3.24. a Manufacturer of Electroniccalculatorsoffers a One-Yearwarranty

3.39.The tensile strength of a metal part is normallydistributedwithmean 40lb and standart deviation 5lb. If 50,000 partsareproduced, how manywouldyouexpectto fail tomeet a minimum specification limit of 35 lb tensile strength? How manywouldhave a tensile strength in excess of 48 lb

3.40. Theoutputvoltage of a powersupply is normallydistributedwithmean 5 V and standart deviation 0.02 V. Ifthelowerandupperspecificationsforvoltageare 4.95 V and 5.05 V, respectively, what is theprobabilitythat a powersupplyselected at randomwillconformtothespecifications on voltage?

3.24. A manufacturer of electroniccalculatorsoffers a one-yearwarranty. Ifthecalculatorfailsforanyreasonduringthisperiod, it is replaced. The time tofailure is wellmodeledbythefollowingprobabilitydistribution:

a) Whatpercentage of thecalculatorswill fail withinthewarrantyperiod ?

b) Themanufacturingcost of a calculator is $50, andtheprofitpersale is $25. What is theeffect of warrantyreplacement on profit ?

4.1.Thediameters of aluminumalloyrodsproduced on an extrusionmachineareknowntohave a standarddeviation of 0.0001 in. A randomsample of25 rods has an averagediameter of 0.5046 in.

a) Test thehypothesisthatmeanroddiameter is 0.5025 in. Assume atwo-sidedalternativeanduse
b)Findthe P-valueforthis test.
c)Construct a two-sided 95% confidenceinterval on themeanroddiameter.

5.23. Considerthe time-varyingprocessbehaviourshownbelow. Matcheach of theseseveralpatterns of processperformancetothecorresponding and R charts shown in figures (a) to (e) below ?

Question : Applythe Western electricrulestothecontrolchartspresentedbelow. Wouldtheserulesresult in anyout of controlsignal ?

Xbar - chart

R-chart

Checkingforout of controlconditionswehavethefollowing 8 tests:

Test1 : Extremepoints -> points 8, 20, 32, 44 on x bar chartnoextremepoints on R chart.

Test 2: Twoout of Three Points in orbeyondZone A -> 20, 21

Test 3: Fourout of FivePoints in orbeyondZone B -> 25, 26, 27

Test 4: RunsAboveorBelowtheCenterline (Eightormoreconsecutivepoints) -> No pointssatisfyingthisconditionboth on x bar and R charts.

Test 5: Linear Trend Identification (Sixormoreconsecutivepoints) -> 25,26

Test 6: Oscillatory Trend Identification( 14 ormoreconsecutivepoints) -> No points

Test 7: Avoidance of Zone C (8 ormoreconsecutivepoints) -> No points

Test 8: Run in Zone C (15 ormoreconsecutivepoints) -> No points

Wecheckforall of the 8 testsaboveforx bar chart. Howeverfor R chart, wedon’tapplyteststhatcontainzones (tests2,3,7and 8), thustheyare not neededto be checked. (Only1,4,5,6thtestsshould be checkedfor an R chart)