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Control Charts for Variables

By Kristen Diaz,2014-08-09 11:47
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Control Charts for Variables

MGT 6421 Quality Management II

    Control Charts for Variables

    ( Our objectives for this section are to learn how to use control charts to

    monitor continuous data. We want to learn the assumptions behind

    the charts, their application, and their interpretation.

    ( Since statistical control for continuous data depends on both the mean

    and the variability, variables control charts are constructed to monitor

    each. The most commonly used chart to monitor the mean is called

    the chart. There are two commonly used charts used to monitor the X

    variability: the R chart and the s chart.

( Procedure for using variables control charts:

    1. Determine the variable to monitor.

    2. At predetermined, even intervals, take samples of size n (usually

    n=4 or 5).

    3. Compute each sample, and plot them on their X and R (or s) for

    respective control charts. Use the following relationships:

    nn2()XXXii

    i1i1Xs , R = X- X, . maxminnn1

     Variables Control Charts - 1

    MGT 6421 Quality Management II

    4. After collecting a sufficient number of samples, k (k>20), compute the control limits for the charts (see the table on page 4 for the appropriate control limit calculations). The following additional calculations will be necessary:

    kkk

    XRsjjj

    jjj111XRs, , .

    kkk

    5. If any points fall outside of the control limits, conclude that the process is out of control, and begin a search for an assignable or special cause. When the special cause is identified, remove that point and return to step 4 to re-evaluate the remaining points.

    6. If all the points are within limits, conclude that the process is in control, and use the calculated limits for future monitoring of the process.

    ( Because the limits of the chart are based on the variability of the X

    process, we will first discuss the variability charts. I suggest that you first determine if the R chart (or s chart) shows a lack of control. If so, you cannot draw conclusions from the chart. X

     Variables Control Charts - 2

MGT 6421 Quality Management II

    The R chart

    ( The R chart is used to monitor process variability when sample sizes

    are small (n<10), or to simplify the calculations made by process

    operators.

    ( This chart is called the R chart because the statistic being plotted is

    the sample range.

    ;( Using the R chart, the estimate of the process standard deviation, , is

    R.

    d2

    The s chart

    ( The s chart is used to monitor process variability when sample sizes

    are large (n10), or when a computer is available to automate the

    calculations.

    ( This chart is called the s chart because the statistic being plotted is the

    sample standard deviation.

    ;( Using the s chart, the estimate of the process standard deviation, , is

    s.

    c4

    The Chart: X

( This chart is called the chart because the statistic being plotted is X

    the sample mean. The reason for taking a sample is because we are

    not always sure of the process distribution. By using the sample mean

    we can "invoke" the central limit theorem to assume normality.

     Variables Control Charts - 3

    MGT 6421 Quality Management II

    Limits for Variables Control Charts Variability Standards Measure Chart Limits (,;and;!)

     ;Range Known ,;? A X

    Range Not Known ? A ;RX X2

     ;Standard Known ,;? A X

    Deviation

    Standard Not Known ;? A sX X3Deviation

     centerline=d 2Range Known R LCL=D!;;;1

    UCL=D 2

     centerline= RRange Not Known R LCL=D;;;R3

    UCL=D R4

    Standard centerline=c 4Deviation Known s LCL=B!;;;5

     UCL=B 6

    Standard centerline=s Deviation Not Known s LCL=Bs;;;3

     UCL=Bs 4

     Variables Control Charts - 4

    MGT 6421 Quality Management