Controls

Data and Answers

As a quality analyst you are also responsible for controlling the weight of a box of cereal. The Operations Manager asks you to identify the ways in which statistical quality control methods can be applied to the weights of the boxes. Provide your recommendations to the Operations Manager in a two-page report. Using the data provided in the Doc Sharing area, create Xbar and R charts.
Your report should indicate the following along with valid justifications of your answers:
The control limits of the weights of the boxes.
Nonrandom patterns or trends, if any.
If the process is in control.
The appropriate action if the process is not in control.
	Sample	Box 1	Box 2	Box 3	Sample Means	Maximum	Minimum	Sample Range
	1	6.300	6.280	6.260	6.280	6.300	6.260	0.040
	2	6.320	6.320	6.330	6.323	6.330	6.320	0.010
	3	6.290	6.330	6.360	6.327	6.360	6.290	0.070
	4	6.300	6.290	6.340	6.310	6.340	6.290	0.050
	5	6.295	6.315	6.390	6.333	6.390	6.295	0.095
	6	6.292	6.319	6.330	6.314	6.330	6.292	0.038
	7	6.289	6.323	6.400	6.337	6.400	6.289	0.111
	8	6.286	6.327	6.471	6.361	6.471	6.286	0.185
	9	6.283	6.331	6.498	6.371	6.498	6.283	0.215
	10	6.280	6.335	6.525	6.380	6.525	6.280	0.245
	11	6.277	6.339	6.390	6.335	6.390	6.277	0.113
	12	6.274	6.343	6.400	6.339	6.400	6.274	0.126
	See all the other sheets in this file.
	(a) The control limits are: (a) For Mean weight, LCL = 6.3087 ounces, UCL = 6.3696 ounces and (b) For Range, LCL = 0.0324 ounes, UCL = 0.1964 ounce
	(b) At the time measurements were taken on the 5th through 9th samples, the mean weights and the range of weights appears to have been increasing in a somewhat linear pattern. It appears that the filling machine has gradually gone off setting during this period. This is the only non-random variation observed at the time of taking the 12 measurements.
	(c ) The process is not in control since we see points lying outside the control limits in both x-bar chart and R chart.
	(d) Corrective action in terms of resetting the machine is required. Trials should be run and again more samples drawn to check if the process has come under control.
	See all the sheets for the calculations and tables. The process is in statistical control.

XBar Chart

1	1	1	1
2	2	2	2
3	3	3	3
4	4	4	4
5	5	5	5
6	6	6	6
7	7	7	7
8	8	8	8
9	9	9	9
10	10	10	10
11	11	11	11

RChart

1	1	1	1
2	2	2	2
3	3	3	3
4	4	4	4
5	5	5	5
6	6	6	6
7	7	7	7
8	8	8	8
9	9	9	9
10	10	10	10
11	11	11	11

ForCharts

Number	XBar	Range	LCL-R	Center-R	UCL-R	LCL-X	Center-X	UCL-X
1	6.3233333333	0.01	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
2	6.3266666667	0.07	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
3	6.31	0.05	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
4	6.3333333333	0.095	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
5	6.3136666667	0.038	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
6	6.3373333333	0.111	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
7	6.3613333333	0.185	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
8	6.3706666667	0.215	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
9	6.38	0.245	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
10	6.3353333333	0.113	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424
11	6.339	0.126	0.0323649091	0.1143636364	0.1963623636	6.3087307879	6.3391515152	6.3695722424

Calculations

Control Chart Calculations
			Control Chart Factors Table.
Data			Subgroup size	D3	D4	A2
Sample/Subgroup Size	12		2	0	3.267	1.880
			3	0	2.575	1.023
R Chart Intermediate Calculations			4	0	2.282	0.729
RBar	0.1143636364		5	0	2.114	0.577
D3 Factor	0.283		6	0	2.004	0.483
D4 Factor	1.717		7	0.076	1.924	0.419
			8	0.136	1.864	0.373
R Chart Control Limits			9	0.184	1.816	0.337
Lower Control Limit	0.0323649091		10	0.223	1.777	0.308
Center	0.1143636364		11	0.256	1.744	0.285
Upper Control Limit	0.1963623636		12	0.283	1.717	0.266
			13	0.307	1.693	0.249
XBar Chart Intemediate Calculations			14	0.328	1.672	0.235
Average of Subgroup Averages	6.3391515152		15	0.347	1.653	0.223
A2 Factor	0.266		16	0.363	1.637	0.212
A2 Factor * RBar	0.0304207273		17	0.378	1.622	0.203
			18	0.391	1.609	0.194
XBar Chart Control Limits			19	0.404	1.596	0.187
Lower Control Limit	6.3087307879		20	0.415	1.585	0.180
Center	6.3391515152		21	0.425	1.575	0.173
Upper Control Limit	6.3695722424		22	0.435	1.565	0.167
			23	0.443	1.557	0.162
			24	0.452	1.548	0.157
			25	0.459	1.541	0.153
			26	Factor value not available. Possible error in sample/subgroup size.	Factor value not available. Possible error in sample/subgroup size.	Factor value not available. Possible error in sample/subgroup size.
			Factor value not available. Possible error in sample/subgroup size.