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However, there are other events that are similarly improbable and should prompt a user to stop collecting data. Each of the the three control charts below contain a problem which resulted in the instrument being serviced after the final control sample. Determine what the problem is for each chart and (assuming the x-axis is measuring days) explain why the instrument needed recalibration or repair on the final day. 0.01 0.008 UCL 0.006 0.004 0.002 0 A -0.002 -0.004 -0.01 0.01 0.008 -0.006 Lower warning -0.008 LCL 0.006 0.004 0.002 0 1 -0.002 -0.004 -0.01 0.01 0.006 Upper warning 0.004 0.002 1 0 -0.002 -0.004 -0.006 -0.008 -0.01 UCL 0.008 UCL -0.006 Lower warning -0.008 LCL 1 Upper warning ● 1 3 ● ● Upper warning 3 ● 3 Lower warning LCL ● ● 5 6 . 7 7 9 9 • 11 11 13 13 13 15 15

However, there are other events that are similarly improbable and should prompt a user to stop collecting data. Each of the the three control charts below contain a problem which resulted in the instrument being serviced after the final control sample. Determine what the problem is for each chart and (assuming the x-axis is measuring days) explain why the instrument needed recalibration or repair on the final day. 0.01 0.008 UCL 0.006 0.004 0.002 0 A -0.002 -0.004 -0.01 0.01 0.008 -0.006 Lower warning -0.008 LCL 0.006 0.004 0.002 0 1 -0.002 -0.004 -0.01 0.01 0.006 Upper warning 0.004 0.002 1 0 -0.002 -0.004 -0.006 -0.008 -0.01 UCL 0.008 UCL -0.006 Lower warning -0.008 LCL 1 Upper warning ● 1 3 ● ● Upper warning 3 ● 3 Lower warning LCL ● ● 5 6 . 7 7 9 9 • 11 11 13 13 13 15 15

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. A control chart is used to track the response of an instrument over time (see Sect. 8E-3 from the analytical textbook). For example, each day the instrument is used a control sample might be analyzed and plotted on the chart. The purpose of the chart is to allow a user to determine when the instrument is possibly not reporting accurate values. Control charts have upper and lower control limits at ±3 standard deviations of the mean. The charts I provide below also have upper and lower warning lines placed at ±2 standard deviations of the mean. There is a 99.7% probability that a single measurement of a control sample will fall within 3 standard deviation of the mean, and a 95.5% probability that a measurement will fall within ±2 standard deviations of the mean. A point that falls outside the upper or lower limits is less than 0.3% probable and indicates a problem may exist. (Often 0.2% is the cutoff, but 0.3% is adequate, at least for us). When such a point occurs, the instrument should be recalibrated (or repaired) before collecting any additional data. However, there are other events that are similarly improbable and should prompt a user to stop collecting data. Each of the the three control charts below contain a problem which resulted in the instrument being serviced after the final control sample. Determine what the problem is for each chart and (assuming the x-axis is measuring days) explain why the instrument needed recalibration or repair on the final day. 0.01 0.008 0.006 0.004 0.002 0 -1 -0.002 -0.004 -0.01 0.01 0.004 -0.006 Lower warning -0.008 LCL 0.002 0 -1 -0.002 0.008 UCL 0.006 -0.004 -0.01 UCL 0.01 Upper warning 1 0.004 0.002 ● -0.01 Upper warning 1 ● -0.006 Lower warning -0.008 LCL 3 0.008 UCL 0.006 Upper warning 3 ● 1 ● 0 -1 -0.002 -0.004 -0.006 Lower warning -0.008 LCL 3 5 5 ● 5 7 7 8 9 ● 11 11 13 13 R 15 15 15
Transcribed Image Text:2. A control chart is used to track the response of an instrument over time (see Sect. 8E-3 from the analytical textbook). For example, each day the instrument is used a control sample might be analyzed and plotted on the chart. The purpose of the chart is to allow a user to determine when the instrument is possibly not reporting accurate values. Control charts have upper and lower control limits at ±3 standard deviations of the mean. The charts I provide below also have upper and lower warning lines placed at ±2 standard deviations of the mean. There is a 99.7% probability that a single measurement of a control sample will fall within 3 standard deviation of the mean, and a 95.5% probability that a measurement will fall within ±2 standard deviations of the mean. A point that falls outside the upper or lower limits is less than 0.3% probable and indicates a problem may exist. (Often 0.2% is the cutoff, but 0.3% is adequate, at least for us). When such a point occurs, the instrument should be recalibrated (or repaired) before collecting any additional data. However, there are other events that are similarly improbable and should prompt a user to stop collecting data. Each of the the three control charts below contain a problem which resulted in the instrument being serviced after the final control sample. Determine what the problem is for each chart and (assuming the x-axis is measuring days) explain why the instrument needed recalibration or repair on the final day. 0.01 0.008 0.006 0.004 0.002 0 -1 -0.002 -0.004 -0.01 0.01 0.004 -0.006 Lower warning -0.008 LCL 0.002 0 -1 -0.002 0.008 UCL 0.006 -0.004 -0.01 UCL 0.01 Upper warning 1 0.004 0.002 ● -0.01 Upper warning 1 ● -0.006 Lower warning -0.008 LCL 3 0.008 UCL 0.006 Upper warning 3 ● 1 ● 0 -1 -0.002 -0.004 -0.006 Lower warning -0.008 LCL 3 5 5 ● 5 7 7 8 9 ● 11 11 13 13 R 15 15 15
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