , but not capable of producing within control limits. A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; and (c) Out of control. A process out of control having assignable causes of variation. (a) In statistical control and capable of producing within control limits. A process with only natural causes of variation and capable of producing within the specified control limits .
13. 13. The Relationship Between Population and Sampling Distributions Uniform Normal Beta Distribution of sample means Standard deviation of the sample means (mean) Three population distributions
14. 14. Sampling Distribution of Means, and Process Distribution Sampling distribution of the means Process distribution of the sample
15. 15. Process Control Charts
16. 16. <ul><li>Show changes in data pattern </li></ul><ul><ul><li>e.g., trends </li></ul></ul><ul><ul><ul><li>Make corrections before process is out of control </li></ul></ul></ul><ul><li>Show causes of changes in data </li></ul><ul><ul><li>Assignable causes </li></ul></ul><ul><ul><ul><li>Data outside control limits or trend in data </li></ul></ul></ul><ul><ul><li>Natural causes </li></ul></ul><ul><ul><ul><li>Random variations around average </li></ul></ul></ul>Control Chart Purposes
17. 17. Theoretical Basis of Control Charts As sample size gets large enough, sampling distribution becomes almost normal regardless of population distribution. Central Limit Theorem
18. 18. Theoretical Basis of Control Charts Mean Central Limit Theorem Standard deviation
19. 19. Theoretical Basis of Control Charts Properties of normal distribution
20. 20. Control Chart Types Control Charts R Chart Variables Charts Attributes Charts X Chart P Chart C Chart Continuous Numerical Data Categorical or Discrete Numerical Data
21. 21. Statistical Process Control Steps Produce Good Provide Service Stop Process Yes No Take Sample Inspect Sample Find Out Why Create Control Chart Start Can we assign causes?
22. 22. <ul><li>Type of variables control chart </li></ul><ul><ul><li>Interval or ratio scaled numerical data </li></ul></ul><ul><li>Shows sample means over time </li></ul><ul><li>Monitors process average </li></ul><ul><li>Example: Weigh samples of coffee & compute means of samples; Plot </li></ul> X Chart
23. 23. Control Chart for Samples of 9 Boxes Variation due to natural causes 17=UCL 16=Mean 15=LCL Variation due to assignable causes Variation due to assignable causes Out of control 1 2 3 4 5 6 7 8 9 10 11 12 Sample Number
24. 24.  X Chart Control Limits Range for sample i # Samples Mean for sample i From Table S6.1
25. 25. Factors for Computing Control Chart Limits
26. 26. <ul><li>Type of variables control chart </li></ul><ul><ul><li>Interval or ratio scaled numerical data </li></ul></ul><ul><li>Shows sample ranges over time </li></ul><ul><ul><li>Difference between smallest & largest values in inspection sample </li></ul></ul><ul><li>Monitors variability in process </li></ul><ul><li>Example: Weigh samples of coffee & compute ranges of samples; Plot </li></ul>R Chart
27. 27. R Chart Control Limits Range for Sample i # Samples From Table S6.1
28. 28. Steps to Follow When Using Control Charts <ul><li>Collect 20 to 25 samples of n=4 or n=5 from a stable process and compute the mean. </li></ul><ul><li>Compute the overall means, set approximate control limits,and calculate the preliminary upper and lower control limits. If the process is not currently stable , use the desired mean instead of the overall mean to calculate limits. </li></ul><ul><li>Graph the sample means and ranges on their respective control charts and determine whether they fall outside the acceptable limits. </li></ul>
29. 29. Steps to Follow When Using Control Charts - continued <ul><li>Investigate points or patterns that indicate the process is out of control. Assign causes for the variations. </li></ul><ul><li>Collect additional samples and revalidate the control limits. </li></ul>
30. 30. Mean and Range Charts Complement Each Other
31. 31. <ul><li>Type of attributes control chart </li></ul><ul><ul><li>Nominally scaled categorical data </li></ul></ul><ul><ul><ul><li>e.g., good-bad </li></ul></ul></ul><ul><li>Shows % of nonconforming items </li></ul><ul><li>Example: Count # defective chairs & divide by total chairs inspected; Plot </li></ul><ul><ul><li>Chair is either defective or not defective </li></ul></ul>p Chart
32. 32. p Chart Control Limits # Defective Items in Sample i Size of sample i z = 2 for 95.5% limits; z = 3 for 99.7% limits
33. 33. P-Chart for Data Entry Example UCL p =0.10 LCL p =0.00
34. 34. <ul><li>Type of attributes control chart </li></ul><ul><ul><li>Discrete quantitative data </li></ul></ul><ul><li>Shows number of nonconformities (defects) in a unit </li></ul><ul><ul><li>Unit may be chair, steel sheet, car etc. </li></ul></ul><ul><ul><li>Size of unit must be constant </li></ul></ul><ul><li>Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot </li></ul>c Chart
35. 35. c Chart Control Limits # Defects in Unit i # Units Sampled Use 3 for 99.7% limits
36. 36. Patterns to Look for in Control Charts
37. 37. Deciding Which Control Chart to Use <ul><li>Using an X and R chart: </li></ul><ul><ul><li>Observations are variables </li></ul></ul><ul><ul><li>Collect 20-25 samples of n=4, or n=5, or more each from a stable process and compute the mean for the X chart and range for the R chart. </li></ul></ul><ul><ul><li>Track samples of n observations each. </li></ul></ul><ul><li>Using the P-Chart: </li></ul><ul><ul><li>We deal with fraction, proportion, or percent defectives </li></ul></ul><ul><ul><li>Observations are attributes that can be categorized in two states </li></ul></ul><ul><ul><li>Have several samples, each with many observations </li></ul></ul><ul><ul><li>Assume a binomial distribution unless the number of samples is very large – then assume a normal distribution. </li></ul></ul>
38. 38. Deciding Which Control Chart to Use <ul><li>Using a C-Chart: </li></ul><ul><ul><li>Observations are attributes whose defects per unit of output can be counted </li></ul></ul><ul><ul><li>The number counted is often a small part of the possible occurrences </li></ul></ul><ul><ul><li>Assume a Poisson distribution </li></ul></ul><ul><ul><li>Defects such as: number of blemishes on a desk, number of typos in a page of text, flaws in a bolt of cloth </li></ul></ul>
39. 39. Process Capability Ratio, C p
40. 40. Process Capability C pk <ul><li>Assumes that the process is : </li></ul><ul><ul><li>under control </li></ul></ul><ul><ul><li>normally distributed </li></ul></ul>
41. 41. Meanings of C pk Measures C pk = negative number C pk = zero C pk = between 0 and 1 C pk = 1 C pk > 1
42. 42. <ul><li>Form of quality testing used for incoming materials or finished goods </li></ul><ul><ul><li>e.g., purchased material & components </li></ul></ul><ul><li>Procedure </li></ul><ul><ul><li>Take one or more samples at random from a lot (shipment) of items </li></ul></ul><ul><ul><li>Inspect each of the items in the sample </li></ul></ul><ul><ul><li>Decide whether to reject the whole lot based on the inspection results </li></ul></ul>What Is Acceptance Sampling?
43. 43. <ul><li>Set of procedures for inspecting incoming materials or finished goods </li></ul><ul><li>Identifies </li></ul><ul><ul><li>Type of sample </li></ul></ul><ul><ul><li>Sample size ( n ) </li></ul></ul><ul><ul><li>Criteria ( c ) used to reject or accept a lot </li></ul></ul><ul><li>Producer (supplier) & consumer (buyer) must negotiate </li></ul>What Is an Acceptance Plan?
44. 44. <ul><li>Shows how well a sampling plan discriminates between good & bad lots (shipments) </li></ul><ul><li>Shows the relationship between the probability of accepting a lot & its quality </li></ul>Operating Characteristics Curve
45. 45. OC Curve 100% Inspection % Defective in Lot P(Accept Whole Shipment) 100% 0% Cut-Off Return whole shipment Keep whole shipment 1 2 3 4 5 6 7 8 9 10 0
46. 46. OC Curve with Less than 100% Sampling P(Accept Whole Shipment) 100% 0% % Defective in Lot Cut-Off 1 2 3 4 5 6 7 8 9 10 0 Return whole shipment Keep whole shipment Probability is not 100%: Risk of keeping bad shipment or returning good one.
47. 47. <ul><li>Acceptable quality level (AQL) </li></ul><ul><ul><li>Quality level of a good lot </li></ul></ul><ul><ul><li>Producer (supplier) does not want lots with fewer defects than AQL rejected </li></ul></ul><ul><li>Lot tolerance percent defective (LTPD) </li></ul><ul><ul><li>Quality level of a bad lot </li></ul></ul><ul><ul><li>Consumer (buyer) does not want lots with more defects than LTPD accepted </li></ul></ul>AQL & LTPD
48. 48. <ul><li>Producer's risk (  ) </li></ul><ul><ul><li>Probability of rejecting a good lot </li></ul></ul><ul><ul><li>Probability of rejecting a lot when fraction defective is AQL </li></ul></ul><ul><li>Consumer's risk (ß) </li></ul><ul><ul><li>Probability of accepting a bad lot </li></ul></ul><ul><ul><li>Probability of accepting a lot when fraction defective is LTPD </li></ul></ul>Producer’s & Consumer’s Risk
49. 49. An Operating Characteristic (OC) Curve Showing Risks  = 0.05 producer’s risk for AQL  = 0.10 Consumer’s risk for LTPD Probability of Acceptance Percent Defective Bad lots Indifference zone Good lots LTPD AQL 0 1 2 3 4 5 6 7 8 100 95 75 50 25 10 0
50. 50. OC Curves for Different Sampling Plans 1 2 3 4 5 6 7 8 9 10 0 % Defective in Lot P(Accept Whole Shipment) 100% 0% LTPD AQL n = 50, c = 1 n = 100, c = 2
51. 51. Average Outgoing Quality Where: P d = true percent defective of the lot P a = probability of accepting the lot N = number of items in the lot n = number of items in the sample
52. 52. <ul><li>Negotiate between producer (supplier) and consumer (buyer) </li></ul><ul><li>Both parties attempt to minimize risk </li></ul><ul><ul><li>Affects sample size & cut-off criterion </li></ul></ul><ul><li>Methods </li></ul><ul><ul><li>MIL-STD-105D Tables </li></ul></ul><ul><ul><li>Dodge-Romig Tables </li></ul></ul><ul><ul><li>Statistical Formulas </li></ul></ul>Developing a Sample Plan
53. 53. Statistical Process Control - Identify and Reduce Process Variability Lower specification limit Upper specification limit (a) Acceptance sampling –[ Some bad units accepted; the “lot” is good or bad] (b) Statistical process control – [Keep the process in “control”] (c) c pk >1 – [Design a process that is in control]