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Our Process Tower Elevation Front Arm Back 1 Operational Definition • Need two things: – a method of measurement or test – a set of criteria for judgment • For example, what are operational definitions for the following: – on-time delivery – good service – 50% wool blanket 2 source: Moen, Nolan and Provost, Improving Quality Through Planned Experimentation Data Collection • • • Collect 5 data points for each team member Plot run chart (use chart wizard) Construct a histogram (Data | Data Analysis | Histogram) • Construct a box and whiskers plot (use box&whiskers.xls) • Calculate x-bar and s (Data | Data Analysis | Descriptive Statistics) • Discuss results and be prepared to brief results to other groups 3 Data | Data Analysis Descriptive Statistics Histogram 4 Insert | Line Chart Box and Whiskers XLS 5 What the Exercise Statistics Reveal • The sample mean (x-bar) describes typical distances in one number. • Other measures of central tendency include: median and mode. • The sample standard deviation (s) provides a measure of the ‘average’ deviation around the mean. 6 Using x-bar and s • The empirical rule assumes the underlying distribution is normal: – 68% within ± 1 s – 95% within ± 2 s – 99 % within ±3 s • For any distribution: – At least 75% within ± 2 s – At least 89% within ± 3 s 7 Histograms • Shows the distribution of process outcomes. • Look for center, shape and spread • Compare to: – your expectations and knowledge – target and specification requirements – across shifts, operators, machines, etc 8 Process capability Cp USL x x LSL USL LSL or C pk min , 6 * sigma 3 * sigma 3 * sigma EXCEL: =Normdist(x, mean, std dev, 1) to calculate percent non-conforming material. 9 The Statistical Meaning of Six Sigma Process capability measure Upper Specification Limit (USL) Lower Specification Limit (LSL) Process A (with st. dev sA) X-3sA X-2sA X-1sA X X+1sA X+2s X+3sA 3s Process B (with st. dev sB) X-6sB X Cp USL LSL 6sˆ xs Cp P{defect} ppm 1s 0.33 0.317 317,000 2s 0.67 0.0455 45,500 3s 1.00 0.0027 2,700 4s 1.33 0.0001 63 5s 1.67 0.0000006 0,6 6s 2.00 2x10-9 0,00 X+6sB • Estimate standard deviation: ŝ =R /d2 • Look at standard deviation relative to specification limits • Don’t confuse control limits with specification limits: a process can be out of control, yet be incapable 10 11