Class 09 - Control Charts for Variables2 (1 of 2)

8/11/2019 Class 09 - Control Charts for Variables2 (1 of 2)

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Patterns of Control ChartsIndustrial Engineering

x-bar and R

ControlCharts

Examples

Control ChartIn Statistical Control

Out of Control

Assignable Cause

Types the control charts

Process Flowchart

PFMEA

Patterns ofControlCharts


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Nonrandom patterns can indicate out-of-control conditions

Patterns such as cycles, trends, are often of considerable diagnostic valueLook for runs - this is a sequence of observations of the same type (all above

the center line, or all below the center line)

Runs of say 8 observations or more could indicate an out-of-control situation.

Run up: a series of observations are increasing

Run down: a series of observations are decreasing

Pattern is very nonrandom in appearance

x-bar and R

ControlCharts

Examples



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x-bar and R

ControlCharts

Examples



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x-bar and R

ControlCharts

Examples



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x-bar and R

ControlCharts

Examples



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x-bar and R Control ChartsIndustrial Engineering

Types the control chart

Variables Control Chartsx-bar and R-charts

x-bar and s-charts

Charts for individuals (x-charts)

Attributes Control Charts

For defectives (p-chart, np-chart)

For defects (c-chart, u-chart)

Variable - a single quality characteristic that can be measured on a numerical

scale.

When working with variables, we should monitor both the mean value of thecharacteristic and the variability associated with the characteristic.

x-bar and R

ControlCharts

Examples



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Ri= range of the values in the ith sample

Ri= x

max- x

min

average range for all m samples

There exist , the true process mean

There exist is the true process standard deviation

R

m

R

R

m

i

i

1

x-bar and R

ControlCharts

Examples



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The x-bar chart

A typical quality control plan requires sampling one or more items from aproduction process periodically, and making the appropriate qualitymeasurements.

Usually more than one items are measured each time to increase accuracy andmeasure variability.

The x-bar chart helps the quality control person decide whether the center (or

average, or the location of central tendency) of the measurement has shifted.

Statistical Basis of the Charts

Assume the quality characteristic of interest is normally distributed with mean ,and standard deviation, .

If x1, x

2, x

nis a sample of size n, then he average of this sample is

n

xxxx

n

21

x-bar and R

ControlCharts

Examples



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Statistical Basis of the Charts

Assume the quality characteristic of interest is normally distributed with mean ,and standard deviation, .

If x1, x

2, x

nis a sample of size n, then he average of this sample is

is normally distributed with mean, , and standard deviation,

The probability is 1 - that any sample mean will fall between

The above can be used as upper and lower control limits on a control chart forsample means, if the process parameters are known.

n

xxx

x n

21

nZZand

nZZ

xx

2/2/2/2/

x-bar and R

ControlCharts

Examples



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x-bar and R Control Charts

Introduction

Industrial Engineering

x-bar and R

ControlCharts

Examples

Estimating the Process Standard Deviation

d2

can also be found in Table I in Appendix II for various values of n.

2

d

R

Sample ofA2

, D4, D

3and

d2

are Table


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x-bar and R Control Charts

Introduction


x-bar and R

ControlCharts

Examples

Two basic types: x-bar-chart and R-chart one used to monitorcentering of the process, the other for variation.

A2, D

4, D

3are found in Table I in Appendix II for various values of n.

RAxLCLRDLCL

RAxUCLRDUCL

m

x

xm

R

R

xR

xR

m

i

i

m

i

i

23

24

11

;

;

;


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Examples

Introduction


x-bar and R

ControlCharts

Examples

The waiting time to speak with technician in IT service company is an importantquality characteristic to be monitored. The wait times were recorded over 20days in a one-month period. Four specimens were randomly selected per day

and the times (in seconds) recorded. The times as well as the subgroupaverages and ranges are given in following table


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Examples

Introduction


x-bar and R

ControlCharts

Examples

Draw the X-bar and R control charts and specify the UCL and LCL

From n = 4, A2 = 0.729, D3 = 0, and D4 = 2.282. The control limits for the X-bar

control chart are

The control limits for the R control chart are


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Examples

Introduction


x-bar and RControlCharts

Examples

Documents

Class 09 - Control Charts for Variables2 (1 of 2)