From the Niebel\'s Methods, Standards, and Work Design 13th Editon textbook Chap

Question

From the Niebel's Methods, Standards, and Work Design 13th Editon textbook Chapter #14 Problem #1:

1.) The analyst in the Dorben Reference Library decides to use the work sampling technique to establish standards. Twenty employees are involved. The operations include cataloging, charging books out , returning books to their proper location, cleaning books, record keeping, packing books for shipment, and handling correspondence. A preliminary investigation resulted in the estimate that 30 percent of the group's time was spent in cataloging. How many work sampling observations would be made if it were desirable to be 95 percent confident that the observed data were within a tolerance of +/- 10 percent of the population data? Describe how the random observations should be made. The following table illustrates some of the data gathered from 6 of the 20 employees. The number of volumes cataloged equals 14,612. From these data, determine standard, in hours per hundred, for cataloging. Then design a control chart based on +/- 3 sigma limits for the daily observations. Operators   

Item Smith Apple Brown Green Baird Thomas   

Total hours worked 78 80 80    65 72 75 Total observations (all elements) 152 170 181 114 143 158 Observations involving cataloging 50 55 48 29 40 45 Average rating 90 95 105 85 90 100

Explanation / Answer

Use a Binomial distribution:

sd of binomial is sqrt(np(1-p) where p is observed rate

here p 0.3

we wnat this to be within +- 10% of mean : mean is np

so sqrt(n*.7.3)= 0.1(np)=0.1(n*.3)

at 95% confidence, 1.96 (sqrt( n*.21)= .1*n*.3

squaring: n= 1.96^2 *.21/ (.01*.09) =896.37

Since measurements have alreayd been made, continue over several days,divided equally over the study period.

The timing of each observation to be done using a random numbe generato, say 50 per day. Since many different activities occur, must divide equally over the span of study, some times work is slack, others more busy.

From the data for the six workers, ignoring the weightage of rating:

mean per worker for cataloging 34.42 per hundred

sd 13.965 over 6 samples

3sigma= 3* 13.965 =41.85

Hence the control limits Mean _+ 3sigma = 34.42 + 41.95, min 0

If normed over 100, sd= 1.3965, 3sd= 4.19

UCL   34.42+4.19=38.61

LCL= 34.42- 4.19 = 30.23

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