Raw material variability in food manufacturing: a data-driven snack food industry case

Figures & data

Table 1. Flour attribute, manufacturing control, and quality summaries

Flour Attributes
Moisture	Flour moisture, percentage of weight
Protein	Flour protein content, percentage of weight
Ash	Flour ash content, percentage of weight
MTI	Mixing tolerance index, in Brabender Units
Control Variables
Water	Water added at the mixing stage in pounds
Mix time	Mix time for each batch in minutes
Extruder	Extrusion pressure for the batch in pounds/square inch
Salt	Topical salt applied prior to baking in pounds per batch
Kiln	Speed of the dryer kiln, engineering units^a
Quality Measure
Final Moisture	Finished goods moisture, percent of weight

^aKiln speed is in proprietary engineering units.

Table 2. Flour quality descriptive statistics by supplier

	Supplier 1		Supplier 2		Supplier 3		Total Sample
Attribute	Mean	(St. Dev.)	Mean	(St. Dev.)	Mean	(St. Dev.)	Mean	(St. Dev.)
Moisture	13.32	(0.19)	13.08	(0.20)	13.06	(0.26)	13.17	(0.26)
Protein	8.61	(0.36)	8.64	(0.14)	8.89	(0.18)	8.73	(0.29)
Ash	0.47	(0.02)	0.49	(0.01)	0.48	(0.01)	0.48	(0.02)
MTI	84.39	(12.02)	79.04	(11.13)	70.66	(9.88)	77.90	(12.62)
$pric{e}_{flour}$	$0.1483/lb		$0.1505/lb		$0.1507/lb		$0.1498/lb
Observations	647		340		633

Note: Section A2 in the Appendix provides monthly mean and variance for the flour attributes by supplier.

Figure 1. Data-driven process optimization framework.

Figure 2. Diagram of the manufacturing process.

Table 3. Descriptive statistics of manufacturing controls

	Mean	(St. Dev.)	Max	Min	Unit
Mix time	6.799	(0.533)	7.5	5.5	minutes
Salt	47.177	(2.962)	55	38.3	pounds
Extruder	84.548	(7.139)	105	68	pounds/square inch
Water	161.330	(1.438)	165	158	pounds
Kiln Speed	708.531	(128.305)	990	420	units

Table 4. Estimated regression coefficients

	Dependent variable: Finished Goods Moisture
	Estimate	Std. Error	t value	Pr
Intercept	−1534.642	496.661	−3.090	0.002	**
Month4	0.279	0.061	4.560	0.0000114	***
Ash^2	87.916	21.145	4.158	0.0000571	***
Zone2	−0.020	0.009	−2.066	0.041	*
Zone3	3.484	1.103	3.158	0.002	**
Zone4	3.418	1.114	3.069	0.003	**
MTI:Moisture	0.004	0.001	4.16	0.0000574	***
MTI:Salt	−0.001	0.000262	−4.47	0.0000165	***
Ash:Moisture	−5.363	1.391	−3.855	0.000179	***
Ash:Mix Time	−1.54	0.356	−4.31	0.0000309	***
Moisture:Water	0.014	0.004	3.707	0.000306	***
Protein:Extruder	0.000465	0.000318	1.464	0.146
Salt:Mix Time	0.015	0.003	4.456	0.0000174	***
Water:Kiln	−0.000313	0.0000724	−4.320	0.0000302	***
Zone3:Zone4	−0.008	0.002	−3.15	0.002	**
Kiln:Zone4	0.000114	0.0000262	4.34	0.0000274	***
Observations	150
$R^2$	0.383
Adjusted $R^2$	0.314
Residual $\sigma$	0.175	($df$ = 134)
F-Statistic	5.545 ${ }^{\ast \ast \ast }$	($df$ = 15; 134)	$p$ =: 1.151e-08

Note: ${ }^{\ast }$$p$$<$ 0.1; ${ }^{\ast \ast }$$p$$<$ 0.05; ${ }^{\ast \ast \ast }$$p$$<$ 0.01

Table 5. Estimated regression distribution tests

Residuals Tests of Normality
Shapiro–Wilk ($H_0\sim N$)	$W$ = 0.991, $p$ = 0.445
Jarque–Bera ($H_0\sim N$)	${\chi }^2$ = 1.584, $df$ = 2, $p$ = 0.453

Table 6. Observed vs. optimized results

		Observed	$P_{NR}$ (1)	$P_{NR}$ (2)
Kiln Speed	Mean	720.133	720.133	1000
(Engineering Unit)	(St. Dev.)	(128.742)	(128.742)	(0)
Salt	Mean	47.126	36.067	35.00
(Pounds/batch)	(St. Dev.)	(3.056)	(3.458)	(0)
Water	Mean	161.260	158.693	158.636
(Pounds/batch)	(St. Dev.)	(1.458)	(5.944)	(1.491)
Mix Time	Mean	6.787	6.972	7.500
(Minutes)	(St. Dev.)	(0.560)	(0.470)	(0)
Extruder	Mean	84.860	80.390	65.057
(P.S.I.)	(St. Dev.)	(6.907)	(18.487)	(0.704)
Final Moisture	Mean	3.240	3.495	3.500
(Percentage)	(St. Dev.)	(0.212)	(0)	(0)
Pr(Prem)	Mean	0.787	0.983	0.984
	(St. Dev.)	(0.213)	(0.002)	(0)
NR/hr	Mean	313.686	371.664	516.266
	(St. Dev.)	(83.255)	(66.557)	(0.002)

Table 7. Supplier results

		Supplier 1		Supplier 2		Supplier 3
Panel		Mean	(St. Dev.)	Mean	(St. Dev.)	Mean	(St. Dev.)
A	Kiln Speed	1000	(0.00)	1000	(0.00)	1000	(0.00)
	Salt	35.00	(0.00)	35.00	(0.00)	35.00	(0.00)
	Water	157.81	(1.24)	157.36	(0.92)	156.66	(0.848)
	Mix Time	7.50	(0.00)	7.50	(0.00)	7.49	(0.02)
	Extruder	65.02	(0.34)	65.00	(0.00)	65.12	(0.88)
B	$Pr\left[prem\right]$	0.996	(0)	0.996	(0)	0.996	(0)
	$pric{e}_{flour}$	$0.1483/lb		$0.1505/lb		$0.1507/lb
	$E\left[NR/hr\right]$	$527.50	(0.002)	$524.54	(0.001)	$524.277	(0.001)
	Observations	647		339		633

Table A1. Estimated regression coefficients of Model B

	Dependent variable: Finished Goods Moisture
	Estimate	Std. Error	t value	Pr
Intercept	5.825	1.912	3.047	0.003	***
Month4	0.230	0.065	3.511	0.001	***
Moisture^2	0.021	0.008	2.654	0.009	***
Water:Moisture	−0.002	0.001	−1.824	0.070	*
Zone1:Zone2	0.0001	0.0001	−2.877	0.005	***
Ash:MTI	−0.005	0.003	−1.994	0.048	**
Zone3:Zone4	0.0001	0.0001	1.940	0.054	*
Observations	150
$R^2$	0.200
Adjusted $R^2$	0.166
Residual $\sigma$	0.193	($df$ = 143)
F-Statistic	5.959 ${ }^{\ast \ast \ast }$	($df$ = 6; 143)

Table A2. Estimated regression coefficients of Model C

	Dependent variable: Finished Goods Moisture
	Estimate	Std. Error	t value	Pr
Intercept	−2209.797	652.373	−3.387	0.001	***
Month4	0.364	0.080	4.528	0.0001	***
MTI^2	0.0001	0.0001	2.492	0.014	**
Ash^2	171.335	43.748	3.916	0.0001	***
Protein	−28.309	11.383	−2.487	0.014	**
Moisture	−57.578	22.048	−2.611	0.010	***
Water	−3.128	1.6237	−1.911	0.058	*
Salt	−0.209	0.130	−1,603	0.112
Salt^2	0.002	0.001	1.557	0.122
Extruder^2	−0.001	0.000	−2.083	0.039	**
Mixtime	6.419	4.102	1.565	0.120
Zone 2	1.809	0.571	3.186	0.002	***
Zone 3	6.705	1.427	4.700	0.0001	***
Zone 4	4.654	1.286	3.619	0.0001	***
Protein:MTI	0.025	0.009	2.681	0.008	***
Moisture:MTI	0.024	0.010	2.472	0.015	**
Protein:Moisture	1.789	0.825	2.167	0.032	**
Moisture:Ash	−9.540	3.020	−3.159	0.002	***
Water:Mixtime	−0.047	0.027	−1.738	0.085	*
Protein:Mixtime	0.320	0.196	1.630	0.106
Mixtime:MTI	0.006	0.004	1.753	0.082	*
Mixtime:Ash	−4.599	2.102	−2.188	0.031	**
Water:Extruder	0.001	0.0001	2.243	0.027	**
Mositure:Water	0.278	0.119	2.330	0.021	**
Water:MTI	−0.004	0.001	−3.374	0.001	***
Zone2:Zone3	−0.004	0.001	−3.212	0.002	***
Zone3:Zone4	−0.011	0.003	−3.704	0.0001	***
Zone3:Kiln	0.0001	0.0001	−2.935	0.004	***
Zone4:Kiln	0.0001	0.0001	2.947	0.004	***
Observations	150
$R^2$	0.407
Adjusted $R^2$	0.269
Residual $\sigma$	0.181	($df$ = 121)
F-Statistic	2.961 ${ }^{\ast \ast \ast }$	($df$ = 28; 121)

Table A3. Comparison between the three candidate models

	Adj. R-squared	Predicted R-squared	Accuracy	AIC	BIC	Bias
Selected model	0.314	0.231	92.7%	−79.5	−28.3	5.67%
Model B	0.166	0.127	94.2%	−58.5	−34.3	5.9%
Model C	0.269	0.061	89.2%	−59.34	30.9	5.4%

Figure A1. Observed flour protein monthly mean and variance by supplier.

Figure A2. Observed flour moisture monthly mean and variance by supplier.

Figure A3. Observed flour mixing tolerance index monthly mean and variance by supplier.

Figure A4. Observed flour ash monthly mean and variance by supplier.

Table A4. Correlation matrix Supplier 1 Added water and Flour batch attributes

	Added water	Moisture	Protein	Ash	MTI
Added water	1
Moisture	0.280	1
Protein	−0.542	−0.574	1
Ash	−0.333	0.199	0.191	1
MTI	0.832	0.167	−0.451	−0.036	1

Table A5. Correlation matrix Supplier 2 Added water and Flour batch attributes

	Added water	Moisture	Protein	Ash	MTI
Added water	1
Moisture	−0.403	1
Protein	0.199	−0.286	1
Ash	0.181	−0.039	0.161	1
MTI	0.910	−0.261	0.050	−0.168	1

Table A6. Correlation matrix Supplier 3 Added water and Flour batch attributes

	Added water	Moisture	Protein	Ash	MTI
Added water	1
Moisture	−0.119	1
Protein	0.138	0.181	1
Ash	0.427	0.026	0.331	1
MTI	0.878	0.041	0.028	0.118	1