Question

A service process has three stages. The error percentages are: 8% at stage one, 7% at stage two, and 9% at stage three. The connection logic of the three stages is that a good overall outcome happens only when all stages individually have good outcomes. (a)[4] Draw the event tree for this situation with all necessary details. (b)[10] Find the probabilities of defective and good overall outcomes (6 decimals). (c)[2] Calculate and interpret the EPMO of this process (1 decimal). (d)[4] Calculate the sigma level of the process (2 decimals) and state it. Sketch the sigma level.

Answer 1

Answer:

(b) Probabilities =  0.221404 (overall defective outcome)

                               0.778596 (overall good outcome)

(c) EMPO = 221404.

Step-by-step explanation:

concerning the question, we shall analyze it at its simplest form.

we are given error percentages and told to represent their probabilities showing their defective and good overall outcomes.

From the question, we are to provide a event tree.

(a).  From the images uploaded below, we can see that the three stages    

    along with their respective probabilities of Good and Defective outcomes              

      are displayed.

    We notice here that at each stage, further branching is only possible    

   when the previous event has a good outcome, therefore, the branches  

    are discontinued after every defective outcome.

(b). The question has asked us to calculate the  Overall Probability of

     Defective and Good Overall outcomes, this can be achieved by  

      by multiplying  the individual probabilities of successive events.

• Overall Good Outcome has a probability = 0.92 * 0.93 * 0.91 = 0.778596
• Overall Defective Outcome has a probability = 1 - Probability of Overall Good outcome = 1 - 0.778596 = 0.221404

(c). So we are asked to calculate and interpret the EMPO of the process.

   Using the Overall Defective Outcome(error rate ),

   EPMO can be calculated by multiplying Overall Error Rate Probability by 1 million , that is , EPMO = 0.221404 * 1000000 = 221404.

The EPMO value simply  indicates the number of defective outcomes when a million trials of the process is performed.

cheers i hope this helps.