Introduction
In this case report, the analysis of General Mills through discrete probability distribution to be able to answer the following
Key Problems:
What is the probability of a shutdown?
With all current processes functioning properly, the probability of a shutdown is 6.42%.
Are there any issues with the GM’s method for shutting down production?
The method is feasible because the probability of shutdown is so low.
How many boxes can contain errors if GM only wants a shutdown to occur 1% of the time when properly working during production.
There can be a minimum of 23 errors in the sample of 25 in order to obtain this result.
How can the production process be improved in order to reduce the probability of at least 5 boxes in the sample containing an error to 1%?
The percentage of error in production would need to be lowered from 8% with the current production processes in place, to 1.235% in order to yield this result.
Is it worth it to continue to produce this product?
Yes, because the probability of the company needing to shut down production is so low that it may rarely occur, if it ever does occur. Additionally, with the addition of sufficient resources, staff may be able to reduce the risk of shutdown to 1% or less, which would mean that there can be an almost 0% chance of having to shut down production. This would be a successful process and would generate profits for GM with little risks involved in production.
Background
General Mills is a manufacturing and sales outlet for a variety of cereals breakfast. Recently, General Mills in its developed laboratory came up with a new banana-flavored and rice flakes marshmallows. The Marketing Research Team has thoroughly presented the new cereals and found that customers were satisfied with them. 16-ounce boxes include not more than 1.6 ounces of bananas, and not more than 2.4 ounces of the bananas used to evaluate the distinct distribution of chance.
Ms. Finkle, the VP of Production, and her team have come up with a production process in which only 8% of all boxes of Cheerios have an error in the weight of marshmallows that they contain.
GM management has decided to take a weekly sample of 25 boxes of Cheerios to test the weight of the marshmallows contained within each box. If 5 or more boxes have an error based on the customer preferences listed previously, then production will be shut down.
Analysis: Probability That a Weekly Sample Will Result in a Shutdown
The chance that the sample for a weekly outcome in a production shutdown can be discovered as follows:
P(Sd)= P(errors in production)P(the sample has more than 5 errors) The probability of there being an error in production was given to us. Under Ms. Finkle’s designed production process, the probability of there being an error is 8% of the total number of boxes produced. The probability of the sample containing more than 5 errors can be found by listing all possible outcomes in the sample. I found that there were 26 possible outcomes, and 21 of those 26 had five or more errors. This means that the probability of there being five or more errors in the sample is about 81%. Therefore, P(Shutdown)=0.08 (or 8%) 0.81 (or 81%)
P(Sd)= 0.08*0.81= about 6.46%
Analysis: Probability That a Weekly Sample Will Result in a Shutdown
GM’s policy seems to be a good feasible considering the probability of there NOT being a shutdown of production is 93.54%. This means that there is almost a 94% chance that the samples will not cause a shutdown, and that the company can continue with production.
Since there is such a low probability of there being a shutdown, it does not pose GM a big risk to move forward with production. If there is a shutdown of production as a result of too many errors being found in the sample, GM can assume that there is too large of an error in production to continue with the same method, and they can work to fix any underlying issues.
Analysis: Appropriate Number of Error Boxes For a 1% Chance of a Shutdown
The suitable sum of the weekly boxes in the sample that can fail to meet production standards if GM wants there to only be a shutdown 1% of the time can be determined as follows:
The number of possible outcomes for the sample of 25 boxes of Cheerios (listed in the Excel Document) is 26.
P(Shutdown)=1%
1%=8%P(More than X Errors) 1%/8%=P(More than X Errors)=12.5% 12.5%= X/26 X=12.5%26
X=3.25 occurrences of event
My test outcome list and current practices, if I begin with 0 boxes that satisfy the norm, are known to be: 0 Passes/25 Errors, 1 Pass/24 Errors, and 2 Passes/23 Errors. I have also analyzed these findings. More than that, a greater likelihood of a shutdown would result. Therefore, there will be 23 or more of 25 boxes that make sure that only 1 percent of time is shut down.
The suitable sum of fault sample of the boxes to yield a 1% chance of shutdown is a minimum of 23 error boxes in a sample of 25.
Analysis: What Level Should Finkle Reduce the Percentage of Error Boxes in Order to Reduce the Probability of Error to 1% or less
If GM decides to keep all current requirements in place (a shutdown if 5 out of 25 sample boxes are flawed) but still wants to yield a 1% probability of shut down or less, the percent of error that is acceptable in production can be determined as follows:
The probability of 5 or more boxes not meeting requirements is found by finding the total number of possible outcomes, and counting how many of those outcomes contain 5 errors or more (see next slide for Possible Outcomes chart). Since there are 26 possible outcomes, and 21 of those outcomes contain 5 errors or more, the probability of there being 5 or more boxes with errors is about 81%
Since GM wants the probability of a shutdown to be 1% or less, we need to decide what percent of error is allowed in production.
P(Shutdown)=1%= X81% 1%=X81%
X=1%/81%
X= 1.235%
The maximum percent of Cheerios boxes that do not meet the standards of production given that there is only a 1% chance of a production shutdown is 1.235%.
Analysis: What Level Should Finkle Reduce the Percentage of Error Boxes in Order to Reduce the Probability of Error to 1% or less
Since the original percent of error in production was 8% under Ms. Finkle and her team’s designed production process, they would need to decrease that chance of error by at least 6.765% in order to only have a shutdown of production 1% of the time or less.
In order to reach this goal, GM must provide Finkle and her team with adequate resources, as well as provide them with sufficient time to develop a new production process that will yield the desired results.
Recommendations
GM should use the third strategy of production: Attempting to limit the probability of shutting down production to 1% or less by minimizing the probability of there being errors during production from 8% to 1.235% or less. This may take the company some time and resources, however the cost of developing the optimal production plan far outweigh the cost of shutting down production to fix a mistake.
Either way, this product is worth producing because it will yield necessary profits for the company, while maintaining minimal risks associated with shutting down productions.
References
Josselin, Jean-Michel, and Benoît Le Maux. “Descriptive Statistics and Interval Estimation.” Statistical Tools for Program Evaluation. Springer, Cham, 2017. 45-88.
Nersesian, Roy L., and Kenneth David Strang. “Risk planning with discrete distribution analysis applied to petroleum spills.” International Journal of Risk and Contingency Management (IJRCM) 2.4 (2013): 61-78.
