Company X is a manufacturer of AA batteries. Consider lifetimes (in hours) of AA batterieswhenputinconstantuse,i.e.,keepingflashlight'on'tillthebatterydies.Recently,withadvancement in technology, other companies manufacturing AA batteries claim that the lifetimeof AA battery is significantly greater than the ones manufactured by company X. This motivatedcompany X to investigate several quality characteristics for AA batteries. The objectives of theinvestigationareas follows:

1. Figuring outif indeed the lifetime of AA battery manufactured by company X islessthan their friendly competitor, company Y, who is ready to help company X by sharingprocessdata
2. Identifying the action items to be carried out if indeed the lifetimes of the batteriesmanufactured by company X are significantly lesser than the ones manufactured bycompanyY
3. Verifyingwhether themanufacturingprocessis in controlandcapable
4. Devisingasingleacceptancesamplingplanbeforereleasinganybatterylotforsaletothemarket

Followingarethedetailswithrespecttothe objectives.

ObjectiveI:

Thefollowingdata were obtained onAAbatterylifetimes in hours:

CompanyX:

3,	4.5,	4.5,	3.9,	5.2,	6.2,	3.9,	2.2,	3.6,	6,
3.2,	5.6,	3.7,	4.6,	4.4,	5.4,	4.2,	5.1,	3.3,	4.9,
2.3,	4.5,	3.7,	4.1,	3.9,	3.8,	4.7,	4.8,	4.1,	4.1

CompanyY:

10.9,	8.2,	5.7,	5,	6.6,	5.6,	7.4,	6.7,	7.1,	4.5,
7.7,	6.2,	7.4,	6,	8.2,	9.1,	8.2,	6.5,	6.6,	9.6,
8.6,	7.2,	7.3,	6.8,	10.2,	8.6,	6.8,	8.6,	7.3,	9

Theabovedataaregiven inanexcelsheettitled'lifetime_data.xlsx'.

If shapes of the distributions of battery lifetimes for both companies show similarity and theaverage battery lifetime for company X is less than average battery lifetime for company Y by 2hours, then the manufacturing process indicates difference and battery lifetime for company Xwill beconsidered significantlylesserthan thebatterylifetime forcompanyY.

ObjectiveII:

In case of the battery lifetime for company X is significantly lesser than that the battery lifetimeforcompanyY, thefollowingaction items aresuggested.

1. InstallanR&Dteam for thefollowingtasks:
   1. TofindalternativematerialstoZinc(Zn,fornegativeelectrode)andManganese Dioxide (MnO₂, for positive electrode). If cheaper alternatives areavailable,assessthealkalinetoxicityandsuggestmaterialswhichcanneutralizethetoxicity.Ifcheaperalternativesarenotavailable,thenotherstructural changes of battery should be considered in a team meeting after aperiodof6 months.
   2. To reduce the width of the cylindrical wall of battery by 10% and check theeffectonthe battery lifetime. Carry outthe experimentfor 1000batteries.Applyregressionmodeltoanalyzedata.Ifmorethan5%ofbatteriesgettoohot(>40C), then stop theprocess.
   3. Typically,batteryshelf-life,whenstoredinroomtemperature,isbetween5to10years. Carry out an experiment to study the shelf-life of batteries for a period of 1 yearto check what percentage of batteries show shelf-life of less than 1year. During thisone year if the head of experimenter team changes, then the assistant will be made theheadof theteam and anew personwill be hiredasan assistant.

ObjectiveIII:

1. Anemployeeisresponsibleforcollectingmanufacturedbatterysampleofsizebetween50and60everydayat4pmforaperiodofconsecutive25daysevery3

months,andcollectdataonthedailynumber of defectivebatteries.Arelevantqualitycontrolchart isgiven inFigure1.