control limits: x-bar & r-charts - edxtumx+qemx+2t2015+type@asset+bl… · control limits:...
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Control Limits: X-bar & R-Charts
Need first 25 samples: X-bar-bar = 21.37 R-bar = 3.02
Control limits for X-bar chart: Control limits for R-chart:
RAXXLCL
XXCL
RAXXUCL
2
2
)(
)(
)(
−=
=
+=
RDRLCLRRCL
RDRUCL
3
4
)()()(
=
=
=
Holly Ott Quality Engineering & Management – Module 8 14
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
Second step: Now we need to look up the constants: A2, D3 and D4
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Factors for Calculating Limits for Variable Control Charts
Holly Ott Quality Engineering & Management – Module 8 15
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Control Limits: X-bar & R-Charts
Need first 25 samples: X-bar-bar = 21.37 R-bar = 3.02
Control limits for X-bar chart: Control limits for R-chart:
Holly Ott Quality Engineering & Management – Module 8 16
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
Constants for n= 5: A2 = 0.577, D3 = 0, and D4 = 2.114
RAXXLCL
XXCL
RAXXUCL
2
2
)(
)(
)(
−=
=
+=
RDRLCLRRCL
RDRUCL
3
4
)()()(
=
=
=
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Holly Ott Quality Engineering & Management – Module 8 17
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Recalculating Limits With “Remaining Data”
• If data falls outside the limits, then the process is not in control. The assignable causes must be found and eliminated.
• Then those values of X-bar and/or R that are outside the limits can be removed from the data, after eliminating the assignable cause(s).
• New limits can be recalculated for future use from the “remaining” data to save time and money.
• (Note: while making these recalculations, start with the R-chart first because calculation of limits for the X-bar chart requires the value for a good R-bar.)
• How many of the original samples can be thrown out, leaving only samples that will be considered enough for calculating the limits?
Holly Ott Quality Engineering & Management – Module 8 18
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
X-bar & R-Charts – Example
The one R value outside the upper limit is removed, assuming that the reason for the value being outside the limit was found and rectified. The new R-bar = 2.85 is calculated from the remaining 23 observations of R. This results in new limits:
Holly Ott Quality Engineering & Management – Module 8 19
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Recalculated Limits with “Remaining Data”
Holly Ott Quality Engineering & Management – Module 8 20
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Holly Ott Quality Engineering & Management – Module 8 21
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
A Few Notes about the X-bar & R-Charts
• Uses of the control charts • To control a process at a given target or nominal value. • To maintain a process at its current level. • As a trouble shooting tool • As an acceptance tool
• Selecting the variable for charting: only important variables should be tracked using the charts.
• Preparing instruments: often lack of adequate instruments is cause for poor quality.
• Rational Sub-Grouping: when an assignable cause is present, the subgrouping enables its discovery.
Holly Ott Quality Engineering & Management – Module 8 22
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
• Control vs. Capability: • Process in control simply means process is consistent. • Capability means the process is producing products within
customer’s specifications. • A process in control does not automatically mean that the
process is capable. • A capability study is needed to verify if the process in- control is
also in-specification (or capable)
Holly Ott Quality Engineering & Management – Module 8 23
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
A Few Notes about the X-bar & R-Charts
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
• False alarm in X-bar chart: • The Type I error in control chart is called False alarm. • When a control chart declares a process not-in-control
when in fact it is in-control, it is a false alarm. • The Shewhart charts with 3-sigma limits have a false
alarm probability of 0.0027 in any one sample. • That is, approximately 3 out of 1000 samples could cause
false alarm.
Holly Ott Quality Engineering & Management – Module 8 24
A Few Notes about the X-bar & R-Charts
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Western Electric Rules
• Use of warning limits drawn at 1-sigma or 2-sigma distances from the center line
Holly Ott Quality Engineering & Management – Module 8 25
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Western Electric Rules “Western Electric”* rules to increase the sensitivity of the X-bar chart are used in addition to the rule that any one point outside of the 3-sigma limit will indicate an out-of-control situation: 1. Two of three consecutive plots fall outside of a 2-sigma warning limit
on the same side of the center line. 2. Four of five consecutive plots fall outside of a 1-sigma warning limit
on the same side. 3. More than seven consecutive plots fall above or below the
centerline. 4. More than seven consecutive plots are in a run-up or a run-down.
Holly Ott Quality Engineering & Management – Module 8 26
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
*Originally published in a handbook by Western Electric Col, republished as the Statistical Control Quality Handbook (AT&T 1985).
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Western Electric Rules • Use of Runs
Holly Ott Quality Engineering & Management – Module 8 27
©2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Quality in Production - 28
Statistical Process Control
Holly Ott Quality Engineering & Management – Module 8
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Coming Up
Lecture 9.1: Six Sigma
Holly Ott Quality Engineering & Management – Module 8 29
TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universität München
Practice
Now let's practice calculating control limits for the X-bar and R-chart.
Please complete the next "Practice" module before continuing with Lecture 9.1.
Holly Ott Quality Engineering & Management – Module 8