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Attribute Control Charts

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Attribute Control Charts

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    2. Learning Objectives Defective vs Defect Binomial and Poisson Distribution p Chart np Chart c Chart u Chart Tests for Instability

    3. Shewhart Control Charts - Overview

    4. Defective and Defect Defective A unit of product that does not meet customer’s requirement or specification. Also known as a non-conforming unit. Example A base casting that fails porosity specification is a defective. A disc clamp that does not meet the parallelism specification is a defective.

    5. Defect A flaw or a single quality characteristic that does not meet customer’s requirement or specification. Also known as a non-conformity. There can be one or more defects in a defective. Example A dent on a VCM pole that fails customer’s specification is a defect. A stain on a cover that fails customer’s specification is a defect. Defective and Defect

    6. Shewhart Control Charts for Attribute Data There are 4 types of Attribute Control Charts:

    7. Learning Objectives Defective vs Defect Binomial and Poisson Distribution p Chart np Chart c Chart u Chart Tests for Instability

    8. Types of Data and Distributions Discrete Data (Attribute) Binomial Poisson Continuous Data (Variable) Normal Exponential Weibull Lognormal t c2 F This information is primarily reviewThis information is primarily review

    9. Types of Distributions

    10. Discrete Distributions

    11. Discrete Distributions

    12. Binomial Distribution Commonly used in Acceptance Sampling, where p is the probability of success (defective rate), n is the number of trials (sample size), and x is the number of successes (defectives found).

    13. Binomial Distribution Properties: each trial has only 2 possible outcomes - success or failure probability of success p remains constant throughout the n trials the trials are statistically independent the mean and variance of a Binomial Distribution are

    15. James Bernoulli

    17. Discrete Distributions

    18. Poisson Distribution This distribution have been found to be relevant for applications involving error rates, particle count, chemical concentration, etc, where ? is the mean number of events (or defect rate) within a given unit of time or space.

    19. Poisson Distribution Properties: number of outcomes in a time interval (or space region) is independent of the outcomes in another time interval (or space region) probability of an occurrence within a very short time interval (or space region) is proportional to the time interval (or space region) probability of more than 1 outcome occurring within a short time interval (or space region) is negligible the mean and variance for a Poisson Distribution are

    21. Simeon D Poisson

    22. Summary of Approximation

    23. Learning Objectives Defective vs Defect Binomial and Poisson Distribution p Chart np Chart c Chart u Chart Tests for Instability

    24. p Chart Fraction Non-Conforming Reject Rate / Defective Rate Percent Fallout

    25. p Chart Fraction non-conforming (p) Ratio of number of defectives (or non-conforming items) in a population to the number of items in that population. Sample fraction non-conforming (p) Ratio of number of defectives (d) in a sample to the sample size (n), i.e.

    26. The underlying principles of the p chart are based on the binomial distribution. This means that if a process has a typical fraction non-conforming, p, the mean and variance of the distribution for p’s are computed from the binomial equation, giving: p Chart

    27. The p chart also assumes a symmetrical bell-shape distribution, with symmetrical control limits on each side of the center line. This implies that the binomial distribution is approximately close to the shape of the normal distribution, which can happen under certain conditions of p and n: p ? 1/2 and n > 10 implying np > 5 For other values of p, the general guideline is to have np > 10 to get a satisfactory approximation of the normal to the binomial. p Chart

    28. p Chart Following Shewhart’s principle, the Center Line and Control Limits of a p chart are:

    29. If the sample size is not constant, then the Control Limits of a p chart may be computed by either method: a) Variable Control Limits where ni is the actual sample size of each sampling i b) Control Limits Based on Average Sample Size where n is the average (or typical) sample size of all the samples p Chart

    30. When to Use Control Limits Based on Average Sample Size instead of Variable Control Limits Smallest subgroup size, nmin, is at least 30% of the largest subgroup size, nmax. Future sample sizes will not differ greatly from those previously observed. When using Control Limits Based on Average Sample Size, the exact control limits of a point should be determined and examined relative to that value if: There is an unusually large variation in the size of a particular sample There is a point which is near the control limits. p Chart - Average Sample Size

    31. Example 1: p Chart S/N Sampled Rejects 1 50 12 2 50 15 3 50 8 4 50 10 5 50 4 6 50 7 7 50 16 8 50 9 9 50 14 10 50 10 11 50 5 12 50 6 13 50 17 14 50 12 15 50 22 16 50 8 17 50 10 18 50 5 19 50 13 20 50 11

    32. MiniTab: Stat ? Control Charts ? P Example 1: p Chart

    33. Example 1: p Chart

    34. Example 1: p Chart

    35. Example 1: p Chart

    36. Establish Trial Control Limits When to use it? New process, modified process, no historical data available to calculate p How to do it? Calculate p based on the preliminary 20 to 25 subgroups. Calculate the trial control limits using the formula mentioned in slide 21 or 22. Sample values of p from the preliminary subgroups to be plotted against the trial control limits. Any points exceed the trial control limits should be investigated. If assignable causes for these points are discovered, they should be discarded and new trial control limits to be determined.

    37. np Chart If the sample size is constant, it is possible to base a control chart on the number nonconforming (np), rather than the fraction nonconforming (p). The Center Line and Control Limits of an np chart are:

    38. Example 2: np Chart S/N Sampled Rejects 1 50 12 2 50 15 3 50 8 4 50 10 5 50 4 6 50 7 7 50 16 8 50 9 9 50 14 10 50 10 11 50 5 12 50 6 13 50 17 14 50 12 15 50 22 16 50 8 17 50 10 18 50 5 19 50 13 20 50 11

    39. Example 2: np Chart MiniTab: Stat ? Control Charts ? NP

    40. Example 2: np Chart

    41. p Chart vs np Chart For ease of recording, the np chart is preferred. The p chart offers the following advantages: accommodation for variable sample size provides information about process capability

    43. Learning Objectives Defective vs Defect Binomial and Poisson Distribution p Chart np Chart c Chart u Chart Tests for Instability

    44. c Chart Defects per Unit (DPU) Error Rate / Defect Rate Defects per Opportunity

    45. c Chart Each specific point at which a specification is not satisfied results in a defect or nonconformity. The c chart is a control chart for the total number of defects in an inspection unit based on the normal distribution as an approximation for the Poisson distribution, which can happen when: c or ? ? 15

    46. c Chart Inspection Unit The area of opportunity for the occurrence of nonconformities. e.g. a HSA, a media, a PCBA This is an entity chosen for convenience of record-keeping. It may constitute more than 1 unit of product. e.g. a HSA, both surfaces of a media, 10 pieces of PCBA

    47. c Chart If the number of nonconformities (defects) per inspection unit is denoted by c, then: The Center Line and Control Limits of a c chart are:

    48. u Chart In cases where the number of inspection units is not constant, the u chart may be used instead, with: If the average number of defects per inspection unit is denoted by u, then

    49. u Chart The Center Line and Control Limits of a u chart are:

    50. Example 3: c and u Charts S/N Units Defects 1 5 10 2 5 12 3 5 8 4 5 14 5 5 10 6 5 16 7 5 11 8 5 7 9 5 10 10 5 15 11 5 9 12 5 5 13 5 7 14 5 11 15 5 12 16 5 6 17 5 8 18 5 10 19 5 7 20 5 5

    51. Example 3: c and u Charts MiniTab’s Stat ? Control Charts ? C

    52. Example 3: c and u Charts MiniTab’s Stat ? Control Charts ? U

    53. Example 3: c and u Charts

    54. u (or c) Chart vs p (np) Chart The u (or c) chart offers the following advantages: More informative as the type of nonconformity is noted. Facilitates Pareto analysis. Facilitates Cause & Effect Analysis.

    55. Learning Objectives Defective vs Defect Binomial and Poisson Distribution p Chart np Chart c Chart u Chart Tests for Instability

    56. c - Chart Measures the total number of defects in a subgroup The subgroup size can be 1 unit of product if we expect to have a relatively large number of defects/unit Requires a constant subgroup size u - Chart Measures the number of defects/unit of product (dpu) The subgroup size can be constant or variable p - Chart Measures the proportion of defective units in a subgroup The subgroup size can be constant or variable np - Chart Measures the number of defective items in a subgroup Requires a constant subgroup size Selecting the Appropriate Chart

    57. Exercise #1 Strength of 5 test pieces sampled every hour(Xbar-R) Number of defectives in 100 parts(np) Number of solder defects in a printed circuit board assembly(C) Diameter of 40 units of products sampled every day(Xbar-S) Percent defective of a lot produced in every 30-min period(p) Surface defects of surface area of varying sizes(u) In a maintenance group dealing with repair work, the number of maintenance requests that require a second call to complete the repair every week

    58. Test for Instability

    59. Tests for Instability CAUTION : Do not apply “tests” blindly Not every “test” is relevant for all charts Excessive number of “tests” ? Increased ?-error Nature of application

    60. Variables vs Attributes Charts Attributes Control Charts facilitate monitoring of more than 1 quality characteristics. Variables Control Charts provide leading indicators of trouble; Attributes Control Charts react after the process has actually produced bad parts. For a specified level of protection against process drift, Variables Control Charts require a smaller sample size.

    61. Learning Objectives Defective vs Defect Binomial and Poisson Distribution p Chart np Chart c Chart u Chart Tests for Instability

    62. End of Topic What Question Do You Have

    63. Reading Reference Introduction to Statistical Quality Control, Douglas C. Montgomery, John Wiley & Sons, ISBN 0-471-30353-4

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