Statistical Quality Control Management

Question: Describe about the Statistical Quality Control? Answer: Executive Summary For the study of statistical quality control for the variable net weight in oz over some time interval, we use different statistical methods. First we find out the some descriptive or numerical statistical analysis for the variable net weight in oz. We get average net weight as 20.0122 oz with the standard deviation of 79.3056 oz. The histogram shows that the distribution of the net weight follows an approximate normal distribution. One sample Kolmogorov Smirnov test also proves the claim that the variable net weight follows an approximately normal distribution. The box plots for the given eight days shows that the average net weights for all the days are not same. The p-plot for the distribution of the variable net weight in oz shows that the distribution follows an approximate normal distribution. Time series plot for the variable net weight over the given dates or days shows that there is a specific same repeated pattern observed for each day. Time series plot for the variable net weight over the given time also shows that there is a specific same repeated pattern observed for each day. The x-bar control chart for the variable net weight shows that the process is out of control, because for the date 13.01.2015, the samples mean found out of 3 sigma limits. The range chart shows that the process for the variable net weight is in control. Although the control chart for the range chart shows that the process is in control, but actually process is out of control and there is one non-confirming point which is out of given 3 sigma limits. Introduction For the study of the variable net weight in oz, we have to use different statistical methods for analysis purpose. We have to use the descriptive statistics for describing the variable net weight in detail. Then after, we have to see some graphical analysis for the variable under study. We have see the histogram for the variable net weight and also we have to see the different box plots for each day for the variable net weight. We have to check whether there is any difference in the averages for the variable net weight for given eight days. Also we have to see the time series for this variable and we have to check whether there is any particular pattern observed or not. We have to study the x-bar and R control charts for the given variable. Let us see all this data analysis in the next topic in detail. Results and Discussion: Let us see the some descriptive statistics for the variable net weight in detail given below: Descriptive Statistics N Minimum Sum Mean Std. Deviation Variance Net_weight_oz 384 14.73 7684.70 20.0122 79.30555 6289.370 Valid N (listwise) 384 The average net weight is given as 20.0122 oz with the standard deviation 79.3056 oz. Some other descriptive statistics are given below: Descriptive Statistics N Range Maximum Mean Skewness Kurtosis Statistic Statistic Statistic Std. Error Statistic Std. Error Statistic Std. Error Net_weight_oz 384 1555.27 1570.00 4.04704 19.595 .125 383.970 .248 Valid N (listwise) 384 The histogram for the variable net weight is given below: The above histogram shows that the distribution for the variable net weight follows an approximate normal distribution. The box plots for the net weight for the given eight days are given below: The above box plots shows that the average net weight for each day is not same. The average net weight is different for all days. The histogram with the normal curve is given below: Now, we have to see the one sample Kolmogorov Smirnov test for the normality. The test for normality is given below: Descriptive Statistics N Mean Std. Deviation Minimum Maximum Percentiles 25th 50th (Median) 75th Net_weight_oz 384 15.9628 .49788 14.73 17.21 15.5600 15.9450 16.3800 One-Sample Kolmogorov-Smirnov Test Net_weight_oz N 384 Normal Parametersa,b Mean 15.9628 Std. Deviation .49788 Most Extreme Differences Absolute .101 Positive .070 Negative -.101 Kolmogorov-Smirnov Z 1.978 Asymp. Sig. (2-tailed) .001 a. Test distribution is Normal. b. Calculated from data. Model Description Model Name MOD_1 Series or Sequence 1 Net_weight_oz Transformation None Non-Seasonal Differencing 0 Seasonal Differencing 0 Length of Seasonal Period No periodicity Standardization Not applied Distribution Type Normal Location estimated Scale estimated Fractional Rank Estimation Method Blom's Rank Assigned to Ties Mean rank of tied values Applying the model specifications from MOD_1 Case Processing Summary Net_weight_oz Series or Sequence Length 384 Number of Missing Values in the Plot User-Missing 0 System-Missing 0 The cases are unweighted. Estimated Distribution Parameters Net_weight_oz Normal Distribution Location 15.9628 Scale .49788 The cases are unweighted. The p-plot for the distribution of the variable net weight in oz shows that the distribution follows an approximate normal distribution. Now, we have to see the time series plot for the net weight over given days. The time series plot is given below: Time series plot for the variable net weight over the given dates or days shows that there is a specific same repeated pattern observed for each day. This pattern is shown in the above time series plot. Time series plot for the variable net weight over the given time also shows that there is a specific same repeated pattern observed for each day. This pattern is shown in the above time series plot. Now, we have to see the control charts such as x-bar and R control chart for checking whether the process is in statistical control or out of statistical control. Also we have to see how many observations are confirming and how many observations is non-conforming the given specific limit. Here, we use the 3 sigma limits for the given variable under study. First, let us see the x-bar control chart given below: The x-bar control chart for the variable net weight shows that the process is out of control, because for the date 13.01.2015, the samples mean found out of 3 sigma limits. Now, let us see the R control chart given below: The range chart shows that the process for the variable net weight is in control. Although the control chart for the range chart shows that the process is in control, but actually process is out of control and there is one non-confirming point which is out of given 3 sigma limits. Conclusions and Recommendations 1) We get average net weight as 20.0122 oz with the standard deviation of 79.3056 oz. 2) The histogram shows that the distribution of the net weight follows an approximate normal distribution. One sample Kolmogorov Smirnov test also proves the claim that the variable net weight follows an approximately normal distribution. 3) The box plots for the given eight days shows that the average net weights for all the days are not same. 4) The p-plot for the distribution of the variable net weight in oz shows that the distribution follows an approximate normal distribution. 5) Time series plot for the variable net weight over the given dates or days shows that there is a specific same repeated pattern observed for each day. 6) Time series plot for the variable net weight over the given time also shows that there is a specific same repeated pattern observed for each day. 7) The x-bar control chart for the variable net weight shows that the process is out of control, because for the date 13.01 .2015, the samples mean found out of 3 sigma limits. The range chart shows that the process for the variable net weight is in control. Although the control chart for the range chart shows that the process is in control, but actually process is out of control and there is one non-confirming point which is out of given 3 sigma limits. Appendices: The data set is given as below: Date Time Net Weight (oz) 12/01/2015 0:00 15.96 12/01/2015 0:30 15.90 12/01/2015 1:00 15.12 12/01/2015 1:30 15.36 12/01/2015 2:00 15.60 12/01/2015 2:30 15.48 12/01/2015 3:00 16.25 12/01/2015 3:30 15.89 12/01/2015 4:00 15.52 12/01/2015 4:30 15.98 12/01/2015 5:00 15.98 12/01/2015 5:30 15.63 12/01/2015 6:00 16.28 12/01/2015 6:30 16.07 12/01/2015 7:00 16.23 12/01/2015 7:30 16.31 12/01/2015 8:00 15.88 12/01/2015 8:30 16.17 12/01/2015 9:00 15.44 12/01/2015 9:30 16.74 12/01/2015 10:00 16.66 12/01/2015 10:30 15.88 12/01/2015 11:00 16.25 12/01/2015 11:30 16.62 12/01/2015 12:00 16.38 12/01/2015 12:30 16.26 12/01/2015 13:00 16.95 12/01/2015 13:30 17.03 12/01/2015 14:00 17.01 12/01/2015 14:30 16.65 12/01/2015 15:00 16.37 12/01/2015 15:30 16.22 12/01/2015 16:00 16.59 12/01/2015 16:30 16.32 12/01/2015 17:00 15.91 12/01/2015 17:30 15.95 12/01/2015 18:00 16.45 12/01/2015 18:30 16.38 12/01/2015 19:00 16.00 12/01/2015 19:30 16.38 12/01/2015 20:00 15.75 12/01/2015 20:30 16.29 12/01/2015 21:00 16.44 12/01/2015 21:30 16.44 12/01/2015 22:00 16.38 12/01/2015 22:30 15.41 12/01/2015 23:00 15.13 12/01/2015 23:30 15.64 13/01/2015 0:00 15.36 13/01/2015 0:30 15.33 13/01/2015 1:00 15.11 13/01/2015 1:30 15.04 13/01/2015 2:00 15.33 13/01/2015 2:30 15.35 13/01/2015 3:00 15.36 13/01/2015 3:30 15.26 13/01/2015 4:00 15.33 13/01/2015 4:30 15.48 13/01/2015 5:00 15.48 13/01/2015 5:30 15.67 13/01/2015 6:00 15.37 13/01/2015 6:30 15.33 13/01/2015 7:00 15.00 13/01/2015 7:30 15.05 13/01/2015 8:00 15.19 13/01/2015 8:30 15.61 13/01/2015 9:00 16.65 13/01/2015 9:30 16.71 13/01/2015 10:00 15.75 13/01/2015 10:30 15.79 13/01/2015 11:00 15.91 13/01/2015 11:30 15.84 13/01/2015 12:00 15.80 13/01/2015 12:30 16.49 13/01/2015 13:00 16.24 13/01/2015 13:30 15.99 13/01/2015 14:00 16.40 13/01/2015 14:30 16.22 13/01/2015 15:00 15.90 13/01/2015 15:30 16.33 13/01/2015 16:00 16.37 13/01/2015 16:30 15.81 13/01/2015 17:00 15.80 13/01/2015 17:30 15.59 13/01/2015 18:00 15.56 13/01/2015 18:30 15.58 13/01/2015 19:00 15.64 13/01/2015 19:30 15.33 13/01/2015 20:00 15.31 13/01/2015 20:30 15.33 13/01/2015 21:00 15.32 13/01/2015 21:30 15.24 13/01/2015 22:00 15.22 13/01/2015 22:30 15.05 13/01/2015 23:00 15.31 13/01/2015 23:30 15.56 14/01/2015 0:00 15.60 14/01/2015 0:30 15.50 14/01/2015 1:00 15.41 14/01/2015 1:30 15.46 14/01/2015 2:00 15.61 14/01/2015 2:30 15.32 14/01/2015 3:00 15.29 14/01/2015 3:30 15.81 14/01/2015 4:00 15.65 14/01/2015 4:30 15.68 14/01/2015 5:00 15.54 14/01/2015 5:30 15.47 14/01/2015 6:00 16.46 14/01/2015 6:30 16.22 14/01/2015 7:00 16.40 14/01/2015 7:30 15.96 14/01/2015 8:00 15.72 14/01/2015 8:30 16.38 14/01/2015 9:00 15.51 14/01/2015 9:30 16.43 14/01/2015 10:00 15.85 14/01/2015 10:30 16.48 14/01/2015 11:00 16.53 14/01/2015 11:30 16.31 14/01/2015 12:00 16.53 14/01/2015 12:30 16.01 14/01/2015 13:00 16.25 14/01/2015 13:30 16.55 14/01/2015 14:00 16.64 14/01/2015 14:30 16.64 14/01/2015 15:00 16.47 14/01/2015 15:30 16.67 14/01/2015 16:00 16.09 14/01/2015 16:30 16.42 14/01/2015 17:00 16.35 14/01/2015 17:30 16.31 14/01/2015 18:00 16.79 14/01/2015 18:30 16.51 14/01/2015 19:00 16.50 14/01/2015 19:30 15.89 14/01/2015 20:00 16.28 14/01/2015 20:30 15.61 14/01/2015 21:00 16.41 14/01/2015 21:30 16.45 14/01/2015 22:00 15.71 14/01/2015 22:30 15.39 14/01/2015 23:00 15.33 14/01/2015 23:30 15.58 15/01/2015 0:00 15.31 15/01/2015 0:30 15.88 15/01/2015 1:00 15.32 15/01/2015 1:30 15.03 15/01/2015 2:00 15.51 15/01/2015 2:30 15.22 15/01/2015 3:00 15.32 15/01/2015 3:30 16.32 15/01/2015 4:00 16.24 15/01/2015 4:30 15.73 15/01/2015 5:00 16.27 15/01/2015 5:30 16.50 15/01/2015 6:00 15.86 15/01/2015 6:30 15.26 15/01/2015 7:00 15.46 15/01/2015 7:30 15.65 15/01/2015 8:00 15.18 15/01/2015 8:30 15.18 15/01/2015 9:00 16.36 15/01/2015 9:30 1570 15/01/2015 10:00 15.62 15/01/2015 10:30 16.24 15/01/2015 11:00 16.68 15/01/2015 11:30 15.86 15/01/2015 12:00 16.47 15/01/2015 12:30 16.52 15/01/2015 13:00 16.09 15/01/2015 13:30 16.60 15/01/2015 14:00 16.64 15/01/2015 14:30 16.33 15/01/2015 15:00 16.82 15/01/2015 15:30 16.43 15/01/2015 16:00 16.65 15/01/2015 16:30 15.75 15/01/2015 17:00 15.97 15/01/2015 17:30 16.08 15/01/2015 18:00 15.93 15/01/2015 18:30 16.00 15/01/2015 19:00 16.27 15/01/2015 19:30 15.82 15/01/2015 20:00 15.53 15/01/2015 20:30 15.47 15/01/2015 21:00 15.35 15/01/2015 21:30 15.23 15/01/2015 22:00 15.32 15/01/2015 22:30 14.73 15/01/2015 23:00 15.64 15/01/2015 23:30 15.37 16/01/2015 0:00 15.65 16/01/2015 0:30 15.96 16/01/2015 1:00 15.33 16/01/2015 1:30 15.30 16/01/2015 2:00 15.66 16/01/2015 2:30 15.62 16/01/2015 3:00 15.64 16/01/2015 3:30 15.62 16/01/2015 4:00 15.43 16/01/2015 4:30 15.92 16/01/2015 5:00 15.52 16/01/2015 5:30 15.28 16/01/2015 6:00 15.65 16/01/2015 6:30 16.39 16/01/2015 7:00 15.73 16/01/2015 7:30 16.67 16/01/2015 8:00 16.32 16/01/2015 8:30 16.64 16/01/2015 9:00 15.39 16/01/2015 9:30 16.22 16/01/2015 10:00 15.75 16/01/2015 10:30 15.79 16/01/2015 11:00 16.58 16/01/2015 11:30 16.25 16/01/2015 12:00 16.38 16/01/2015 12:30 16.44 16/01/2015 13:00 16.42 16/01/2015 13:30 16.68 16/01/2015 14:00 16.57 16/01/2015 14:30 16.78 16/01/2015 15:00 16.44 16/01/2015 15:30 16.63 16/01/2015 16:00 16.60 16/01/2015 16:30 16.15 16/01/2015 17:00 16.31 16/01/2015 17:30 16.51 16/01/2015 18:00 16.09 16/01/2015 18:30 16.40 16/01/2015 19:00 16.72 16/01/2015 19:30 16.31 16/01/2015 20:00 15.74 16/01/2015 20:30 15.77 16/01/2015 21:00 15.63 16/01/2015 21:30 16.40 16/01/2015 22:00 15.66 16/01/2015 22:30 15.44 16/01/2015 23:00 15.89 16/01/2015 23:30 15.03 17/01/2015 0:00 15.78 17/01/2015 0:30 15.32 17/01/2015 1:00 15.43 17/01/2015 1:30 15.67 17/01/2015 2:00 15.18 17/01/2015 2:30 15.16 17/01/2015 3:00 15.81 17/01/2015 3:30 15.73 17/01/2015 4:00 15.57 17/01/2015 4:30 15.76 17/01/2015 5:00 15.12 17/01/2015 5:30 15.70 17/01/2015 6:00 16.27 17/01/2015 6:30 16.27 17/01/2015 7:00 15.74 17/01/2015 7:30 16.10 17/01/2015 8:00 15.64 17/01/2015 8:30 16.46 17/01/2015 9:00 15.51 17/01/2015 9:30 15.78 17/01/2015 10:00 16.67 17/01/2015 10:30 15.86 17/01/2015 11:00 16.16 17/01/2015 11:30 16.21 17/01/2015 12:00 16.59 17/01/2015 12:30 16.31 17/01/2015 13:00 16.18 17/01/2015 13:30 16.65 17/01/2015 14:00 16.31 17/01/2015 14:30 16.48 17/01/2015 15:00 16.42 17/01/2015 15:30 16.43 17/01/2015 16:00 16.93 17/01/2015 16:30 16.51 17/01/2015 17:00 16.42 17/01/2015 17:30 16.34 17/01/2015 18:00 16.68 17/01/2015 18:30 16.67 17/01/2015 19:00 16.84 17/01/2015 19:30 16.66 17/01/2015 20:00 15.66 17/01/2015 20:30 15.75 17/01/2015 21:00 16.36 17/01/2015 21:30 16.45 17/01/2015 22:00 16.21 17/01/2015 22:30 15.55 17/01/2015 23:00 15.32 17/01/2015 23:30 15.78 18/01/2015 0:00 15.95 18/01/2015 0:30 15.82 18/01/2015 1:00 15.37 18/01/2015 1:30 15.33 18/01/2015 2:00 15.66 18/01/2015 2:30 15.01 18/01/2015 3:00 15.52 18/01/2015 3:30 16.06 18/01/2015 4:00 15.35 18/01/2015 4:30 15.46 18/01/2015 5:00 16.17 18/01/2015 5:30 15.95 18/01/2015 6:00 15.46 18/01/2015 6:30 16.31 18/01/2015 7:00 16.28 18/01/2015 7:30 15.90 18/01/2015 8:00 15.58 18/01/2015 8:30 16.37 18/01/2015 9:00 15.51 18/01/2015 9:30 15.79 18/01/2015 10:00 16.41 18/01/2015 10:30 15.79 18/01/2015 11:00 16.61 18/01/2015 11:30 16.04 18/01/2015 12:00 16.11 18/01/2015 12:30 16.54 18/01/2015 13:00 16.11 18/01/2015 13:30 16.56 18/01/2015 14:00 16.67 18/01/2015 14:30 16.26 18/01/2015 15:00 16.44 18/01/2015 15:30 16.43 18/01/2015 16:00 16.58 18/01/2015 16:30 16.45 18/01/2015 17:00 16.11 18/01/2015 17:30 16.83 18/01/2015 18:00 16.49 18/01/2015 18:30 16.35 18/01/2015 19:00 16.23 18/01/2015 19:30 15.96 18/01/2015 20:00 15.64 18/01/2015 20:30 16.45 18/01/2015 21:00 16.16 18/01/2015 21:30 16.32 18/01/2015 22:00 16.24 18/01/2015 22:30 15.62 18/01/2015 23:00 15.30 18/01/2015 23:30 15.33 19/01/2015 0:00 15.58 19/01/2015 0:30 15.02 19/01/2015 1:00 15.06 19/01/2015 1:30 15.47 19/01/2015 2:00 15.86 19/01/2015 2:30 15.76 19/01/2015 3:00 15.70 19/01/2015 3:30 15.51 19/01/2015 4:00 16.35 19/01/2015 4:30 16.38 19/01/2015 5:00 16.39 19/01/2015 5:30 16.35 19/01/2015 6:00 15.75 19/01/2015 6:30 15.51 19/01/2015 7:00 15.56 19/01/2015 7:30 15.91 19/01/2015 8:00 15.84 19/01/2015 8:30 15.35 19/01/2015 9:00 15.64 19/01/2015 9:30 15.57 19/01/2015 10:00 15.47 19/01/2015 10:30 16.46 19/01/2015 11:00 16.57 19/01/2015 11:30 16.60 19/01/2015 12:00 16.07 19/01/2015 12:30 16.64 19/01/2015 13:00 16.55 19/01/2015 13:30 16.67 19/01/2015 14:00 16.03 19/01/2015 14:30 16.58 19/01/2015 15:00 16.23 19/01/2015 15:30 16.42 19/01/2015 16:00 17.21 19/01/2015 16:30 17.19 19/01/2015 17:00 15.89 19/01/2015 17:30 15.97 19/01/2015 18:00 15.94 19/01/2015 18:30 16.27 19/01/2015 19:00 16.34 19/01/2015 19:30 16.20 19/01/2015 20:00 16.26 19/01/2015 20:30 15.80 19/01/2015 21:00 15.62 19/01/2015 21:30 15.83 19/01/2015 22:00 15.33 19/01/2015 22:30 15.16 19/01/2015 23:00 16.36 19/01/2015 23:30 15.70