Please include a complete step-by-step explanation. I shall be grateful and will
ID: 357592 • Letter: P
Question
Please include a complete step-by-step explanation. I shall be grateful and will give thumbs up!
If you need more details, please mention it in the comments. Don't add answer stating "More details are needed." Thanks :)
Please include a complete step-by-step explanation. I shall be grateful and will give thumbs up
Whole Foods sells Trikes breakfast ceral in one-pound boxes. According to Food and Drug Administration (FDA) regulations, a one-pound box must contain at least 15.5 ounces of cereal. However, Natural Food's box-filling process is not perfect: its precision, expressed in terms of the standard deviation of the weight of a one-pound box filled, is 0.5 ounces. a). What is the Cpk of the process if the mean fill is set at 16.5? b). While underweight boxes might prompt FDA action, overweight boxes certainly cost Whole Foods in terms of higher material costs. Therefore, quality control manager Mandy Bright wants to monitor the cereal-filling process in order to ensure that its mean does not deviate from 16.5. She plans to weigh five randomly selected boxes at random time intervals and plot the average weight on a chart. At one point, she finds an average weight of 15.8 ounces. The company's legal staff is pleased that this performance is better than the FDA requirement of 15.5 ounces. What action, if any, should Mandy take?Explanation / Answer
1. Cpk = min [(USL - mean / 3*SD), (Mean - LSL / 3*SD)]
where USL = Upper specified limit (not provided in this case)
Mean = 16.5
SD = Standard deviation = 0.5
LSL = Lower specified limit = 15.5
So, Cpk = (Mean - LSL / 3*SD)
= (16.5 - 15.5 / 3*0.5)
= 1/1.5
= 0.67
So Cpk = 0.67
2. Mandy must specify upper control limit as 17.5 ounces and lower control limit as 15.5 ounces because she does not want the weight of the boxes to go below 15.5 ounces as it will prompt FDA action and above 17.5 ounces will increase material costs. After that, Mandy must develop control chart by collecting data from more samples than just 5 random samples. Then Mandy must construct control chart and analyse the data. Then out-of-control values must be identified on the chart and must be investigated. Then she must document how the investigation was conducted, the learning from the procedure, the cause of error and how was it corrected. That will ensure that the error is identified and controlled and manufacturing process will improve.