Example 26.8: Creating Weighted Pareto Charts

Details of the PARETO Procedure

Example 26.8: Creating Weighted Pareto Charts

See PARETO12 in the SAS/QC Sample Library

In many applications, you can quantify the priority or severity of a problem with a measure such as the cost of repair or the loss to the customer expressed in man-hours. This example shows how to analyze such data with a weighted Pareto chart that incorporates the cost.

Suppose that the cost associated with each of the problems in data set FAILURE7 (see Example 26.6) has been determined and that the costs have been converted to a relative scale. The following statements add the cost information to the data set:

   data failure7;
      length analysis $ 16 ;
      label analysis = 'Basis for Analysis' ;
      set failure7;
      analysis = 'Cost' ;
         if      cause = 'Contamination'  then cost = 3.0 ;
         else if cause = 'Metallization'  then cost = 8.5 ;
         else if cause = 'Oxide Defect'   then cost = 9.5 ;
         else if cause = 'Corrosion'      then cost = 2.5 ;
         else if cause = 'Doping'         then cost = 3.6 ;
         else if cause = 'Silicon Defect' then cost = 3.4 ;
         else                                  cost = 1.0 ;
         output;
      analysis = 'Frequency' ;
         cost = 1.0 ;
         output;
   run;

The classification variable ANALYSIS has two levels, Cost and Frequency. For ANALYSIS=Cost, the value of COST is the relative cost, and for ANALYSIS=Frequency, the value of COST is one.

The following statements create a one-way comparative Pareto chart with ANALYSIS as the classification variable, in which the cells are weighted Pareto charts with COST as the weight variable:

   title 'Pareto Analysis By Cost and Frequency' ;
   proc pareto data=failure7;
      vbar cause / class      = ( analysis )
                   freq       = counts
                   weight     = cost
                   barlabel   = value
                   cframe     = ligr
                   cbars      = vigb
                   cconnect   = salmon
                   cframeside = ligr
                   cframetop  = ligr
                   intertile  = 1.0 ;
   run;

The display is shown in Output 26.8.1.

Output 26.8.1: Taking Cost into Account

Within each cell, the height of a bar is the frequency of the category multiplied by the value of COST, expressed as a percent of the total across all categories. Thus, for the cell in which ANALYSIS is equal to Frequency, the bars simply indicate the frequencies expressed in percent units. This display shows that the most commonly occurring problem (Contamination) is not the most expensive problem (Oxide Defect). The output data set SUMMARY is listed in Output 26.8.2.

Output 26.8.2: The Output Data Set SUMMARY

Obs	analysis	cause	cost	_COUNT_	_WCOUNT_	_PCT_	_CMPCT_
1	Cost	Oxide Defect	9.5	172	1634.0	58.6799	58.680
2	Cost	Contamination	3.0	220	660.0	23.7018	82.382
3	Cost	Metallization	8.5	22	187.0	6.7155	89.097
4	Cost	Silicon Defect	3.4	34	115.6	4.1514	93.249
5	Cost	Corrosion	2.5	32	80.0	2.8729	96.122
6	Cost	Doping	3.6	20	72.0	2.5856	98.707
7	Cost	Miscellaneous	1.0	36	36.0	1.2928	100.000
8	Frequency	Oxide Defect	1.0	172	172.0	32.0896	32.090
9	Frequency	Contamination	1.0	220	220.0	41.0448	73.134
10	Frequency	Metallization	1.0	22	22.0	4.1045	77.239
11	Frequency	Silicon Defect	1.0	34	34.0	6.3433	83.582
12	Frequency	Corrosion	1.0	32	32.0	5.9701	89.552
13	Frequency	Doping	1.0	20	20.0	3.7313	93.284
14	Frequency	Miscellaneous	1.0	36	36.0	6.7164	100.000

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