Ramjanam Singh

As per the given conditions, I would recommend using Standardized Individual Moving Range (Z-MR) control chart. An individual I-MR control chart is preferred when observing a single unique data which is not a collected on a continuous measurement in a data subgroup. This basically used for monitoring the process variability and average when the data sample is collected measuring each unit at timely intervals from a process. An I-chart depicts and measure the process mean. This may not be useful in the given case. Mainly used to check the assignable causes to highlight as a reason for process getting out of control To observe the process performance pre and post solution implementation To observe the production rate is very slow and waiting time is high for collecting more samples Commonly used in batch run processes Standardized Individual Moving Range (Z-MR) is preferred and perfectly suited for this scenario. Z-MR chart is basically used in a short run process to observe the process variations and mean of different parts when sample size is limited. When single machine or process is used to produce various products. The generic method is to assume that each product in the process has its own special average and standard deviation. If the standard deviation and average is obtained, therefore process can be standardized with the help of mean dividing by standard deviation. Z-MR chart depicts by plotting the standard individual observation [Z] and moving ranges to observe samples from the various production on a single control chart. In the given case Dominos makes different product on random basis and delivery locations are varied, each run is short. Z values are plotted over time, and each product has its own average and standard deviations. And moving range chart observes the variations between z values which are consecutive.

Linear Regression: Benefits: Linear regression model works well with all types of dataset sizes Provides information with respect to the relevance of characteristics Simple implementation and easy to interpret Easily interpreted the results Unfitting can be managed by regularisation Linear Regression: Challenges: Volatile to under fitting Outliers have significant impact Linear Borderlines Assumptions for data independence Non-Linear Regression: Benefits: Very complex model but gives very accurate results compare to liner model Analysis produces a curve for showcasing the connections between variables This model provides great adaptability to cater larger scenarios Very good applicability for AI, ML and wide range of industries Provides the best flexi curve fitted model Non-Linear Regression: Challenges: Very complex and difficult to implement Less flexible Very time consuming while selecting the best fit model for the curve shape Randomly data is saved in the history Multiple data layers are involved, highly complex Difficult to calculate P value Selection Criteria: The general principles is to use the linear regression initially to establish curve fitment with the available data set. Only when we are unable to achieve the fitting model with liner regression then we need to consider other non-linear regression models. Commonly linear regression is simple to use, interpret and achieve more statistics to help study the model. Best applicable when the relationship between dependent and independent variable. Non-linear regression fitment is wide in nature and fit major type of curves. Best used for practical applications for providing solution to the real-world challenges.

A multi-vari chart depicts the focuses on the relations between response and factor, this typically shows the variance data analysis in graph manner, majorly during the initial stages of the data observation, relations, and possible root cases of the data variance. This graph basically analyses the process stability. Multi-Vari chart is mainly used in services and manufacturing sectors. There are two types of multi-vari chart study: Passive Nested observed without changing the routine of the process, whereas manipulated crossed observation is oriented towards intentional process changes for observation. This is basically a method of analysing the multivariate in statistical way to stimulate and observe the data, each individual data group is analysed on multiple variables and parameters. Multi-Vari analysis focuses on logical subgrouping of the data set to analyse effects on continuous Y’s of category X’s. This can be measured with nested analysis of variance. Multi-Vari analysis is consist of tow or more dependent components Y1,Y2 together taken for independent variable X1,X2, so on. This can be used in very structured way to study and implement in statistical control. Helps in finding the causes of process variation and quantify them. Within shift, Operator to operator, Within operator, shift to shift, between the shifts etc.. This can be used in six sigma projects to analyse the VOC, Brainstorming, 5S systems, Kaizen, process benchmarking, Poka-Yoke and VSM etc. With this graph we we can interpret the variation by studying pattern of lines and circles, at every variation within each line item, also between cyclical variations. This help in analysing the effect of various category groups input on a continuous output.

The histogram of a data depicts the frequency of results for every number possible, by observing the graph, we will notice that there is a normal distribution. Median, mean, and mode of a data inputs will be equal. Histogram helps to understand the centre of the data set. Also, helps in learning the ratios of overlap in various groups. Histograms are best to study the shape of the distributed data set. It shows which values are common with their spread. We can obtain the statistic with the knowledge of mean and standard deviation. Shape of distribution signifies the quantitative data in a logical sequence, value and low to high order value. The shape of data will depict the patterns which is a produced when data values are plotted in Histogram. Further, Histogram images will show whether the data is Symmetric, skewer, uniform, uni-modal or bimodal distributed. While deciding the number of bins, when we take the square root of the data set and roundup, we calculate the bin width and divide with specification tolerance by the number of bins. So, if we take too many bins, then the data points distributions will give an unclear visual, thus becomes very difficult to interpret the right information from the data set. The most significance criteria of a histogram bin is width, because it controls the information exchange among produced scenarios, either very simple and under information or overly complicated.

The Exponentially Weighted Moving Average (EWMA) control chart used for observing the small changes in the process mean value. The highest weight is given to the latest observation whereas past values considered smallest. The EWMA glowingly stacked moving average graph for statistical control to measure variables to use all the outputs. This chart will identify sigma shift (0.5 – 2) quicker than other charts with same sample value. Its used mainly when the continuous values are available for the life cycle of the process. Difference between EWMA vs traditional control charts: Major difference between Exponentially Weighted Moving Average control chart and other traditional control charts are, a simple moving average chart focuses on similar weight to all the values, whereas EWMA is focused on latest values not the total historical data. Also, EWMA is alert on smallest change in the process compared to trendy Xbar-R or other control charts Advantages of EWMA: Exponentially Weighted Moving Average control chart helps in exploring the variations which are regularly existed in the process. EWMA helps in detecting the potential process failure, also projects the data shifts and patterns in the process. It shows the process future performance potential and failure, very useful in statistical process control. With the help of EWMA, we can improve process quality by innovative ideas. Disadvantages of EWMA: This needed a lot of historical data maintenance for various times and every projected period Mostly avoids complexity of the different variables from the data set Fluctuations in the data goes unnoticed which occurs due to some reason, e.g., special causes, or abnormality due to shift in the work environment

I-MR Individual Chart – Depicts the individual values and observes the shifts in the mean value in the process, wherein data values are gathered at periodic frequency of time. I-Chart also helps to determine the obvious causes in the process Moving Range Chart helps in observing the process variation wherein data values are gathered at periodic frequency of time. X-bar-R When sample size is >2 – 9< Xbar chart helps in study the changes in the mean value over the period. This chart is commonly used in combination with R-Chart to observe the process variation. R-Chart depicts the data range changes periodically in the sub-group. Typically, this chart study the range and process variations. R values shows the defects in measurements and illustrates the sample data range. Xbar-S when sample size is more than >10 X-bar chart depicts the process mean and changes in the process overtime. S-Chart is the scale of standard deviation in the process over period, estimated by data sample moving range.

In this business case, I would prefer to use Xbar-S chart as the sample size is more than >10. And data is collected at different times. This chart will help in study the process variation. Generally, this control chart is used to study the standard deviation and process mean. S chart depicts width of sub-group data. As we know, standard deviation is a good scale of variation over range because here entire data is considered, not only the lowest and highest values. Xbar-S chart will be used here to measure the process stability. Hourly Sample Shift 1 Shift 2 Shift 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Total 8 8 8 Grand Total 24 After computing the X bard and S values, we shall determine the control limits. First sub-group will be used to determine the process mean and standard deviation. Then, after plotting the X Bar and S chart, with the help of result values, we will plat the Sigma and X bar charts. This graph will show the statistical process stability and control limits.

Job Breakdown Sheet is a method to break down the large or complex task into small steps in a process flow chart manner to make it easy to understand and achieve. With this sheet we can identify and what needs to be done, how it can be accomplished and the potential benefits, or the cause of the activity. JBS is helpful in creating process flow charts and value stream mapping to simplify the process and reducing waste. While doing the lean six sigma project, process flow chart is one of the quality tool which is used in almost all the DMAIC project to breakdown the process to understand the flow. Performing JBS is very time consuming task, involves iterations and multiple reviews to finalise. There can be biased, and data is very limited to validate JBS. Also, it is a costly exercise.

A process with higher maturity provides lesser opportunities for DMAIC. Why? A mature process has gone through majority of changes, and eliminated waste, variation with standard operating procedures in place, well managed. DMAIC is very useful or focused on removing or minimizing the process variation. Therefore, a mature process will be statically well controlled. I would agree to the statement of “A highly matured process will limit the usage of DMAIC, as there will be marginal scope of improvement.

Overall equipment effectiveness (OEE) is a term used to evaluate how efficiently a manufacturer's operation is being used. In other words, overall equipment effectiveness helps us in notice a problem in our operations, identify which percentage of manufacturing time is productive and fix it while giving us a standardized gauge for tracking progress. The goal for measuring our OEE is continuous improvement. By optimising OEE, we can increase capacity, reduce costs, improve quality, and/or increase efficiencies in our production lines. OEE stands for “Overall Equipment Effectiveness”. In short, OEE is a key performance indicator (KPI) that compares our equipment’s ideal performance to its real performance. It is a quantifiable (i.e., uses numbers) way to find out how well our equipment, people, and processes do their job by measuring: available time/uptime (availability) maintaining speed and consistency (performance) producing few defects (quality) OEE uses productivity data to find the percentage of good production time on an asset. That means that each piece of equipment gets its own OEE score. Takt time is the rate at which we need to complete a product in order to meet customer demand. Takt Time = (Available Working Time Per Day)/Customer Demand Per Day While scoring each machine may sound putzy, it is worth the effort. OEE measures the machine’s productivity, yes. But it also takes into account the humans that run them. We know that machines aren’t always the problem. Staff and processes are just as likely to lower productivity.