control limits: x-bar & r-charts - edxtumx+qemx+2t2015+type@asset+bl… · control limits:...

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