WK$12-2$: Process Capability Problems

Instructions

Submit an Excel file. $$Show all of your work and answer questions using complete sentences.$$

Q$1)$ A process is in control with$$x$==100$ and$$ s$-=1\mathrm{.}05,$ n $=5.$ The process specifications are at $9510.$ Assume the process follows a normal distribution.$$

$1.$a$)$ Estimate the potential capability.$$

$1.$b$)$ Estimated the actual capability.

$1.$c$)$ Estimate the PPM for this process based on the process capability calculated in parts a band b$.$Explain what this means in terms of the process described.$$

$1.$d$)$ What would you recommend to improve this process?$$

Q$2)$ Data was collected for a process involving the compressive strength of an injection molded part.$$Twenty samples were collected each consisting of five observations.$$ Assume a target of $80+/-15.$

Samplex$1$x$2$x$3$x$4$x$518381\mathrm{.}278\mathrm{.}775\mathrm{.}777288\mathrm{.}678\mathrm{.}378\mathrm{.}87184\mathrm{.}2385\mathrm{.}775\mathrm{.}884\mathrm{.}375\mathrm{.}281480\mathrm{.}874\mathrm{.}482\mathrm{.}574\mathrm{.}175\mathrm{.}7583\mathrm{.}478\mathrm{.}482\mathrm{.}678\mathrm{.}278\mathrm{.}9675\mathrm{.}379\mathrm{.}987\mathrm{.}389\mathrm{.}781\mathrm{.}8774\mathrm{.}57880\mathrm{.}873\mathrm{.}479\mathrm{.}7879\mathrm{.}284\mathrm{.}481\mathrm{.}58674\mathrm{.}5980\mathrm{.}586\mathrm{.}276\mathrm{.}283\mathrm{.}980\mathrm{.}21075\mathrm{.}775\mathrm{.}271\mathrm{.}182\mathrm{.}174\mathrm{.}3118081\mathrm{.}578\mathrm{.}473\mathrm{.}878\mathrm{.}11280\mathrm{.}681\mathrm{.}879\mathrm{.}373\mathrm{.}881\mathrm{.}71382\mathrm{.}781\mathrm{.}379\mathrm{.}18279\mathrm{.}51479\mathrm{.}274\mathrm{.}978\mathrm{.}677\mathrm{.}775\mathrm{.}31585\mathrm{.}582\mathrm{.}182\mathrm{.}873\mathrm{.}471\mathrm{.}71678\mathrm{.}879\mathrm{.}680\mathrm{.}279\mathrm{.}180\mathrm{.}81782\mathrm{.}178\mathrm{.}275\mathrm{.}578\mathrm{.}282\mathrm{.}11884\mathrm{.}576\mathrm{.}983\mathrm{.}581\mathrm{.}279\mathrm{.}2197977\mathrm{.}881\mathrm{.}284\mathrm{.}481\mathrm{.}62084\mathrm{.}573\mathrm{.}178\mathrm{.}678\mathrm{.}780\mathrm{.}6$

$2.$a$)$ Determine if the process is in control

$2.$b$)$ Calculate the process capability Cp as well as Cpk$.$

$2.$c$)$ Estimate the PPM for this process.$$

Q$3)$ Two months after the initial process for the injection molded part in Q$2$ was evaluated, a subsequent set of samples were collected. $$ Assume a target of $80+/-15.$

$2168\mathrm{.}981\mathrm{.}578\mathrm{.}280\mathrm{.}881\mathrm{.}52269\mathrm{.}868\mathrm{.}680\mathrm{.}484\mathrm{.}383\mathrm{.}92378\mathrm{.}585\mathrm{.}278\mathrm{.}480\mathrm{.}381\mathrm{.}72476\mathrm{.}986\mathrm{.}186\mathrm{.}994\mathrm{.}483\mathrm{.}92593\mathrm{.}681\mathrm{.}687\mathrm{.}879\mathrm{.}6712665\mathrm{.}586\mathrm{.}872\mathrm{.}482\mathrm{.}671\mathrm{.}42778\mathrm{.}165\mathrm{.}783\mathrm{.}793\mathrm{.}793\mathrm{.}42874\mathrm{.}972\mathrm{.}681\mathrm{.}687\mathrm{.}272\mathrm{.}72978\mathrm{.}177\mathrm{.}16775\mathrm{.}776\mathrm{.}83078\mathrm{.}785\mathrm{.}477\mathrm{.}790\mathrm{.}776\mathrm{.}7318560\mathrm{.}268\mathrm{.}571\mathrm{.}182\mathrm{.}43286\mathrm{.}479\mathrm{.}279\mathrm{.}88675\mathrm{.}43378\mathrm{.}59978\mathrm{.}371\mathrm{.}481\mathrm{.}83468\mathrm{.}8628277\mathrm{.}576\mathrm{.}1358383\mathrm{.}773\mathrm{.}182\mathrm{.}295\mathrm{.}3$

$3.$a$)$ Evaluate the current process relative to the initial process set up $2$ months earlier.$$ Is the process in control?$$

$3.$b$)$ Calculate the process capability Cp as well as Cpk$.$

$3.$c$)$ Estimate the PPM for this process.$$

Q$4)$ Write a short Memo $($include to$,$ from, and subject in heading$)$ to the Manger of the injection molding department summarizing your analysis of Q$2$ and Q$3.$ Use the results of your statistical analysis to support your conclusion and recommendations.$($You can create this in a text box and include it in one of the tabs in your Excel File.$$ Look at the Rubric for MEMO criteria$)$