Question

3

You are preparing to host the safety meeting for your workgroup. Usually your group averages one or two injuries per month (let’s say 1.5 per month). Last month you had no injuries. Management wants to buy pizza for the meeting in celebration of no injuries this month. What would you recommend and why? How many months at zero would it take to reach a point where it would be truly “unusual” and worthy of celebration? What is the basis for your answer? You are provided with the following information by the company statistician: If we are stable at 1.5 cases per month, and by using a Poisson distribution (which is useful for counting events per month) calculation, I predict there is a 22% chance of going one month without an injury.

Answer 1

If we are stable at 1.5 cases per month, then by using a Poisson distribution there is a 22% chance of going one month without an injury.

Let us assume the significance level to be 0.05 and the event of no injuries in a given time period would be truly “unusual” and worthy of celebration, if the probability of observing it is less than 0.05. Since the probability of observing a month with no injuries is still higher than 0.05, I would not recommend for celebration as the probability of observing no injuries in a month can have occurred by chance.

Let 'k' be the minimum number of consecutive months in which the probability of no injuries is less than 0.05.

k log(0.22) < log(0.05)

k * -1.514128 < -2.995732

k > 2.995732 / 1.514128

k > 1.97852 $\approx$ 2

Thus, if we observe no injuries for two consecutive months for which the probability is less than 0.05, we would consider it as truly “unusual” and worthy of celebration.