3.1.1.

Influence of meal varieties.

Shop food variety is more. Different meals at different times. Out of 235 samples, Gai Bo accounted for 208. So, gai Bo was taken as the representative of the study.

3.1.2.

Customer service impact.

The Chicken Pot is a pull-type production workshop, so customers’ payment is taken as the order entry, and the order time is recorded. After ordering, customers go to the window to pick up their food and record the time. The process is shown in Figure 1.

Figure 1.

Entity flow chart.

3.2.

Data collection and processing

3.2.1.

The data collection.

This paper determines the peak period. 5 data collection times, each collection time ≥90 minutes, total data more than 8 hours. Data collection and sorting Table 1.

Table 1.

First data collection and collation (Part of the content).

3.2.2.

The data processing.

(1) Order interval homogeneity test.

Make access interval pivot tables, draw histograms, as shown in Figure 2 [3].

Figure 2.

Order distance distribution histogram.

According to Figure 2, the time between sequences is approximately exponential. Since all the data samples collected were ≥30, the interval was considered to be approximately normal distribution.

(2) Product processing time-consuming homogeneity test

The product processing time into a pivot table, Figure 3, the product processing time approximately obey exponential distribution. The product times are normally distributed.

Figure 3.

Product processing time histogram.

(3) Stationery test of order interval

Will be five times survey data collected by sorting interval grouping, as shown in Table 2 [4].

Table 2.

Mean value of order intervals and Average product time.

From (1), the mean difference was 1.02min. The sorting time fluctuates near the mean, so it is considered that the sorting interval is stable.

(4) Product processing time-consuming stationarity test

The processing time data collected from sorted out and grouped, as shown in Table 2. The difference of mean value was 1.54min. The time - consuming interval is stationary.

(5) Order interval independence test

The data has no impact and is said to be independent [5]. The time interval between orders collected by the survey is organized into a scatter plot, as shown in Figure 4.

Figure 4.

Scatter diagram of order intervals.

Equation (1) is used to obtain the autocorrelation coefficient between interval time and time.

According to equation (1), the correlation coefficient ρ=0.0716 is obtained. When ρ is close to zero, the data is not correlated and the sorting interval is independent.

(6) Product processing time - consuming independence inspection

The processing time of products was sorted out and made into a scatter plot, as shown in Figure 5.

Figure 5.

Scatter diagram of product processing time.

According to equation (1), the correlation coefficient between processing time and total time is close to zero, and the product processing time is independent. Sample size is 230, ranking interval approximate normal distribution, be determined by Minitab, as shown in Figure 6.

Figure 6.

Distribution map of meal interval.

(7) Parameter estimation and goodness of fit test

Parameter estimation was performed for X, and 230 samples were integrated (only n-1 order interval was investigated each time). The sample mean x=1.82, variance 2.28, standard deviation 1.51.

The maximum likelihood estimation method is shown in equation (3):

The mean μ was tested by standard normal distribution, and null hypothesis Ho was set: population mean μ=1.65; Alternative hypothesis H1: μ≠1.65. Because the order interval X approximately follows a normal distribution, it is a twosided test. n =230, significance level α=0.05, Z*0.025=1.96.

The test statistics are shown in equation (4).

The acceptance domain is (-1.96, 1.96), and the test statistic x ∈ (-1.96, 1.96). μ is in the receiving domain. Conclusion: There is not enough evidence to reject Ho, so μ=1.65.

Variance is tested by chi-square distribution, and null hypothesis Ho: population standard deviation σ=1.45; Alternative hypothesis H1: σ≠1.45. Similarly, n=230, the significance level α=0.1, Z*0.1=1.28. The test statistics are shown in equation (5).

Calculate:

In the accepting domain, σ=1.45.

Namely: the ordering interval x of chicken Pot obeys the normal distribution x ~ N (1.65, 2.1025).

(8) Parameter estimation and fitting Optimization Test of Product processing time

Integrating the sample data, sample mean x=6.57, variance 3.65, standard deviation 1.91.

The maximum likelihood estimation method is shown in Equation (3). Ho: population mean μ=6.5; H1: μ≠6.5. Similarly n=235, the significance level α=0.1, Z0.05=1.645.

The test statistics are shown in equation (6). x ∈(-1.645, 1.645). If μ is in the receiving domain, μ=6.5.Similarly, Ho: σ=1.9; H1: σ≠1.9. n=235, α=0.1, Z0.1=1.28.

The test statistics are shown in equation (5). In the acceptance domain, σ=1.9, the processing time of follows the normal distribution x ~ N (1.65, 3.61).