The relationship between the 20 employees selected and the equivalent production units could be assessed using the monotonic function. The monotonic function is a feature that retains or reverses a given order. If the number of employees is increased, there should be a significant increase in the rate of production. The increase results in a positive correlation coefficient of +1. The ranking is based on the measure quantifying the variables. The reliability of one week’s production rate is determined by calculating the degree of standard error involved.
The reliability of the criterion can be accounted for by comparing the production rate in week two. It is arrived at by holding the number of employees. The second week’s production is then determined with the 20 employees selected. The calculated standard deviation and the covariance are used in computing the estimated error between the two variables, that is, employee and production units. The degree of error calculated in week one is then compared with that of week two. If the resulting standard error in first weeks compared to the second weeks is above either +0.05 or -0.05, then the criterion is unreliable, and the management of XYZ company should drop it to avoid the risk of business failure in the long run.
The reliability of this approach could be achieved in two ways. The management could say that the sampled employees to work on a piecework rate. By this, they will be able to evaluate the common effort of each employee and set targets to the remaining larger number in the long run. The management of XYZ could offer strict supervision for the sampled employees to estimate the overall production rate per employee under such tight control. It could further be relevant in setting targets for the larger number of staff whether the supervisors are present or not. For example, if 20 employees can produce 2000 units, then 5000 employees must produce 50000 units.