EBK OM
EBK OM
6th Edition
ISBN: 9781305888210
Author: Collier
Publisher: YUZU
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Chapter 16, Problem 2CSQD
Summary Introduction

Interpretation: The control over production process is to be assessed using the x¯ and R charts.

Concept Introduction: x¯ and R charts are tools of statistical process control used to monitor the impact of process improvement theories. Data collected as subgroups over a period of time and used for analysis.

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Answer to Problem 2CSQD

The mean and range values are well within the control limits as seen from the x bar and R charts. Hence, the production process is in control.

Explanation of Solution

Given information:

EBK OM, Chapter 16, Problem 2CSQD , additional homework tip  1The x¯ and R charts are plotted to visualize the process means and dispersion of the data distribution. The factors from the standard 3 sigma chart are used to compute the control limits.

The sample mean and range are calculated and shown below:

    SampleX1X2X3Sample mean(X1+X2+X3)/3Sample Range
    131422833.67 {(31+42+28)/3=33.67}14
    226183526.3317
    325303429.679
    417252121.008
    538293534.009
    641423639.676
    721172922.3312
    832262828.676
    941343336.008
    1029173025.3313
    1126314032.3314
    1223192522.336
    1317243224.3315
    1443351731.6726
    1518252924.0011
    1630423134.3312
    1728363232.008
    1840293133.3311
    1918292825.0011
    2022342627.3312
    2118243024.0012
    2224281923.679
    2327322026.3312
    2439261928.0020
    2517322725.3315
       Total 710.67296
       Average28.4311.84

  x¯¯= 28.43

  R¯= 11.84

  n = 3

From the 3-sigma standard control chart, the coefficient values are obtained as follows:

  A2= 1.023D3= 0D4= 2.574

And the control limits are calculated

  Uccle=x¯¯+A2.R¯=28.43+ (1.023×11.84) = 40.54

  Lela=x¯¯ A2.R¯=28.43(1.023×11.84) = 16.32

   UCLR=D4.R¯=2.574 × 11.84 = 30.48

  LCLR=D3.R¯=0 × 11.84 = 0

The x¯ and R charts are plotted with the above values:

EBK OM, Chapter 16, Problem 2CSQD , additional homework tip  2

EBK OM, Chapter 16, Problem 2CSQD , additional homework tip  3

The mean and range values are well within the control limits and hence the process is in control.

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