An automatic cookie machine at AutoCM, Inc. must deposit a specified amount of 25 0.3 grams (g)

Question:

An automatic cookie machine at AutoCM, Inc. must deposit a specified amount of 25 ±0.3 grams (g) of dough for each cookie on a conveyor belt. It costs $0.03 to scrap a defective cookie. A sample of 50 cookies was drawn from the production process, which has been determined to be approximately normally distributed, and the results, in grams, can be found in worksheet tab Prob08-08 in the Excel file Ch08Data.xlsx.

a. What is the value of k in the Taguchi loss function?

b. Determine how much the process varies from the target specification, based on the mean difference and standard deviation of the sample results. What is the expected loss per unit?

AutoCM, Inc.

Descriptive Statistics
Original Data	Sorted Data
		Descriptive Statistics					Bin	Frequency
24.9349	24.8672						24.850	0
25.0666	24.8824	Mean	25.0056				24.875	1
25.0323	24.9180	Standard Error	0.0080				24.900	1
25.0666	24.9196	Median	25.0123				24.925	3
24.9842	24.9210	Mode	#N/A				24.950	2
24.9210	24.9285	Standard Deviation	0.0566				24.975	9
25.0366	24.9349	Sample Variance	0.0032				25.000	7
25.0170	24.9513	Kurtosis	-0.1981				25.025	9
25.0501	24.9621	Skewness	-0.2635				25.050	6
24.9683	24.9639	Range	0.2508				25.075	7
25.0390	24.9683	Minimum	24.8672				25.100	3
25.0114	24.9685	Maximum	25.1180				25.125	2
25.0369	24.9723	Sum	1250.2795				More	0
25.0894	24.9732	Count	50.0000
25.0219	24.9735
24.9962	24.9745
24.8824	24.9758
25.0906	24.9788						Alternate
25.0011	24.9842						Bin	Frequency
25.0171	24.9878						24.850	0
25.0132	24.9880	Original data					24.900	2
25.0654	24.9962						24.950	5
24.9732	24.9978	24.9349	25.0666	25.0323	25.0666	24.9842	25.000	16
24.9758	25.0011	24.9210	25.0366	25.0170	25.0501	24.9683	25.050	15
24.9180	25.0114	25.0390	25.0114	25.0369	25.0894	25.0219	25.100	10
24.9723	25.0132	24.9962	24.8824	25.0906	25.0011	25.0171	25.15	2
24.8672	25.0170	25.0132	25.0654	24.9732	24.9758	24.9180
24.9685	25.0171	24.9723	24.8672	24.9685	24.9788	25.0416
24.9788	25.0197	25.0559	25.0642	25.0205	25.0197	25.0420
25.0416	25.0205	24.9878	24.9639	25.1058	25.1180	24.9621
25.0559	25.0219	24.9880	24.9745	24.9196	25.0864	24.9978
25.0642	25.0241	25.0241	24.9735	24.9513	24.9285	25.0583
25.0205	25.0323
25.0197	25.0366
25.0420	25.0369
24.9878	25.0390
24.9639	25.0416
25.1058	25.0420
25.1180	25.0501
24.9621	25.0559
24.9880	25.0583
24.9745	25.0642
24.9196	25.0654
25.0864	25.0666
24.9978	25.0666
25.0241	25.0864
24.9735	25.0894
24.9513	25.0906
24.9285	25.1058
25.0583	25.1180