Ch 6 Variable CC

# Ch 6 Variable CC - INDE 321 Quality Control Chapter 6...

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Click to edit Master subtitle style 11 INDE 321 Quality Control Chapter 6, Variable Control Charts Instructor : Linda Boyle Industrial and Systems Engineering Civil and Environmental Engineering University of Washington

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22 Control Charts n Two general types of control charts n Variables Control Charts n Apply to data that follows a continuous distribution (measurement data). n Attributes Control Charts n These charts are applied to data that follow a discrete distribution (count data, defects).
33 Control Charts for Variables n Variable - a single quality characteristic that can be measured on a numerical scale. Examples: Weight, Diameter, Age, Length n When working with variables, need to monitor… n the mean value of the characteristic and n the variability associated with the characteristic.

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44 Control Charts for Variables Purpose : to give information about the performance or capability of the process n R chart gives information on whether the process variability is in control n If process variability is in control, then can examine the chart.
55 Control Charts for Variables n = average of the observations in the i th sample (where i = 1, 2, . .., m) n = grand average or “average of the averages (this value is used as the center line of the control chart) i x x

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66 Control Charts for Variables n Let’s say each point represented the average weight for samples collected each day. n and found n n packet 2 weighed 20 g n packet 3 weighed 35 g
77 Control Charts for Variables

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88 Control Charts for Variables Statistical Basis of the Charts n Assume quality characteristic is normally distributed with mean , and standard deviation, . n If x1, x2, …, xn is a sample of size n, then the average of this sample is n is normally distributed with mean, , and standard deviation, n x x x x n 2 1 + + + = x n x / σ =
99 Control Charts for Variables Statistical Basis of the Charts n The probability is 1 - that any sample mean will fall between (LCL) (UCL) 2 / 2 / 2 / 2 / n Z Z and n Z Z x x σ μ α - = - + = +

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1010 Control Charts for Variables n Ri = range of the values in the ith sample Ri = xmax - xmin n = average range for all m samples (subgroup)
1111 Control Charts for Variables n and found n n packet 2 weighed 20 g n packet 3 weighed 35 g

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1212 Control Charts for Variables Estimating the Process Standard Deviation n Can be estimated using a function of the sample average range. n d2 is a function of the sample size (for each subgroup) n Example, if n=5, then d2=2.326 n d2 is defined as the mean of the relative ranges, W ( W=R/ σ ) n Values of d2 found in Appendix VI Obj1 4
1313 Control Charts for Variables A2

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1414 Control Charts for Variables Control Limits for the chart x R A x LCL x Line Center R A x UCL 2 2 - = = + =
1515 Control Charts for Variables Control Limits for the R chart R D LCL R Line Center R D UCL 3 4 = = =

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1616 Appendix VI A2=0.577 D3=0 D4=2.115
1717 Important things to note n Should always start by checking the variability of the process (is it stable over time?).

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Ch 6 Variable CC - INDE 321 Quality Control Chapter 6...

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