Question

The cereal boxes are to be filled 12 ounces plus minus 0.1 ounces.

The standard deviation of the process being used to fill the cereal boxes was estimated to be 0.05 ounces.

A

Is the current process capable of meeting the specifications? Why?

B

What action would you do to make the process capable?

C

What would you do to make the process capable to meet the six-sigma quality?

D

Assuming that the process is capable, what control charts would you use to make sure that the process is in control and why?

Answer 1

A	Is the current process capable of meeting the specifications? Why?

Here, I have considered Mean value 12, however not mentioned in the question,

1	B	C	D
2		Value	Remarks
3	Mean Data let me consider 12	12	Given Data
4	Standard Deviation of the defect	0.05	Given Data
5	Upper Specification Limit - USL	12.1	Given Data
6	Lower Specification Limit - LSL	11.9
7	Lower Bound for the Process Capability Index - a	0.667	Cp value is less than 1.33, thus we can conclude that Process is Not capable to achieve three sigma quality level,thus, not improved, again, as Cpk is equal to Cp , thus, we can conclude that the process is centered or process will produce output exactly in the middle of the Tolerance range (USL and LSL)
8	Upper Bound for the Process Capability Index - b	0.667
9	Process Capability Index Cpk = Min of [ a,b ]	0.667
10	Process Capability Cp	0.667

Formula

1	B	C	D
2		Value	Remarks
3	Mean Data let me consider 12	12	Given Data
4	Standard Deviation of the defect	0.05	Given Data
5	Upper Specification Limit - USL	=12+0.1	Given Data
6	Lower Specification Limit - LSL	=12-0.1
7	Lower Bound for the Process Capability Index - a	=(C3-C6)/(3*C4)	Cp value is less than 1.33, thus we can conclude that Process is Not capable to achieve three sigma quality level,thus, not improved, again, as Cpk is equal to Cp , thus, we can conclude that the process is centered or process will produce output exactly in the middle of the Tolerance range (USL and LSL)
8	Upper Bound for the Process Capability Index - b	=(C5-C3)/(3*C4)
9	Process Capability Index Cpk = Min of [ a,b ]	=MIN(C7:C8)
10	Process Capability Cp	=(C5-C6)/(6*C4)

B	What action would you do to make the process capable?

To make the process capable, either, we have to achieve Process capability of 1.33 for three sigma quality level or process capability of 2.00 for six sigma quality level, we will improve the process to make the process capable, before improving the process, we should check and fix that process is already in statistical control

C	What would you do to make the process capable to meet the six-sigma quality?

To make the process capable to meet the six sigma capability, we need to achieve the process capability value of 2, and if Cpk is equal to Cp, then, we can conclude that the process is centered or process will produce output exactly in the middle of the Tolerance range (USL and LSL)

D

Assuming that the process is capable, what control charts would you use to make sure that the process is in control and why? Capability study is applicable for Continuous Data system, thus, here, we can Use X bar R chart to understand the variability of process data, which can indicate that whether the process is in statistical control or not, X bar R chart is applicable when we take data in the form of sample and subgroup, X bar R chart and Capability study are applicable for continuous Data,