Question

Rosters Chicken advertises “lite” chicken with 30% fewer calories than standard chicken. Rosters wants to use control charts to monitor the calories in its chicken. To do this it periodically takes a sample of 5 chicken breasts off its production line and measures the caloric content of each chicken.

Chicken

Sample #	Obs-1	Obs-2	Obs-3	Obs-4	Obs-5
1	373	428	403	461	407
2	428	424	418	376	423
3	434	452	362	431	442
4	418	419	416	433	420
5	432	434	393	411	451
6	442	418	415	425	408
7	442	428	442	414	396
8	437	454	418	358	430
9	440	383	448	414	442
10	419	418	460	427	444
11	451	411	399	380	431
12	417	448	412	470	448
13	454	464	387	441	446
14	430	427	419	429	402
15	434	440	422	405	46

1. Calculate 3-sigma control limits for the caloric content of chicken breasts produced by this process, for both the means and the range charts.
2. Plot the means and ranges on their respective charts. Can you conclude that the process is in control?

Answer 1

3-sigma control limits for both means and range chart is calculated and they are plotted on the respective charts.

It is concluded that the process is out of control. Because in both Xbar(means )and R(range) chart, one point is very much away from the 3-sigma Control limits. If any point is outside of the 3-sigma control limits, the process is assumed to be out of control.

Control limits values, their calculations and respective charts are given in the images below :

After Calculenting all the sample averages and ranges, we got the table i Sample sample average (x) Range (R) 414-4 413-8 424.2 421.2 424.2 421.6 24 444 4 46 419.4 425.4 433.6 65 414. 4 7). 439 438.4 58 77 .421.4 28 349.4 394

(a.) 3- sigma Control limits : For means chart cx chart): - Upper Control limit (UCL ) = x + A₂R Lowes Control limit (LLL ) X-A₂ Ř where x = Average of Sample averages R - Average of Ranges A- A Constant factor corresponding to a particulas Sample Size for a chart Here for Sample siz 5 Az = 0.58 X = { X R = ER where N = no of Samples = 15 THE M = 418.99 A R = 81.07 UCL = 418.99+ (0.58% 81.07) X = 466.01 LCL X= 418.99 (0.58%81107 - 371.97 For Range chart CR chart): - Upper Control Limit CULL) = D q Ř Lower Control Limit (LLL) = 10₂ Ř where Du&D are Constants, here for a sample Size of 5, D.,= 2.11 & D2=0 for R chart. So, UCL 2.11x. 81.07-171.06 LCL R = 0x81.07 0

470 (X - CHARI) UCLX (466-01) 450 hos 40 435 430 XI 425 C.LCT 418.99 405 400 395 390 370 365 CICL = 4 37197 360 355 350 1 2 3 3 by 5 6 7 8 9 10 11 12 13 Samples 14 15 >

R-CHART huo 360 340 320 300 280 260 240 220 200 171-06 UCLA Cato 160 To TZO C.LR(R) 81.07 -S4 5 6 7 8 9 LCLR (0) 10 11 12 13 14 Samples 15

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