Company X is a manufacturer of AA batteries. Consider lifetimes (in hours) of AA batteries when put in constant use, i.e., keeping flashlight ‘on’ till the battery dies. Recently, with advancement in technology, other companies manufacturing AA batteries claim that the lifetime of AA battery is significantly greater than the ones manufactured by company X. This motivated company X to investigate several quality characteristics for AA batteries. The objectives of the investigation are as follows:

I. Figuring out if indeed the lifetime of AA battery manufactured by company X is less than their friendly competitor, company Y, who is ready to help company X by sharing process data

II. Identifying the action items to be carried out if indeed the lifetimes of the batteries manufactured by company X are significantly lesser than the ones manufactured by company Y

III. Verifying whether the manufacturing process is in control and capable

IV. Devising a single acceptance sampling plan before releasing any battery lot for sale to the market

Following are the details with respect to the objectives.

Objective I:

The following data were obtained on AA battery lifetimes in hours:

Company X: 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

Company Y: 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

The above data are given in an excel sheet titled ‘lifetime_data.xlsx’.

If shapes of the distributions of battery lifetimes for both companies show similarity and the average battery lifetime for company X is less than average battery lifetime for company Y by 2 hours, then the manufacturing process indicates difference and battery lifetime for company X will be considered significantly lesser than the battery lifetime for company Y.

Objective II:

In case of the battery lifetime for company X is significantly lesser than that the battery lifetime for company Y, the following action items are suggested.

1. Install an R&D team for the following tasks:

a. To find alternative materials to Zinc (Zn, for negative electrode) and Manganese Dioxide (MnO2, for positive electrode). If cheaper alternatives are available, assess the alkaline toxicity and suggest materials which can neutralize the toxicity. If cheaper alternatives are not available, then other structural changes of battery should be considered in a team meeting after a period of 6 months.

b. To reduce the width of the cylindrical wall of battery by 10% and check the effect on the battery lifetime. Carry out the experiment for 1000 batteries. Apply regression model to analyze data. If more than 5% of batteries get too hot (>40C), then stop the process.

2. Typically, battery shelf-life, when stored in room temperature, is between 5 to 10 years. Carry out an experiment to study the shelf-life of batteries for a period of 1 year to check what percentage of batteries show shelf-life of less than 1 year. During this one year if the head of experimenter team changes, then the assistant will be made the head of the team and a new person will be hired as an assistant.

Objective III:

1. An employee is responsible for collecting manufactured battery sample of size between 50 and 60 every day at 4 pm for a period of consecutive 25 days every 3 months, and collect data on the daily number of defective batteries. A relevant quality control chart is given in Figure 1.

2. According to customer specifications, standard AA battery length should be between 49.0 mm and 50.5 mm. Assuming the lengths to be normally distributed, the average and the standard deviation of the lengths are 49.9 mm and 0.2 mm, respectively

Objective IV:

Before sending out any batch of batteries (typically of size 10000) to market, company X decides to carry out an acceptance sampling based on a single sampling plan. An internal decision is taken that acceptable quality level/limit (AQL) should be 1% while lot tolerance percent defective (LTPD) is obtained as 5% from a market survey. A producer’s risk of 10% and a consumer’s risk of 8% are considered logical for the plan.

Based on the case study, please do the following.

1. Objective I:

a. What kind of tool/graph will be useful to accomplish objective I?

b. Please use the data given in the excel sheet ‘lifetime_data.xlsx’ and construct the relevant graph/diagram to understand the shapes of the distributions. Copy the relevant graphs as images from the excel sheet and paste on the word document. Properly label them.

c. Comment (with reasons) on whether the manufacturing process indicates difference, and battery lifetime for company X is significantly lesser than the battery lifetime for company Y.

2. Objective II:

Construct a tree diagram and flowchart based process decision program chart (PDPC) from the information given under objective II. Please don’t write any separate logic, just the diagram is sufficient.

3. Objective III:

a. What type of control chart is drawn in Figure 1? Justify.

b. What measure (joined by the red line) is plotted in Figure 1?

c. What do you infer about the process from Figure 1? Justify.

d. What does the center line represent in Figure 1?

e. Is the process distribution with respect to battery length centered? Justify.

f. Calculate relevant process (with respect to battery length) capability index value and comment on the process capability.

4. Objective IV:

a. Use MS Excel to figure out sample size ‘n’ and acceptance number ‘c’ corresponding to the single acceptance sampling plan. Carry out this exercise in EXCEL. Copy-paste the tables from EXCEL to the WORD document file. Include the EXCEL sheet separately as a part of the .zip folder.

b. Construct an operating characteristic curve (OCC) based on ‘n’ and ‘c’ for the using lot proportion of defectives ‘p’={0, 0.01, …, 0.3}. Just copy-paste the graph from EXCEL in your answer sheet with proper labelling.

c. Calculate the average outgoing quality (AOQ) value for p=0.05.