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Control charts (p np c u)

All Control charts for attribute data with easy examples...

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Control charts (p np c u)

1. 1. 1
2. 2. CONTROL CHARTS (For Attributes) Prepared by : VIPUL WADHWA 2
3. 3. ◦ WHAT IS AN ATTRIBUTE? ◦ CONTROL CHARTS FOR ATTRIBUTE DATA ◦ TYPES & SELECTION OF CONTROL CHART ◦ WHAT IS p CHART , np CHART , c CHART , u CHART. ◦ CALCULATE THE PARAMETERS OF THE CONTROL CHARTS ◦ ADVANTAGES OF ATTRIBUTE CONTROL CHARTS Objectives :- 3
4. 4. 4 The term Attribute refers to those quality characteristics that conform to specifications or do not conform to specifications. This data may be expressed as ok/not ok, go/no go, yes/no, or presence/absence of a defect. 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. ◦What is an Attribute?
5. 5. 5 CONTROLCHARTS FOR ATTRIBUTE DATA: 1. Nonconforming Units (based on the Binomial distribution): p chart, np chart. 2. Nonconformities (based on the Poisson distribution): c chart, u chart.
6. 6. 6
7. 7. 7 TYPES & SELECTION OF CONTROLCHART: What type of data do I have? Variable Attribute Counting defects or defectives? X-bar & S Chart I & MR Chart X-bar & R Chart n > 10 1 < n < 10 n = 1 Defectives Defects What subgroup size is available? Constant Sample Size? Constant Opportunity? yes yesNo no np Chart u Chartp Chart c Chart
8. 8. 8 The p chart is for the fraction of defective items in a sample/lot. This chart shows the fraction of nonconforming or defective product produced by a manufacturing process. The fraction defective is the number of defective items in a sample divided by the total number of items in a sample. The fraction defective chart is used when the sample size varies. What is p Chart:
9. 9. 9 Calculatethe parametersof the p Control Chart with thefollowing: Where: p: Average proportion defective (0.0 – 1.0) ni: Average Number inspected in subgroups LCLp: Lower Control Limit on p Chart UCLp: Upper Control Limit on p Chart Total number of defective items Total number of items inspected n p p(1 p) UCL  p 3 Center Line Control Limits in p i p(1 p) LCL  p 3 p =
10. 10. 10 EXAMPLE Sub- group Number Number Inspected Defective Items 1 250 12 2 189 3 3 410 9 4 210 4 5 315 0 6 310 6 7 240 6 8 295 1 19 300 16 25 310 2 Total 7500 138 Average number inspected: 7500 = 300 25 0.018 138 7500 p 300 0.018)0.018(1 LCL 0.018 3 0.005 0.0 0.041 300 0.018)0.018(1 UCL 0.018 3
11. 11. 11 0.053 p-bar LCL UCL p 5 10 15 20 Subgroup 25 0 0.01 0.02 0.03 0.04 Control Chart:
12. 12. 12 What is np Chart: When each data point is based on the same sample size, a special version of the p chart can be used. The np chart is for the number of defective items in a sample. This chart shows the number of nonconforming. The number of defective, np, chart shows the number of defective items in samples rather than the fraction of defective items. It requires that the sample size remains constant.
13. 13. 13 Calculatethe parametersof the np Control Chartwith the following: Center Line Control Limits Where: N : Constant Sample Size p : Average proportion defective (0.0 – 1.0) LCLnp: Lower Control Limit on nP chart UCLnp: Upper Control Limit on nP chart N p Total number of items inspected p = Total number of defective items UCL  N p + 3 np N p (1 p) LCL  N p 3 np N p (1 p)
14. 14. 14 What is c Chart: The c chart is similar to the np chart, in that it requires equal (constant) sample sizes for each data point. This shows the number of defects or nonconformities produced by a manufacturing process. The number of defects (c chart) is based on the Poisson distribution.
15. 15. 15 Calculatethe parametersof the c ControlChart with the following: 2 Center Line Control Limits Total number of subgroups Total number of defects c  UCLc  c 3 c LCLc  c 3 c Where: C : LCLc: UCLc: Total number of defects divided by the total number of subgroups. Lower Control Limit on C Chart. Upper Control Limit on C Chart.
16. 16. 16 Sample No. No. of Defects Sample No. No. of Defects Sample No. No. of Defects Sample No. No. of Defects 1 5 6 4 11 6 16 5 2 4 7 5 12 5 17 4 3 5 8 6 13 4 18 6 4 6 9 8 14 7 19 6 5 4 10 7 15 6 20 6 CL = EXAMPLE
17. 17. 17 c chart LCL UCL C bar
18. 18. 18 What is u Chart: The u chart is a more general version of the c chart for use when the data points do not come from equal-sized samples. The symbol u is used to represent defects per unit. The u chart is used in cases where the samples are of different size. This chart shows the nonconformities per unit produced by a manufacturing process.
19. 19. 19 Calculate the parameters of the u Control Chart with the following: 30 Center Line Control Limits u  Total number of defects Identified Total number of Units Inspected u ni UCLu  u 3 i u nuLCL  u 3 Where: u: Total number of defects divided by the total number of units inspected. ni : Average Number inspected in subgroup LCLu: Lower Control Limit on U Chart. UCLu: Upper Control Limit on U Chart.
20. 20. 20 Advantages of attribute control charts: Allowing for quick summaries, that is, the engineer may simply classify products as acceptable or unacceptable, based on various quality criteria. Thus, attribute charts sometimes bypass the need for expensive, precise devices and time-consuming measurement procedures. Easily understood by managers unfamiliar with quality control procedures.
21. 21. Thank you very much for your attention! 21
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All Control charts for attribute data with easy examples...

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