Question

Case 2 Jackson Manufacturing Company - Dominika Wojdat, vice president of operations at Jackson Manufacturing Company, has just received a request for quote ( RFQ ) from DeKalb Electric Supply for 400 units per week of a motor armature. The components are standard and either easy to work into the existing production schedule or readily available from established suppliers on a JIT ( just-in-time ) basis. But, there is some difference in assembly. Ms. Wojdat has identified eight tasks that Jackson must perform to assemble the armature. Seven of these tasks are very similar to the ones performed by Jackson in the past ; therefore, the average time and resulting labor standard of those tasks is known. The eighth task, an overload test , requires performing a task that is very different from any performed previously, however, Dominika has asked you to conduct a time study on the task to determine the standard time. Then an estimate may be made of the cost to assemble the armature. This information, combined with other cost data, will allow the firm to put together the information needed for the RFQ .

To determine a standard time for the task, an employee from an existing assembly station was trained in the new assembly process. Once proficient, the employee was then asked to perform the task 17 times so a standard could be determined. The actual times observed were as follows ( in minutes ) :


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

2.05 1.92 2.01 1.89 1.77 1.80 1.86 1.83 1.93 1.96 1.95 2.05 1.79 1.82 1.85 1.85 1.99


The worker had a 115% performance rating. The task may be performed in a sitting position at a well-designed ergonomic workstation in an air-conditioned facility. Although the armature itself weights 10.5 pounds, there is a carrier that holds it so the operator need only rotate the armature. But, the detail work remains high :” therefore, the fatigue allowance will be 8%. The company has an established personal allowance of 6%. Delay should be very low. Previous studies of delay in this department average 2%. This standard is to use the same figure.

The workday is 7.5 hours, but operators are paid for 8 hours at an average of $12.50 per hour.

Questions

In your report to Ms. Wojdat , you realize you will want to address several factors :

a) how large should the sample be for a statistically accurate standard ( at ,
say, the 99.73 % confidence level and accuracy of 5% ? )

b) is the sample size adequate ?

c) how many units should be produced at this workstation per day ?

d) what is the cost per unit for this task in direct labor cost ?

Answer 1

(a)

Sample	Observed time
1	2.05
2	1.92
3	2.01
4	1.89
5	1.77
6	1.8
7	1.86
8	1.83
9	1.93
10	1.96
11	1.95
12	2.05
13	1.79
14	1.82
15	1.85
16	1.85
17	1.99
Avg. (A)	1.901
STDEV (s)	0.090

At 99.73% confidence level Z = 3; Accuracy level (E) is given as 5% or 0.05

Required sample size (n) = (Z*s / E*A)² = (3*0.09/(0.05*1.901))² = 8.07 or 9 cycles

(b)

Since they have already taken 17 samples, the sample size seems adequate.

(c)

Normal Time = Observed Time x Rating Factor = 1.901 x 115% = 2.186 minutes

Standard time = Normal Time x (1 + Allowances) = 2.186 x (1 + 0.08+0.06+0.02) = 2.54 minutes

For each workday (7.5 hours), the possible units that can be produced = 7.5 x 60 / 2.54 = 177

But since the demand is 400 units per week and assuming that they will not produce more than demand, the per day production requirement is 400 / 5 = 80 units

(d)

Total payout for the worker = $12.5 x 8 = $100

So, cost per unit produced = $100 / 177 = $0.565 if production is done up to full capacity.

For just to fulfill the demand, the cost per unit becomes = $100 / 80 = $1.25