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X-bar and R chartsExample 3.1 from text

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Data on part thickness  Thickness of parts recorded as amount by

which

  thickness exceeded 0.300 in. (everyone elsehas one metric but!!.."

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Data structure#ample $alue

1 1

1 %

1 &1 %

' 3

'

' )

' )3 %

3 )

3 )

3 * etc.

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+aw data plot* thickness vs

sample number

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  Table 3.' constants for ,-bar and + charts

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+ules for creatin charts

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+ules* etc.

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imits are desined to !./ake sure that the operator does not react to

ommon cause.

ndicate when you are reasonably sure that#pecial ause is present.

f only ommon ause is present in theprocess* then the chance of a false sinal is

about 12* i.e. the probability that the chartwill falsely indicate the presence of #pecialause is about 0.01.

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#imilar to ypothesis Testinn hypothesis testin we say there is a

treatment di4erence if p5alpha60.0)(usually".

 The chance of falsely declarin a treatmentdi4erence exists is then about 1 out of '0.

n 7uality ontrol* we use the 81 out of 1009

criteria to say that our process has morevariation than :ust ommon ause (idea dueto #hewhart* it is simple but e4ective inpractice".

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+-chart and ommon ausef the data in each subroup was collected

under 8homoeneous conditions9* then the+anes should re;ect only ommon ause.

 The chart should not indicate the presence of#pecial ause.

f no sinal of #pecial ause is indicated* thisis not proof that within subroup variation isonly due to ommon ause. (/ore on thislater in +ational #ubroupin."

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+ chart

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,-bar chart and #pecial ause  f the +-chart is in control* i.e.* stable and

predictable* then any shifts in the mean of theprocess come from #pecial ause. f the ,-barchart indicates the process is 8out of control9*i.e.* that #pecial ause is present. <e thenuse a =shbone diaram (or detailed auseand E4ect /atrix" to try to identify and

remove the source of #pecial ause.

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,-bar chart