Question

If you could post the formual too for each answer that would be appriciated

M N G H B C D E F Quality Control Assignment You must do the necessary calculations in the answer cells. Simply providing a number in the answer cell will not receive any credit. When look at the answer cell, I want to see a number, when I click on the cell I want to see the excel formula, for example, if I asked you the sum of cells B5 through D5, this is what I want to see: 7035.0 7035.0 or 3456 1234 2345 Be sure to show all of your work. 6 Problem 1: Use the data that is given below to answer the question that follow. 8 An automated sampling and quality control system experienced a systems failure. You job is to evaluate the data collected over the past 6 hours to detemine if the process being measured was in control the entire time. Six measurements were taken in each sample, and seventy two samples total were gathered. The measurements are the diameter of a hold that drilled in a piece 10 of aluminum. 11 OBSERVATIONS WITHIN SAMPLES Sample 1 2 4 5 1 1.224 1.260 1.272 1.209 1.252 1.276 2 1.299 1.211 1.260 1.213 1.221 1.227 1.271 3 1.244 1.258 1.216 1.244 1.282 4 1.220 1.277 1.252 1.281 1.229 1.206 5 1.204 1.254 1.219 1.296 1.241 1.276 1.293 1.257 1.260 6 1.234 1.256 1.210 1.236 1.227 1.239 1.249 1.215 7 1.242 1.216 1.201 1.271 1.296 1.243 1.205 1.268 1.282 9 1.249 1.297 1.249 1.259 1.285 10 1.276 1.282 1.276 1.247 1.284 1.293 11 1.200 1.246 1.284 1.201 1.200 12 1.230 1.271 1.287 1.256 1.232 1.294 13 1.217 1.293 1.254 1.231 1.246 1.279 14 1.289 1.267 1.220 1.238 1.254 1.267 1.299 15 1.259 1.204 1.271 1.213 1.209 16 1.228 1.226 1.261 1.244 1.265 1.240 1.278 17 1.263 1.227 1.275 1.264 1.247 1.243 1.298 1.234 1.256 1.277 1.228 18 1.283 1.230 19 1.258 1.265 1.253 1.291 20 1.260 1.225 1.218 1.217 1.219 1.286 1.273 21 1.220 1.216 1.247 1.280 1.225 1.251 22 1.201 1.242 1.238 1.256 1.295 1.276 23 1.264 1.241 1.223 1.270 1.280 1.228 24 1.207 1.228 1.240 1.257 1.202 25 1.293 1.293 1.201 1.261 1.263 1.222 26 1.210 1.270 1.283 1.285 1.256 1.280 27 1.297 1.209 1.260 1.215 1.227 1.217 1.235 28 1.215 1.266 1.235 1.204 1.248 29 1.211 1.218 1.245 1.287 1.253 1.283 30 1.267 1.274 1.260 1.253 1.210 1.250 1.203 1.244 1.270 31 1.241 1.244 1.298 1.226 32 1.278 1.234 1.246 1.215 1.215 1.233 1.278 33 1.259 1.290 1.232 1.285 34 1.292 1.201 1.292 1.285 1.250 1.221 1.26 35 1.229 1.238 1.298 1.300 1.248 36 1.262 1.274 1.277 1.203 1.220 1.289 37 1.237 1.285 1.299 1.227 1.279 1.212 1.222 1.257 38 1.297 1.233 1.249 1.206 1.251 1.294 1.224 39 1.244 1.276 1.295 1.211 1.274 1.265 1.289 40 1.247 1.231 1.216 41 1.286 1.249 1.271 1.281 1.255 42 1.206 1.250 1.213 1.285 1.237 1.239 1.270 1.292 1.289 1.224 1.298 1.234 43 1.266 1.206 44 1.294 1.253 1.202 1.204 1.266 1.268 45 1.224 1.287 1.259 1.254 1.253 1.212 46 1.270 1.280 1.219 1.229 1.268 1.281 47 1.233 1.215 1.221 1.264 48 1.269 1.278 1.234 1.283 1.234 1.204 1.216 1.243 49 1.217 1.242 1.207 1.280 1.237 50 1.276 1.293 1.286 1.222 1.205 1.248 1.204 1.236 51 1.243 1.221 1.201 1.207 1.255 1.273 52 1.263 1.224 1.246 1.249 1.211 53 1.232 1.210 1.256 1.287 1.262 1.275 54 1.299 1.265 1.214 1.288 1.250 1.256 1.203 55 1.225 1.217 1.251 1.242 56 1.288 1.289 1.267 1.202 1.249 1.216 57 1.253 1.229 1.277 1.241 1.211 1.203 58 1.291 1.274 1.251 1.224 1.264 1.203 1.235 1.261 1.211 59 1.262 1.254 1.259 1.292 1.225 60 1.396 1.225 1.286 61 1.211 1.283 1.235 1.249 1.203 1.233 1.243 1.238 1.219 62 1.261 1.220 1.254 1.257 63 1.255 1.298 1.204 1.238 1.257 1.209 64 1.209 1.230 1.300 1.273 1.203 1.228 1.228 1.283 1.266 1.245 65 1.267 66 1.249 1.282 1.270 1.202 1.289 1.295 1.216 1.288 67 1.221 1.239 1.297 1.249 1.267 1.243 68 1.298 1.291 1.214 1.210 1.286 1.206 69 1.271 1.213 1.232 1.295 1.226 1.266 1.247 70 1.221 1.209 1.207 1.230 1.242 71 1.214 1.217 1.262 1.205 1.210 1.264 1.240 1.202 1.271 1.250 72 87 88 89 Question 1 Determine the correct control charts to use, then calculate the data needed for each control chart, then create and show the control charts below. 90 91 Question 2 Evaluate each control chart (in the propor order) using the four factors to check identified in the lecture notes to determine if the process is in control If the process is not in control, specifically when did it go out of control? 92 93 Question 3 94 95 96 Grading Rubric Points Points 97 Question Possible Earned Comments 98 0 1 45 99 2 0 45 100 3 10 101 TOTAL 100 C 102 103

Answer 1

-Arswer Ps cleo tha eoch Sample (DFvom the green informafton tt -Bar and s Classfe dfoto 6 Sub qrevps .Therfove fhe data aPpro Priate R chart fs grven more follaurs The formula for R chavt s deved as Rr R(CL) whera R = ma mn ocL= D4 R The formula for X- Bar Ghavt ts detued os folla^: C LcL X Agh Use Menttab to obta^n ^he X-bar. Ghavt 5tat cotrol char t > variabls chart Step choo se for subgroups >kbav for Subgreup 5tep a:- Chcose obsevattons are one Jow Columns and then emtor Colunn o ,o,3,4,5,6 5tep 3 Clc ok

MINITAB output:

Xbar Chart of 1, 2, 3, 4, 5, 6 1.29 UCL-1.28447 1.28 1.27 1.26 -1.24858 125 1.24 123 1.22 LCL-1.21270 1.21 L 1 7 14 21 28 35 49 56 63 70 Sample Sample Mean 42

Concluston From the MItı TAB G leorthat te outputf75 data Ponts Plotted e the LeL and UcL Pres. Hence are ?f Con be Conclude that the Pents ProGessed arc Control ControlThus, Process
MINITAB OUTPUT FOR R CHART:

R Chart of 1,2, 3, 4, 5, 6 0.16 UCL-0.1488 0.14 0.12 0.10 0,08 R 0.0742 0.06 0.04 0,02 0.00 LCL 0 1 7 14 21 28 35 42 49 56 63 70 Sample Sample Range

Use the Same Procedure for Rchart Aftor selectong Vartable charts for Subyroups> 7. Conclustop: rom tke MwITAB output, 'r cleca that the data Petnts plotted wthn the LoL and UcL hoes- arc tHenoe, t Can be Processed Conclud e that the Potots ere Pn Contvol .Thus the proсе Control ess (3The dato Pots cutspde the LcL ne plotted are or UGL ne. ftence, t Can be Conlude that the Pornts CootrolThu the Process Precessed as out o are And also the data Ponts In Contro hocлog ary are CKtmeme Values , at that tme Process fs not Confrol