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Vishwadeep Khatri
Message added by Mayank Gupta,

Z-MR (Standardized Individual Moving Range) is a control chart that is used to monitor the stability of process where relatively few parts are made in each batch (typically known as a short run process). The Z-MR chart plots the standardized individual observations (z) and moving ranges so that one can evaluate data from different batches on a single control chart. Generally it standardizes the data by subtracting the average from the data point and dividing the result by the standard deviation.


An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Khalandar S on 21st May 2023.


Applause for all the respondents - Khalandar S, Arvind Swarup, Ramjanam Singh, Sanjay Bhure, Raghavendra Rao Althar.


Q 566. Domino's promises delivery of pizza within 20 minutes. It is tracking the delivery time of each order to check the stability of the process. Each order is different with respect to items ordered, delivery location etc. The team has suggested to use either the Individual Moving Range (I-MR) or Z-MR (Standardized Individual Moving Range) control chart. Which control chart is more suitable here given that each order is different from the previous one? Why do you think it is more suitable?


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For tracking the delivery time of each order in Domino's, it is recommended to use Z MR chart to check the process stability. For better Understanding, let’s have a quick look on the I MR & Z MR charts.


 I MR Chart:

When you have Single run process (Ex: Mass Production, High Volume - Low Mix Manufacturing process etc.)

When you have good amount of data and more than 25 Data points

Its suitable for long run process

 Z MR Chart:

When you have different runs in a Process (Ex: Batch production, E Commerce, Telecom Service, High Mix & low Volume etc.,)'

It is used for short run processes (Each run has its own process paraments - Process Mean & Standard deviation)

When you have limited data (Short run processes do not have good amount of data for the good estimation of Process parameters)

Like I_MR chart, Z_MR chart has 2 charts, namely Z chart & MR Chart.


In Z Chart, the distribution consists of Observation in X Axis & Standardized Individual Observations (Z values) in Y Axis (Standardized "Z' is nothing but the Z value of each run & the formula of Z = (X  - X bar)/ Std Deviation of each run). The above calculation leads to Z distribution, plots over Process mean (X bar=0) and Process standard deviation (Sigma=1)


On other hand, MR Chart consists Observation data points on X axis and Moving range of Z values on Y Axis. It monitors the variation between consecutive Standardized Individual Observations (Z Values) of the process which has different runs.


The control limits of Z Chart are Straight forward. The Process mean is O & control limits are -3 & 3 


The MR chart has always had UCL = 3.686 (D4*1.128) and LCL =0 and Average Moving Average (MR)= 1.128 because data are standardized in Z chart.


To plot the Z-MR chart in Minitab, Choose - Stat - Control Charts - Variable charts for Individual - Z MR chart

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IMR chart is better because it displays observations and moving ranges for continuous data over a period while Z-MR will be used to monitor the process variation for individual units assuming that measurement scale is consistent and does not consider the disparity. Therefore, the I-MR control chart is more suitable in this case as it allows for the monitoring of individual delivery times, accommodating the variability between different orders.

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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.

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As each order is different with respect to items ordered, delivery location etc. We have two options


1. Create different Individual Moving Range (I-MR) control charts as per item ordered or delivery location. But then we will have too many charts to analyze.

2. Second option is to use one Z-MR (Standardized Individual Moving Range) control chart.


In Z-MR (Standardized Individual Moving Range) control chart, we calculate the z value of each data and plot control chart using z value. The z value can be calculated using formula


z = (x – xbar) / σ


where x = individual data value; xbar = average of all data values; σ = standard deviation of data


We also calculate Moving Range (MR) of each data and plot control chart using MR value.


Z-MR Control chart is useful when every observed or measured data have different conditions which affect the data value.

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Z-MR charts or short run charts, are useful proposition in case of dynamic product groups that has wide variety of products with short production volumes. This version of control chart helps in situations where there are customized solutioning given to the customers. From operations wise this mode of delivery reduces the need of inventory and improves response to customers, but in terms of monitoring the process it will be complex situation. Since the variations is involved in the scope of delivery of the pizzas in terms of each order being different from each other with respect to items ordered, delivery location and so on. This situation needs Z-MR chart, as it accounts all the sub-group of the data point. Z value computation is generalized way of computing the process stability irrespective of the unit of measure. Since the sub-group vary from each other, this generalized approach for assessment helps. Z-MR chart normalizes the data by subtracting the mean value from the data and dividing it with standard deviation so that the data points get centered with common reference to assess from. This helps to have common platform to assess the data coming from various sub-group on common control charts. Other type of control charts will not utilize the variations of all the sub-groups.

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This was a very tricky one. Good to read the viewpoints of the respondents.


While I-MR chart is a universal control chart and can be used in all possible situations. Hence, it can be used in this situation as well. However, for the specific situation given a Z-MR control chart is a better control chart since no two deliveries are same and hence can be considered a short run process. Therefore it is better to standardize the values and use a Z-MR chart.


Winning answer has been given by Khalandar S. Well done!

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