TQM bits Pilani statistical process control attributes of Control chat
- 1. BITS Pilani Hyderabad Campus Total Quality Management Dr. Naga Vamsi Krishna Jasti Asst. Professor Mechanical Engineering Department
- 2. BITS Pilani Hyderabad Campus Statistical Process Control
- 3. BITS Pilani, Hyderabad Campus Scope Control charts for Attributes P Chart NP Chart C Chart U Chart MM ZG522 - Total Quality Management 3
- 4. BITS Pilani, Hyderabad Campus STATISTICAL PROCESS CONTROL: CONTROLCHARTS forATTRIBUTES • What is attribute?, refers to quality characteristics that conform or do not conform to specifications (e.g. OK-NG, Accept-Reject) • Attributes control charts use pass – fail information for charting. • 2 types of usage: 1. Measurements not possible – for example, visually inspected items such as color, missing parts, scratches, and damage 2. Measurements can be made but are not made because of time, cost, or need (e.g. use go-no-go gauge, fitting jig) • 2 important terms to differentiate 1. Defect - items that contribute to nonconformity of a quality characteristics 2. Defective - part/product inspected not conforming or meeting specification (can have > 1 defects) MM ZG522 - Total Quality Management 4
- 5. BITS Pilani, Hyderabad Campus Types ofAttributes control charts The types of attributes control charts include the following: 1. p charts - a single chart that tracks the percentage of nonconforming item in each sample - sample sizes are large, usually 100 pieces or more. Sample size may vary. 2. np charts - tracks the number of nonconforming items in each sample - easier to use than the p chart because the percentage of defective items does not have to be calculated, but it has one restrictions - all the samples must be the same size 3. c charts - graphs the total number of nonconformance found in each piece or unit that is inspected 4. u charts - samples are taken and the total number of nonconformance in the sample is determined - tracks the average number of nonconformance per unit MM ZG522 - Total Quality Management 5
- 6. BITS Pilani, Hyderabad Campus P Chart Attributes are discrete events: yes/no or pass/fail – Use P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisions • Number of leaking caulking tubes in a box of 48 • Number of broken eggs in a carton MM ZG522 - Total Quality Management 6
- 7. BITS Pilani, Hyderabad Campus P-ChartExample:Aproductionmanagerforatirecompanyhasinspectedthenumberofdefective tiresinfiverandomsampleswith20tiresineachsample.Thetablebelowshowsthenumberof defectivetiresineachsampleof20tires.Calculatethecontrollimits. MM ZG522 - Total Quality Management 7
- 8. BITS Pilani, Hyderabad Campus P Chart MM ZG522 - Total Quality Management 8
- 9. BITS Pilani, Hyderabad Campus P chart Steps Construction of p Chart (constant subgroup size) • General procedure same as variable control chart 1. Select quality characteristic - determine use of control chart - p chart can control (one quality characteristic, group of quality characteristic, a part, an entire product, a number of products) - performance control for operator, department, shift, etc. 2. Determine subgroup size and method size subgroup depends on p - NOT A If p = 0.001 and n = 1000 GOOD average number nonconforming np = 1 per subgroup CHART many zeroes - GOOD p = 0.15, n = 50 CHART np = 7.5 minimum n = 50, usually 1000
- 10. BITS Pilani, Hyderabad Campus P Chart steps 3. Collect the data - al least 25 subgroup - for each subgroup p = np/n; np = number of defectives n = number of samples 4. Calculate the trial limits
- 11. P chart steps
- 12. P Chart Steps 5. Establish revised limits - remove data points out of control - establish revised limits out of control situation present (discard) limits can only be calculated until finish inspection
- 13. P Chart steps
- 14. BITS Pilani, Hyderabad Campus P chart steps 6. Achieve the objective - the first five step are planning - the last step involves action and leads to the achievement of the objective - some representative values of inspection results for the month of June are shown in Figure above - analysis of the June results shows that the quality improved and also for entire month of July and August
- 15. BITS Pilani, Hyderabad Campus P chart MM ZG522 - Total Quality Management 15
- 16. P Chart 4. Determine trial limits - first, average proportion nonconforming - since n changes, limits calculated for each subgroup - DO IT DIFFERENT n
- 17. P chart - SINCE n is only changing simplify - Note: as n CL are closer n CL gets wider
- 18. P chart 5. Establish revised central line and control limits - remove data points out of control - establish revised limits out of control situation present (discard) - DO IT CALCULATIONS for MAY 4 and MAY 5
- 19. P Chart minimize Steps Two techniques to minimize effect of variable subgroup size 1. Using average subgroup size - calculate individual limits when subgroup size not within ± 15% of nav
- 20. P Chart minimize Steps 2. Establish control limits for different subgroup sizes
- 21. 21 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. The np Chart
- 22. 22 Number Nonconforming Chart (np): If the fraction nonconforming po is unknown, then it must be determined by collecting data, calculating trial control limits, and obtaining the best estimate of po. The np Chart
- 23. CONTROL CHARTS for ATTRIBUTES
- 24. BITS Pilani, Hyderabad Campus C-ChartExample:Thenumberofweeklycustomercomplaintsaremonitoredinalarge hotelusinga c-chart.Developthreesigmacontrollimitsusingthedatatablebelow. MM ZG522 - Total Quality Management 24
- 25. BITS Pilani, Hyderabad Campus C Chart Control MM ZG522 - Total Quality Management 25
- 26. C Chart Construction of c chart 1. Select the quality characteristics 2. Determine the subgroup size and method For c chart n = 1 - one aeroplane - one dozen of pencils, etc. method – audit or on-line 3. Collect data, calculate trial limits
- 27. BITS Pilani, Hyderabad Campus CONTROL CHARTS for ATTRIBUTES 4. Draw the centerline and control limits on the chart
- 28. CONTROL CHARTS for ATTRIBUTES 5. Interpret the chart - point 6 is out of control and should be investigated to determine the cause of so many nonconformities - except for point 6, the chart is performing in a very steady manner 6. Revising the c chart - the reasons behind special-cause situations have been identified and corrected, c charts can be revised using this formula:
- 29. BITS Pilani, Hyderabad Campus CONTROL CHARTS for ATTRIBUTES Construction of u chart (count of defects per unit) • For unit > 1 • For varying sample size • Also if subgroup size constant • u chart is developed same as c chart, collect 25 subgroup data, calculate trial limits and revise limits Data: Hose Connection Formula
- 30. U Chart
- 31. BITS Pilani, Hyderabad Campus U chart • Interpret the chart - except for point 16, the chart appears to be under statistical control - there are no runs or unusual patterns - point 16 should be investigated to determine the cause of such a large number of nonconformities per unit • Revising the u chart
- 32. BITS Pilani, Hyderabad Campus Selection of Control Charts • ANALYSIS STATE OF CONTROL SAME AS VARIABLE CONTROL CHART • Selection of Control Chart
- 33. BITS Pilani, Hyderabad Campus Control Chart : pattern analysis MM ZG522 - Total Quality Management 33
- 34. Control Chart Rules Rule Rule Name Pattern 1 Beyond Limits One or more points beyond the control limits 2 Zone A 2 out of 3 consecutive points in Zone A or beyond 3 Zone B 4 out of 5 consecutive points in Zone B or beyond 4 Zone C 7 or more consecutive points on one side of the average (in Zone C or beyond) 5 Trend 7 consecutive points trending up or trending down 6 Mixture 8 consecutive points with no points in Zone C 7 Stratification 15 consecutive points in Zone C 8 Over-control 14 consecutive points alternating up and down © Wiley 2010 34 Table 1: Control Chart Rules
- 35. Possible Causes by Pattern Pattern Description Rules Possible Causes Large shifts from the average 1, 2 New person doing the job Wrong setup Measurement error Process step skipped Process step not completed Power failure Equipment breakdown Small shifts from the average 3, 4 Raw material change Change in work instruction Different measurement device/calibration Different shift Person gains greater skills in doing the job Change in maintenance program Change in setup procedure Trends 5 Tooling wear Temperature effects (cooling, heating) Mixtures 6 More than one process present (e.g. shifts, machines, raw material.) Stratifications 7 More than one process present (e.g. shifts, machines, raw materials) Over-control 8 Tampering by operator Alternating raw materials 35
- 36. 36 Process Capability Product Specifications – Preset product or service dimensions, tolerances: bottle fill might be 16 oz. ±.2 oz. (15.8oz.-16.2oz.) – Based on how product is to be used or what the customer expects Process Capability – Cp and Cpk – Assessing capability involves evaluating process variability relative to preset product or service specifications – Cp assumes that the process is centered in the specification range – Cpk helps to address a possible lack of centering of the process 6σ LSL USL width process width ion specificat Cp 3σ LSL μ , 3σ μ USL min Cpk
- 37. 37 Relationship between Process Variability and Specification Width Three possible ranges for Cp – Cp = 1, as in Fig. (a), process variability just meets specifications – Cp ≤ 1, as in Fig. (b), process not capable of producing within specifications – Cp ≥ 1, as in Fig. (c), process exceeds minimal specifications One shortcoming, Cp assumes that the process is centered on the specification range Cp=Cpk when process is centered
- 38. 38 Computing the Cp Value at Cocoa Fizz: 3 bottling machines are being evaluated for possible use at the Fizz plant. The machines must be capable of meeting the design specification of 15.8-16.2 oz. with at least a process capability index of 1.0 (Cp≥1) The table below shows the information gathered from production runs on each machine. Are they all acceptable? Solution: – Machine A – Machine B Cp= – Machine C Cp= Machine σ USL-LSL 6σ A .05 .4 .3 B .1 .4 .6 C .2 .4 1.2 1.33 6(.05) .4 6σ LSL USL Cp
- 39. 39 Computing the Cpk Value at Cocoa Fizz Design specifications call for a target value of 16.0 ±0.2 OZ. (USL = 16.2 & LSL = 15.8) Observed process output has now shifted and has a µ of 15.9 and a σ of 0.1 oz. Cpk is less than 1, revealing that the process is not capable .33 .3 .1 Cpk 3(.1) 15.8 15.9 , 3(.1) 15.9 16.2 min Cpk
- 40. Thank you © Wiley 2010 40