You are employed by a small artisan cheese company on their quality assurance team. The company has been having trouble with its cheddar cheese line. Some of the cheeses have significant flavor and texture defects and the company is not sure why. They are careful about sanitation and they have confirmed that microbial contamination (e.g., spoilage bacteria, molds, yeast) is not the cause of the defects. A diagram of their cheddar cheese production process is shown in Figure 1.

Batch Date	Batch Number	No. of Samples with Defects	Notes
10/13/2019	1	6	One sample has 3 defects, two samples each have 2 defects
10/14/2019	2	5	One sample has 4 defects
10/15/2019	3	5	Three samples each have 3 defects
10/16/2019	4	0
10/17/2019	5	3	One sample has 2 defects
10/18/2019	6	4
10/19/2019	7	5
10/20/2019	8	6	Three samples each have 3 defects, one sample has 2 defects
10/21/2019	9	7	One sample has 3 defects, two samples each have 2 defects
10/22/2019	10	8	Two samples each have 2 defects
10/23/2019	11	6	One sample has 4 defects
10/24/2019	12	6	Three samples each have 2 defects
10/25/2019	13	5
10/26/2019	14	6	Three samples each have 2 defects
10/27/2019	15	3	Two samples have 2 defects each
10/28/2019	16	6
10/29/2019	17	5	Two samples each have two defects
10/30/2019	18	5	Four samples each have 2 defects
10/31/2019	19	4	Two samples each have 3 defects
11/1/2019	20	5	One sample has 2 defects

The company employs a dedicated sensory team that tastes 50 samples total out of every batch and rates the cheeses in terms of flavor and texture. The results from the last 20 batches of cheese are shown in Table 1. The company has made process changes between the batches on 10/18/19 and 10/19/19, and between the batches on 10/22/19 and 10/23/19 to try and reduce the number of defects.

Unless otherwise stated, each defective sample has one defect. As recorded in the right-most column of the table, some samples contain more than one defect. Therefore, the total number of defects in the samples would be greater than the number of samples with defects. For example, the batch on 10/13/19 has 6 samples with defects. Since one sample has 3 defects and two samples have two defects each, the total number of defects in that batch is 3+2+2+1+1+1 = 10 defects. The defects appearing in the cheddar cheese are shown in Table 2 below. The severity of a defect can range from hardly noticeable to a trained evaluator, to noticeable right away by a general consumer.

Notice that pbar = CL = 0.1. Assuming a Test 1 false alarm rate of 0.27%, what is the p-chart UCL? Use 3 decimal places.

For the Better Cheddar data (Table 1 tab of the Excel file), assuming a Test 1 false alarm rate of 0.27%, what is the p-chart LCL?

For the Better Cheddar data (Table 1 tab of the Excel file), assuming a Test 1 false alarm rate of 0.27%, what is the c-chart UCL? Use one decimal place.

For the Better Cheddar data (Table 1 tab of the Excel file), assuming a Test 1 false alarm rate of 0.27%, what is the c-chart LCL? Use one decimal place.