Question

Week 6 17 819 20 21 2223 24 25 14 13 172 ее # of defects per lot 2 19 1418 Problem 3 Chobani has a production line for packaging its Greek yogurt cups. The company specifies that each cup should contain at least 5.2 fl oz (fluid ounces) and at most 5.4 fl oz of Greek yogurt. The packaging process guarantees a volume that is (approximately) normally distributed with a me an of 5.23 fl oz and a standard deviation of 0.031 oz. Chobani aims for 3σ performance for this process. a. Calculate С. Is the process capable of 3ơ performance based on C. Explain your answer. b. Calculate . Does your answer from part (a) regarding process capability change when you use the t measure of process capability? If so, why?

Data for excel

Week	16	17	18	19	20	21	22	23	24	25
# of defects per lot	9	2	19	14	18	7	14	13	17	12

Answer 1

Parameter	Quantitative Value	Remark
Upper specification Limit or USL in Fluid Ounces	5.40	Given
Lower specification Limit or LSL in Fluid Ounces	5.20	Given
Normally Distributed Mean in Fluid Ounces	5.23	Given
Standard Deviation in Fluid Ounces	0.03	Given
Process Capability or Cp	1.11	It can Estimate the capability of the process if the process Mean needs to be centered between the specification limits, as here, value of Cp is less than 1.33, thus we can conclude that Process has Many variation within, and Process is not capable of 3 sigma Performance based on Cp,
Upper Bound for Process Capability Index or Cpu	1.89	Cpu value can estimate that how is the capability of the process to meet the Upper specification limit or It depicts that How process mean is close to the Upper specification Limit
Lower Bound for Process Capability Index or Cpl	0.33	Cpl value can estimate that how is the capability of the process to meet the lower specification limit or it depicts that How process mean is close to the Lower specification Limit
Process Capability Index or Cpk	0.33	Cpk is defined as Minimum Value of Cpu and Cpl, it can estimate the capability of the process and in case Cpk is equal to Cp, then the process is centered at the middle point of the specification limits, value of Cpk with ref. to Cp can determine that how the process is off centered and whether process need potential Improvement or not, here, in actual, Case, as Cpk is not equal to Cp or Cpk is less than Cp, thus we can conclude that the process is off centered from the middle point of the specification limits, Most of the company is looking for Cpk value at Minimum 1.33 and Cpk should be equal to Cp, thus we can conclude that process is Improved and centered, However, here, Cpk value is far less than 1.33, thus Process is not improved and the process is also off centered around the mean

Formula

1	B	C
2	Upper specification Limit or USL in Fluid Ounces	5.4
3	Lower specification Limit or LSL in Fluid Ounces	5.2
4	Normally Distributed Mean in Fluid Ounces	5.23
5	Standard Deviation in Fluid Ounces	0.03
6	Process Capability or Cp	=(C2-C3)/(6*C5)
7	Upper Bound for Process Capability Index or Cpu	=(C2-C4)/(3*C5)
8	Lower Bound for Process Capability Index or Cpl	=(C4-C3)/(3*C5)
9	Process Capability Index or Cpk	=MIN(C7:C8)

based on the Excel data given in the Question, let me prepare C Chart or Defect Chart considering Each Lot contains Constant Number of Item, here, I have taken help from Minitab 2017, using Minitab 2017, Go to Stat > Control Chart > Attribute charts > C - chart > Selecting the Column data for Number of Defects per lot, then go to C Chart Options and selecting Perform all test for special Causes, then Click OK, we will get below control chart and Control Chart options are shown for Reference,

C Chart of Number of defects per lot 25 UCL 23.11 20 C-12.5 10 5 1 LCL-1.89 5 6 7 8 9 10 Sample 1 4

C Chart: Options Parameters Estimate Limits Tests Stages Display Storage Perform all tests for special causes 1 point > K standard deviations from center line K points in a row on same side of center line Kpoints in a row, all increasing or all decreasing K points in a row, alternating up and down 3.0 14 Help OK Cancel
Interpretation: As per above chart, as all defect data points are following and satisfying the control chart options, and No special causes are observed, thus, the process is in Statistical Control,