HEATING COOLING WATER HEATING PRODUCTS DSQR Training Attribute

HEATING, COOLING & WATER HEATING PRODUCTS DSQR Training Attribute Control Charts Ted Fisher/Fred Nunez Corporate Quality

* * - Constant Sample Size Required 2

ATTRIBUTE CONTROL CHARTS Two Major Types ü p charts and np charts ü C charts and U charts To decide which to use, you need to ask: What is being counted? Two ways to count: • Count how many sample units have (or do not have) the attribute (use a p chart or np chart) • Count how many occurrences of the attribute are in the sample (use a C chart or U chart) 3

The Objective of Attribute Control Charts is Similar to Control Charts for Measurement Data • Sample data is collected in an ordered sequence of subgroups • Control limits are placed at + 3 Sigma above and below a center line • Objective is to differentiate between Common and Special causes by detecting non-random patterns of variation Attribute Control Charts are used to evaluate performance in terms of: p - proportion of units having one or more nonconformances np - number of units having one or more nonconformances C - number of nonconformances in a sample U - number of nonconformances per unit 4

Selecting a Control Chart Start Type of data Discrete Counting items with an attribute or counting occurrences? Items with attribute Continuous Need to detect small shifts quickly? Yes Occurrences No No Equal Yes Equal Opportunity? No Sample sizes? Individual measurements or subgroups? Either/Or chart p pchart Individual measurements Yes np np chart Rational Subgroups uuchart Do limits look right? ccchart Yes Individuals chart EWMA R chart X, X, R chart Yes chart Do limits look right? 5 No Try individuals chart No Try transformation to make data normal

Which chart to use? Defects Defectives Variable Sample Size u chart p chart Constant Sample Size c chart np chart 6

Computation of p, np, C, U p = # of units having one or more occurrences # of units in the subgroup np = Average # of units in the subgroup having that attribute C = U = Average # of occurrences in the subgroup having that attribute # of occurrences of the attribute # of units in the subgroup 7

Constructing Control Charts for Discrete Data Chart p chart Control Limit Calculations p± 3 p (1 - p ) n np chart n p ± 3 n p (1 - p ) c chart c ± 3 c u chart u± 3 u a 8

Considerations Notes: 1. Data for p charts may be expressed either as a fraction or as a percentage. 2. For p charts: sample size (n) should be >50 such that the average number of occurrences is >4. To simplify calculations, equal size samples are recommended. However, if n for all subgroups is within 25% of the average sample size, you may use the average sample size in control limit calculations. 3. For np charts: n should be >50, such that the average number of occurrences is >4. Subgroups must be of equal size. 4. For C charts: n should be large enough, such that the average number of occurrences is >1. Subgroups must be of equal size. 5. For U charts: n should be large enough, such that the average number of occurrences is >1. To simplify calculations, equal size samples are recommended. However, if n for all subgroups is within 25% of the average sample size, you may use the average sample size in control limit calculations. 9

p Chart The calculation of control limits for this example could have been simplified by the use of average sample sizes for some, though not all subgroups. 10

np Chart Because calculated LCL < 0, LCL = 0. 11

c Chart Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total Average Because calculated LCL < 0, LCL = 0 or n/a. UCL 10. 2 LCL -2. 0 Defects 7 5 3 4 3 8 2 3 4 3 6 3 2 7 2 4 7 4 2 3 82 4. 1 12

u Chart Because calculated LCL < 0, LCL = 0 or n/a. Sample Size (sq ft) Num Holes per sq ft UCL Calc LCL Actual LCL 1 1. 0 4 4. 0 8. 11 -2. 20 n/a 2 1. 0 5 5. 0 8. 11 -2. 20 n/a 3 1. 0 3 3. 0 8. 11 -2. 20 n/a 4 1. 0 3 3. 0 8. 11 -2. 20 n/a 5 1. 0 5 5. 0 8. 11 -2. 20 n/a 6 1. 3 2 1. 5 7. 47 -1. 57 n/a 7 1. 3 5 3. 8 7. 47 -1. 57 n/a 8 1. 3 3 2. 3 7. 47 -1. 57 n/a 9 1. 3 2 1. 5 7. 47 -1. 57 n/a 10 1. 3 1 0. 8 7. 47 -1. 57 n/a 11 1. 3 5 3. 8 7. 47 -1. 57 n/a 12 1. 3 2 1. 5 7. 47 -1. 57 n/a 13 1. 3 4 3. 1 7. 47 -1. 57 n/a 14 1. 3 2 1. 5 7. 47 -1. 57 n/a 15 1. 2 6 5. 0 7. 66 -1. 75 n/a 16 1. 2 4 3. 3 7. 66 -1. 75 n/a 17 1. 2 0 0. 0 7. 66 -1. 75 n/a 18 1. 7 8 4. 7 6. 91 -1. 00 n/a 19 1. 7 3 1. 8 6. 91 -1. 00 n/a 20 1. 7 8 4. 7 6. 91 -1. 00 n/a Total 25. 4 75. 0 Average 2. 95 13

Comparison of Control Charts Variables Data (Measurements) Attribute Data (Pass/Fail; Count Data) Uses Average, Range, Standard Deviation Uses, p, np, C, or U Efficient - can use small sample sizes Not efficient - must use large sample sizes Costs per test may be expensive Costs per test generally small Generally used to monitor a single quality characteristic Can monitor single or multiple quality characteristics 14

Questions? Comments? 15

HEATING, COOLING & WATER HEATING PRODUCTS DSQR Training Process Capability & Performance Fred Nunez Corporate Quality

Goals At the end of this section you’ll be able to – apply the basic methods for assessing process capability (Cp, Cpk, Ppk). – use the properties of a Normal Curve that are important to process capability calculations. – explain the Minitab “ 6 pack” and Minitab capability report for the Normal distribution case. 17

Process Capability Indices Process capability and performance indices are ways for measuring how the process distribution is aligned with the specification. LSL USL Voice of the Customer Voice of the Process -3 s +3 s 18

Process Capability 15 % above the Upper Spec Limit 3 % below the Lower Spec Limit Normal process variation This is an example of a situation where the distribution of values for this in-control process does not fall within the allowable tolerances. What shall we do? Since this process is in-control but not capable, one of three actions must occur: 1. 2. 3. 4. Change the specifications “Suffer and Sort” Make a fundamental change to the process Don’t tell anyone 19

Process Capability Here is a situation in which the process average is on-target, but the spread of the values are barely within allowable tolerances. Target But if we only control process variability but don’t control the process average, we might get this. Target And if we control process average only, and fail to control process variability, we might get this. 20

The Normal Curve and Process Capability When continuous data are normally distributed, calculating a process capability index is really equivalent to finding the area under the normal (or bell-shaped) curve that is outside the spec limits, as depicted in the diagram below. LSL USL 21

Normal Distribution 34. 13% 0. 13% 2. 14% – 3 S 13. 60% – 2 S – 1 S 13. 60% 0 +1 S 2. 14% +2 S 0. 13% +3 S 68. 26% 95. 46% 99. 73% 22

Common Process Capability Indices: The C and P families Pp - Process Performance This is the performance index which is defined as the tolerance width divided by the performance, irrespective of process centering. Where: USL = upper specification limit LSL = lower specification limit 6 s = 6 times the sample standard deviation 23

Common Process Capability Indices: The C and P families Pp - Process Performance Pictorially, the process performance Pp is the tolerance width divided by the process spread. 24

Common Process Capability Indices: The C and P families Pp - Process Performance The Pp is determined by the tolerance and spread of the process, location is not considered. The red (left) and blue (right) distributions have the same Pp. Virtually all of the parts produced on the red (left) process will be in specification, while virtually all of the parts from the blue (right) process will be out of specification. 25

Common Process Capability Indices: The C and P families Ppk - Process Performance The process performance index, Ppk, , which accounts for process centering and is defined as: To estimate the Ppk perform both calculation above and report the smaller value. A quicker way is to determine which specification limit (USL or LSL) is closest to the average and only do that calculation, it will be the smallest. 26

Common Process Capability Indices: The C and P families Ppk - Process Performance The Ppk is determined by the tolerance, spread and distance from specification. 27

Common Process Capability Indices: The C and P families Ppk - Process Performance Here we can see the impact of the specification in the definition of Ppk. Both processes above will have the same Pp, same spread and tolerance. The Ppk for the blue (left) process will be lower because (Xbar-LSL) is smaller. 28

Interpreting Ppk LSL 29 USL LSL USL Ppk ~ 2. 0 Ppk ~ 0. 4 Ppk ~ 1. 3 Ppk ~ 0. 0 Ppk ~ 1. 0 Ppk ~ -1. 0 Notice that although the variability is the same for each distribution and Pp=2. 0, Ppk changes dramatically depending on where the process is centered.

Common Process Capability Indices: The C and P families Cp, Cpk, Ppk Ø The only difference between the C and P capability indices is the method used to estimate the standard deviation. Ø When you see an index with a “C” the standard deviation was estimated using the average range from a control chart. Ø When you see an index with a “P” the standard deviation was estimated using the standard deviation of all the data. Ø Both calculations assume that the data is normally distributed. 30

Ppu or Ppl vs. Amount Out-of-Spec Ppu or Ppl % Out-of-Spec p. p. m. Out-of-Spec These values apply only to the tail of the distribution with the higher % out-of-spec (smaller index). Actual % out-of-spec may be as much as double these values when both tails (upper & lower) are considered. 31

Common Process Capability Indices: The C and P families Index Symbol Index Name Default Formula in Minitab (Normal Distribution Case) Notes Cp Capability Index (USL-LSL)/6 swithin Pp Performance Index (USL-LSL)/ 6 soverall CPU (USL- X )/3 swithin (USL- X )/3 soverall C pk Upper Capability Index Upper Performance Index Lower Capability Index Lower Performance Index Capability Index The index is not defined unless both the upper and lower specification limits are used. P pk Performance Index Minimum of { PPU, PPL} PPU CPL PPL ( X -LSL)/3 swithin ( X -LSL)/3 soverall Minimum of { CPU, CPL} Cpk takes into account the process center while Cp does not. Ppk takes into account the process center while Pp does not. 32

Process Capability Statistics Data: C: Six. SigmaDatap. Hexample. mtw Use the following Minitab command to obtain descriptive statistics: Stat>Basic Statistics> Graphical Summary 33

Process Capability Statistics 34

Process Capability Statistics Data: C: Six. SigmaDatap. Hexample. mtw Use the following Minitab command to compute the process capability statistics: Stat>Quality Tools>Capability Analysis (Normal) Enter these values 35

Process Capability Statistics Mean Standard Deviation Cp & Cpk Specification Pp & Ppk Actual Observed PPM Estimated PPM 36

Capability Sixpack Data: C: Six. SigmaDatap. Hexample. mtw Use the following Minitab command to compute the create the Sixpack analysis: Stat>Quality Tools>Capability Sixpack (Normal) 37

Capability Sixpack See next slide Enter these values 38

Capability Sixpack, cont. You may select all the test or only one. For subgroup size >1, default is pooled standard deviation to obtain denominator in C family 39

Process Capability Sixpack for Production p. H 2 1 4 3 40

Process Capability Sixpack for Production p. H 1. The control charts show no signals of special causes, so the C and P family indices should give about the same values. 2. The individual observations match the reference line, so the normal distribution will provide a useful model. 3. The capability plot shows how well the process is centered as well as shows the amount of tolerance used by the process. 4. As Cp is about 1. 0, the short-term process tolerance length is about the same length as the distance between upper and lower specifications. 41

Application Exercise – Process Capability 1. Which two processes are the most variable? _____ and _____ a 2. Which two processes are not potentially capable? _____ and _____ 3. Which two processes have the highest % out-of-spec? b _____ and _____. 4. Which process has the highest Cp? _____ c 5. For which three processes are Cpk and Cp equal? _____, ____ and ______ 6. Which process is potentially capable but not meeting specs? d _____ 7. Which process is supplying the most material at target value? _____ e 8. If these materials were stored in the warehouses of six different suppliers (all other things being equal) which one would you prefer? _____ 9. If the process average could be adjusted for future production, which supplier would you prefer? _____ 10. Calculate Cp and Cpk for c) & d). f 42

Application Exercise – Process Capability 1. Which two processes are the most variable? _____ and _____ e f 2. Which two processes are not potentially capable? _____ and _____ e f a 3. Which two processes have the highest % out-of-spec? _____ and _____. f c 4. Which process has the highest Cp? b _____ d 5. For which three processes are Cpk and Cp equal? Cp=1. 00 c Cpk=0. 53 _____, ____ and ______ b a e 6. Which process is potentially capable but not meeting specs? _____ c Cp=2. 00 d 7. Which process is supplying the most material at target value? Cpk=1. 33 _____ a 8. If these materials were stored in the warehouses of six different suppliers (all other things being equal) which one would you prefer? _____ a 9. If the process average could be adjusted for future production, which supplier would you prefer? _____ d 10. Calculate Cp and Cpk for c) & d). e f 43

Process Capability and Normality The calculated capability indices and the corresponding % out-ofspec values are only valid when the individual data points are normally distributed. Special causes tend to distort the Normal curve. 44