A Durability Model for Analysis of Switching Direct Current Surge Degradation of Metal Oxide Varistors

Abstract

In this study, a durability model for predicting the lifetime of MOV devices used to prevent DC switch damage due to occasional switching surges is proposed and validated. In addition, MOV devices are subjected to induced switching DC surges of a constant amplitude and variable time durations. Each MOV of the 270 selected devices sourced from three different manufacturers with similar size and electrical specifications was subjected to 5000 degrading surges. Three samples of 30 of the selected MOV devices from each manufacturer were degraded by induced switching DC surge durations of 2, 3, and 4 ms in order to reach an undesirable degradation level of 10% change in V_{1 mA}. A statistical analysis of the three MOV manufacturer sample averages of the accumulated conduction charge transfer at 10% change in V_{1 mA} supported the proposed durability model irrespective of the surge charge content variation and MOV material differences. The results show that MOV device durability or resilience may be more accurately modelled by using the surge average accumulated conduction charge transfer of a statistically significant MOV device sample.

1. Introduction

1.1. Background Theory

The interruption of direct current (DC) flow can be achieved by the use of a mechanical contactor, circuit breaker, electronic solid-state switch or a hybrid DC switch that consists of a solid-state and mechanical combination type switch [1,2,3,4]. There is no zero-current crossing in DC systems, which can allow natural commutation or circuit interruption when no current flows [2,3]. When circuit switch contacts open, the dissipation of energy stored in DC line inductance is a considerable challenge to the lifetime performance of a DC switch [1,2,3]. According to several studies, the residual energy stored in the DC line inductance is the cause of harmful arc discharges or induced switching DC surges when opening the circuit break contacts [1,4]. To mitigate or quench arc discharges by clamping induced switching DC surges, one technique is to connect in parallel a metal oxide varistor (MOV) across the circuit switch. For this type of application, when the DC switch is closed, the voltage across the parallel-connected MOV is near zero and only when the switch is opened will the device experience a switching surge. The parallel connection of MOV devices has proven to be more technically viable in larger DC circuit installations compared to using freewheeling protection diodes that are connected across the entire DC line inductance to prevent harmful switching surges [5,6]. The MOV device consists of a sintered ceramic semiconductor block mostly formed of zinc oxide (ZnO) grains that have inter-granular regions. Several other oxide additives are usually part of the MOV device microstructure, in order to optimize the V-I response and energy-absorbing capability over that of a single-diode P-N junction [6,7]. The MOV device clamps and diverts induced switching DC surges by transferring accumulated charge away from the circuit opening switch and any absorbed MOV surge energy is subsequently dissipation to ambiance in the form of heat [8,9]. The industrial demand for using MOV devices is fundamentally due to the excellent technical qualities of the nonlinear V-I response, fast time response in nanoseconds and higher energy handling or absorption capability [3]. The nonlinear MOV device V-I characteristic curve is due to the many grain boundary micro-scale Schottky barrier accumulated behavior, which acts like a random connected circuit of back-to-back zener diodes [7].

1.2. Problem Definition

To ensure the effective performance of DC switches, the surge protecting MOV device is expected not to fail before the switch anticipated lifetime operation [2]. The opening of DC switch contacts in installation applications usually occurs occasionally and therefore, there is time for any absorbed surge energy by the MOV device material to dissipate in the form of heat to ambience [1]. Therefore, the MOV device will not be degraded by higher temperatures occurring due to multiple surges with very short time delay intervals between surge events [10]. However, the occasionally induced switching DC surges will degrade the protecting MOV device material as time progresses and, thereby, reduce its energy absorption capability [5,7].

When a constant DC current of 1 mA passes through the MOV material, the voltage drop across the device is referred to as V_{1 mA} [10,11]. Changes in the measured V_{1 mA} indicate MOV material ageing and can be used as a precursor to detect the irreversible degradation level damage [12,13]. Accordingly, the degradation level of the MOV material is assessed at room temperature by determining the percentage change in V_{1 mA} from the initial V_{1 mA} value [14]. For both the IEC and IEEE impulse withstand tests, a percentage change in V_{1 mA} greater than 5% is considered as an indication of MOV device failure [13,15,16]. However, when degraded by repeated occasional switching DC surges, the V_{1 mA} of the MOV initially changes rapidly, thereby quickly reaching a 5% change, and then takes a much longer time to reach a 10% change in V_{1 mA} [5]. This constitutes the basis of why it is more widely accepted that if the MOV measured V_{1 mA} changes from its initial value by more than 10%, the MOV device material has reached an unacceptable degradation level [7]. Therefore, for this specific type of MOV energy handling capability (EHC), a 10% change in V_{1 mA} will indicate that the device should no longer be considered technically viable as a parallel DC switch protection device.

The available literature suggests that MOV device durability or resilience under induced occasional switching DC surge degradation, is not well understood [2]. The surge average accumulated conduction charge transfer that causes a 10% change in V_{1 mA} for each MOV of a statistically significant sample is proposed as a more accurate and useful durability model to estimate device resilience for this specific type of degradation. In addition, a major advantage will be to verify that this proposed durability model for occasional switching DC surge degradation is consistent across different types of manufacturer MOV material microstructures that have similar size and electrical specifications. Our aim is to validate a durability model that more accurately estimates MOV resilience to switching DC surges with delay intervals between surge events for sufficient thermal recovery.

2. Methodology

To demonstrate that the proposed durability model is an effective estimation for this specific type of degradation, the application of different induced switching DC surge charge content sizes should not significantly change the average accumulated conduction charge transfer that caused a 10% change in V_{1 mA}. If separated statistically significant MOV samples are subjected to different switching DC surge charge content sizes, the durability model value of the samples should deviate from each other as would be expected to happen simply from variation due to random device sampling. According to IEEE standard C62.33, a statistically significant sample of at least 30 MOV devices is required in order to obtain valid electrical component characteristics [17]. This is because during production process, the MOV is manufactured from a non-homogeneous material that results in high non-uniformity of ZnO grains, which leads to varying power internal dissipation and current distribution in the device [18,19]. To verify the proposed durability model as significant, three samples of 30 MOV devices were occasionally subjected to different repeated switching DC surge charge content sizes, to avoid thermal degradation. If the determined average of the accumulated conduction charge transfer of each sample at 10% change in V_{1 mA} is statistically equivalent, it can then be considered as an effective model for this type of EHC degradation. This should verify that when the determined durability model value is reached, it will result in a similar unacceptable degradation level even if the charge content per switching DC surge varies. The verification method will also be applied to three different manufacturers with similar MOV device specification ratings, in order to determine if this proposed durability model could be considered as an effective durability model estimation across different manufacturers MOV designs. The research method flowchart used to determine the MOV device accumulated conduction charge transfer that causes a 10% change in V_{1 mA}, is shown in Figure 1.

The MOV measured voltages corresponding to a $10\mathsf{\mu }\mathrm{A}$, $100\mathsf{\mu }\mathrm{A}$, $1\mathrm{mA}$, and $10\mathrm{mA}$ constant current flows at room temperature was recorded. These reference voltages that are expressed as V_{10 µA}, V_{100 µA}, V_{1 mA}, and V_{10 mA} are used to track the percentage change in V_{1 mA} including the non-linear coefficient (α) and characteristic V-I curve shift to verify when a 10% change in V_{1 mA} is exceeded in order to obtain the accumulated conduction charge transfer. Reference [5] provides the characteristics and results of these average measured data per sample. The percentage change in V_{1 mA} after each induced switching DC surge across the MOV device is determined by the following equation:

$$\%\Delta {\mathrm{V}}_{1\mathrm{mA}}=\left({\mathrm{iniV}}_{1\mathrm{mA}}-{\mathrm{curV}}_{1\mathrm{mA}}/{\mathrm{iniV}}_{1\mathrm{mA}}\right)\times 100$$

(1)

where %ΔV_{1 mA} is the percentage change in V_{1 mA} after an induced switching DC surge, iniV_{1 mA} is the initial V_{1 mA} before any applied switching DC surges, and curV_{1 mA} is the recent or current V_{1 mA} measurement after an induced switching DC surge application. The change in the non-linear coefficient (α) after each induced switching DC surge across a MOV device is calculated by using the following equation:

$$\mathsf{\alpha }=\frac{1}{{\mathrm{logV}}_{1\mathrm{mA}}-{\mathrm{logV}}_{100\mathsf{\mu }\mathrm{A}}}$$

(2)

where α is the non-linear coefficient with V_{100 µA} and V_{1 mA} measured after an induced switching DC surge. The obtained α represents the steepness or non-linearity of the MOV characteristic V-I curve that is between $100\mathsf{\mu }\mathrm{A}$ and $1\mathrm{mA}$, which becomes more steep or linear as the device degrades [5]. Typical values of non-linear coefficient for new MOV devices are between 20 and 30, and a value of α lower than 20 is considered an indication of device material degradation failure [7,11,20]. Therefore, a non-linear coefficient value of less than 20 is used for the purpose of verifying an unacceptable MOV device material degradation level at 10% change in V_{1 mA}.

The reference voltages obtained after each switching DC surge are used to check the percentage change in V_{1 mA} as well as the change in the α value. By gradually degrading the MOV device, the recorded reference voltages are used to closely detect when an unacceptable 10% change in V_{1 mA} has just been exceeded. Both V_{10 µA} and V_{100 µA} are related to reference points within the leakage current region, whereas both V_{1 mA} and V_{10 mA} are related to reference points within the conduction current region of the MOV device V-I curve. As the MOV is degraded by occasional induced switching DC surges, the leakage current region resistance decreases and conduction current region resistance increases, which reveals that leakage current and conduction current paths are different throughout the device material [5]. Therefore, the device V-I curve shift from the initially recorded V_{10 µA}, V_{100 µA}, V_{1 mA} and V_{10 mA} to the values measured when 10% change in V_{1 mA} has just been exceeded is also used to confirm an unacceptable degradation level.

Two independent temperature sensors are used to measure the MOV surface and the room temperature to verify that the device temperature is not rising after the application of each induced switching DC surge. Experimentally, a time delay interval was determined and inserted between generated induced switching surges to avoid device thermal degradation, as required for this specific type of EHC degradation. It was experimentally established that 5000 switching DC surges will ensure the degradation of the three selected manufacturer MOV devices, beyond a 10% change in V_{1 mA}.

Subsequent to each induced surge event, the MOV charge transfers resulting from the applied switching DC surge, including V_{1 mA} and V_{10 mA} conduction charge measurements, were determined and then added together. According to the IEEE C62.11 [16], a switching DC surge current consists of a rectangular-type wave shape that has a relatively constant current magnitude over its entire event duration. Therefore, the switching DC surge charge content consists of the peak average measured surge current multiplied by the surge event duration [10]. This type of long energy surge duration injection is considered a close approximation to typical MOV device stress experienced during an actual switching DC surge event. The IEEE C62.11 standard [16] specifies that energy ratings are estimated to be valid within a range of 2 to 3.2 ms because of the failure probability in this time range due to established general technical knowledge. However, switching DC current surges with rectangular durations from 2 to 4 ms were carried out on MOV device test samples by the IEEE C62.11 standard. Therefore, switching DC surge durations for the three samples of each selected manufacturer that will be compared are 2, 3 and 4 ms, respectively. The MOV device is in the conduction region of the V-I characteristic curve when a switching DC surge is applied including when V_{1 mA} and V_{10 mA} measurements are carried out. Therefore, the charge transferred in the conduction region can be determined as follows:

$${\mathrm{Q}}_{\mathrm{MOV}}{=(\mathrm{I}}_{\mathrm{SURGE}}{\times \mathrm{t}}_{\mathrm{SURGE}})+\left[\left(1\mathrm{mA}+10\mathrm{mA}\right)\times 200\mathrm{ms}\right]$$

(3)

where ${\mathrm{Q}}_{\mathrm{MOV}}$ is the MOV device conduction charge transfer after the application of an induced switching DC surge including the carried-out measurements of V_{1 mA} and V_{10 mA}. The ${\mathrm{I}}_{\mathrm{SURGE}}$ is the recorded peak average measured surge current and ${\mathrm{t}}_{\mathrm{SURGE}}$ is either a 2, 3 or 4 ms surge event duration. The conduction charge transferred content of V_{1 mA} and V_{10 mA} measurements is determined by multiplying 1 mA and 10 mA constant currents by the fixed measurement duration of 200 ms.

A running total of the accumulated conduction charge transfer (${\mathrm{Q}}_{\mathrm{TOT}}$) can then be determined by taking the previous accumulated conduction charge transfer and adding it to the next calculated value, as expressed in the following equation:

$${\mathrm{Q}}_{\mathrm{TOT}}{=\mathrm{Q}}_{\mathrm{TOT}\_\mathrm{PRE}}{+\mathrm{Q}}_{\mathrm{MOV}}$$

(4)

where ${\mathrm{Q}}_{\mathrm{TOT}\_\mathrm{PRE}}$ is the previously accumulated conduction charge transferred and ${\mathrm{Q}}_{\mathrm{MOV}}$ is the new determined conduction charge transferred through the MOV device due to the next induced switching DC surge, including V_{1 mA} and V_{10 mA} measurements.

The average accumulated conduction charge transfer for a statistically significant sample of 30 MOV devices is then determined by averaging ${\mathrm{Q}}_{\mathrm{TOT}}$ of each MOV at 10% change in V_{1 mA}. Reference [5] describes the details of this research method, which includes the circuit used for inducing switching DC surges and the voltage reference measurement circuit that is used to find the ${\mathrm{Q}}_{\mathrm{TOT}}$ for each MOV device at 10% change in V_{1 mA}. For this reason, the focus of this study is on the acquired average ${\mathrm{Q}}_{\mathrm{TOT}}$ of the three MOV samples for each selected manufacturer, to determine by statistical analysis if the proposed durability model can be considered an effective estimation of device resilience for this specific type of EHC degradation.

3. Results and Discussion

Three leading manufacturers of MOV devices that have similar size and electrical specifications were selected and assigned to the following group identification codes: UV, WX, and YZ. These MOV devices are commercially sourced low-voltage, radial wire lead, 14 mm disk diameter types that were epoxy coated in a fluidized bed. Three statistically significant samples of 30 random MOV devices from each manufacturer were selected for this analysis. The similar electrical specification ratings of the three selected manufacturer MOV devices are shown for comparison in

Table 1. Selected manufacturer metal oxide varistor device specification rating comparison.

Specifications	UV	WX	YZ
Max VDC:	14 VDC	14 VDC	14 VDC
V1 mA:	18 V ± 10%	18 V ± 10%	18 V ± 10%
Max VC:	36 V	36 V	36 V
Max IC:	10 A	10 A	10 A
${\mathrm{i}}_{\max }$(8/20 μs):	1000 A	1000 A	1000 A
2 ms energy rating:	4.7 J	3.3 J	4 J

.

To ensure that transients are generated within the switching surge conduction region of the MOV, the induced DC voltage surge level was set at 85% of the clamping voltage’s (V_C) specified level. This also ensures that the MOV devices gradually degraded, thereby providing an adequate number of measured V_{1 mA} data that can be used to detect more precisely when an undesirable degradation level of 10% change in V_{1 mA} has been reached. The size of the surge conduction charge content applied to the three samples of each manufacturer was varied by the switching DC surge durations of either 2, 3, or 4 ms. The ${\mathrm{Q}}_{\mathrm{TOT}}$ at 10% change in V_{1 mA} of each MOV device was used to find the average accumulated conduction charge transfer ($\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$) for the 2, 3, and 4 ms switching DC surge sample sizes ($\mathrm{n}$) of 30 MOV devices, for each manufacturer using the following equation:

$$\overline{{\mathrm{Q}}_{\mathrm{TOT}}}=\frac{{{\displaystyle \sum }}^{}{\mathrm{Q}}_{\mathrm{TOT}}}{\mathrm{n}}$$

(5)

where $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ is the average of the sample and ${\mathrm{Q}}_{\mathrm{TOT}}$ is the individual accumulated conduction charge transfer of each MOV device that caused a measured 10% change in V_{1 mA} to be exceeded. The population standard deviation (σ) can then be estimated from the sample by using the following sample standard deviation (S) calculation:

$$\mathrm{S}=\sqrt{\frac{\sum {\left({\mathrm{Q}}_{\mathrm{TOT}}-\overline{{\mathrm{Q}}_{\mathrm{TOT}}}\right)}^2}{\mathrm{n}-1}}$$

(6)

where S is a measure of the determined quantitative ${\mathrm{Q}}_{\mathrm{TOT}}$ sample data spread from calculated $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ which that reveals how well the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ represents the sample data. However, the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and associated S calculation is normally only appropriate when ${\mathrm{Q}}_{\mathrm{TOT}}$ sample data do not have any outliers or its data distribution is not significantly skewed. An outlier ${\mathrm{Q}}_{\mathrm{TOT}}$ data value is atypical, surprising and numerically distant from all ${\mathrm{Q}}_{\mathrm{TOT}}$ sample data and it affects $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ measure of center and associated S calculation. Therefore, if a sample has no outliers or is not significantly skewed, the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and the associated S calculations are valid estimations that can be used by inferential statistics to deduce or infer conclusions about the MOV device population.

A more appropriate approach to describe sample ${\mathrm{Q}}_{\mathrm{TOT}}$ data distribution is to use a five-number summary and associated boxplot graph. A five-number summary divides the magnitude ordered ${\mathrm{Q}}_{\mathrm{TOT}}$ sample data into four equal quartiles of 25% each, and the boxplot is then a visual representation of this summary [21]. Boxplots are used for analyzing data distribution skewness, for comparing mean with median values, for the identification of outliers and for visually comparing statistical characteristics across a series of samples. In addition, outliers or skewed sample data have not so great an effect on quartiles including the median. The inter-quartile range ($\mathrm{IQR}$) is determined as follows:

$$\mathrm{IQR}=(\mathrm{Q}3-\mathrm{Q}1)$$

(7)

where IQR is the middle 50% data value of an ordered ${\mathrm{Q}}_{\mathrm{TOT}}$ sample data, Q1 is the first 25% quartile and Q3 is the third 25% quartile. Outliers are sometimes not obvious, but mathematically the presence of outliers can be determined. A sample ${\mathrm{Q}}_{\mathrm{TOT}}$ data value is not an outlier if it remains within the limits of the following equation [21]:

$$\mathrm{Q}1-(\mathrm{IQR}\times 1.5)\le {\mathrm{Q}}_{\mathrm{TOT}}\le \mathrm{Q}3+(\mathrm{IQR}\times 1.5)$$

(8)

The five-number summary, calculated $\mathrm{IQR}$, outlier limits, $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and associated S for the UV manufacturer 2, 3, and 4 ms switching DC surged samples are shown in

Table 2. UV five-number summary and outlier limits.

UV Statistics	2 ms_QTOT (C)	3 ms_QTOT (C)	4 ms_QTOT (C)
Minimum:	1.51	1.26	1.24
Quartile Q1:	5.29	4.94	6.65
Median:	8.39	10.19	13.12
Quartile Q3:	21.43	18.70	18.12
Maximum:	44.73	36.70	33.48
$\mathrm{IQR}=(\mathrm{Q}3-\mathrm{Q}1):$	16.15	13.76	11.47
$\mathrm{Q}1-(\mathrm{IQR}\times 1.5):$	−18.93	−15.70	−10.55
$\mathrm{Q}3+(\mathrm{IQR}\times 1.5)$:	45.65	39.35	35.32
$\mathrm{Mean}(\overline{{\mathrm{Q}}_{\mathrm{TOT}}})$:	14.81	13.76	13.68
StDev (S):	12.97	11.42	9.26

.

Side-by-side boxplots can be used to make an easier visual mathematical comparison between the three UV manufacturer samples, as shown in Figure 2. It can be observed that the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ values (marked by “×”) between samples are almost equivalent, the ${\mathrm{Q}}_{\mathrm{TOT}}$ data values are within the limits and the distributions are not significantly skewed.

The five-number summary, calculated $\mathrm{IQR}$, outlier limits, $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and associated S for the WX manufacturer 2, 3, and 4 ms switching DC surged samples are shown in

Table 3. WX five-number summary and outlier limits.

WX Statistics	2 ms_QTOT (C)	3 ms_QTOT (C)	4 ms_QTOT (C)
Minimum:	0.57	1.89	0.89
Quartile Q1:	2.73	3.35	2.36
Median:	5.62	4.24	4.29
Quartile Q3:	6.08	5.91	6.97
Maximum:	9.29	9.54	10.67
$\mathrm{IQR}=(\mathrm{Q}3-\mathrm{Q}1):$	3.35	2.56	4.61
$\mathrm{Q}1-(\mathrm{IQR}\times 1.5):$	−2.29	−0.49	−4.56
$\mathrm{Q}3+(\mathrm{IQR}\times 1.5)$:	11.11	9.76	13.89
$\mathrm{Mean}(\overline{{\mathrm{Q}}_{\mathrm{TOT}}})$:	4.87	4.60	4.92
StDev(S):	2.46	2.01	2.88

.

The side-by-side boxplots between the three WX manufacturer samples are shown in Figure 3. It can be observed that the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ values between samples are almost equivalent, ${\mathrm{Q}}_{\mathrm{TOT}}$ values are within the limits and distributions are not significantly skewed.

The five-number summary, calculated $\mathrm{IQR}$, outlier limits, $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and associated S for the YZ manufacturer 2, 3, and 4 ms switching DC surged samples are shown in

Table 4. YZ five-number summary and outlier limits.

YZ Statistics	2 ms_QTOT (C)	3 ms_QTOT (C)	4 ms_QTOT (C)
Minimum:	0.10	0.06	0.16
Quartile Q1:	1.11	1.30	1.02
Median:	2.32	2.56	3.09
Quartile Q3:	5.29	5.18	5.13
Maximum:	10.58	8.43	8.01
$\mathrm{IQR}=(\mathrm{Q}3-\mathrm{Q}1):$	4.18	3.88	4.10
$\mathrm{Q}1-(\mathrm{IQR}\times 1.5):$	−5.16	−4.53	−5.14
$\mathrm{Q}3+(\mathrm{IQR}\times 1.5)$:	11.55	11.01	11.28
$\mathrm{Mean}(\overline{{\mathrm{Q}}_{\mathrm{TOT}}})$:	3.47	3.30	3.21
StDev(S):	3.07	2.44	2.33

.

The side-by-side boxplots between the three YZ manufacturer samples are shown in Figure 4. It can be observed that the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ between samples are almost equivalent, ${\mathrm{Q}}_{\mathrm{TOT}}$ values are within the limits and distributions are not significantly skewed.

Quartiles are useful but limited because they do not take into account all the ${\mathrm{Q}}_{\mathrm{TOT}}$ data values in a sample. Therefore, the associated S is more representative of the spread because each ${\mathrm{Q}}_{\mathrm{TOT}}$ data value is taken into account. In Table 2, Table 3 and Table 4, the minimum and maximum ${\mathrm{Q}}_{\mathrm{TOT}}$ values in either the 2, 3, or 4 ms switching DC surged samples are not outside of the calculated outlier limits. Therefore, the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ value with the associated S calculation provided in the tables can be considered as a valid estimation for the selected manufacturer MOV device populations.

3.1. Confidence Intervals

The obtained $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ of a sample can be used to estimate the true population mean parameter (${\mathsf{\mu }}_{\mathrm{QTOT}}$). A sample is only a small selection of MOV devices and, therefore, it can never be a perfect representation of the larger MOV device population. Therefore, different samples from the same population will yield different $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ results because of variations due to random MOV device sampling. For this reason, the required amount of certainty or level of confidence (LOC) is frequently set to 95% and it is used to estimate a population parameter. Therefore, the amount of accepted uncertainty or level of significance (LOS) will be 5%, as expressed by the following equation:

$$\mathrm{LOS}=(1-\mathrm{LOC})$$

(9)

An estimate of a population parameter should always be expressed as a confidence interval range to communicate how accurate the estimate is likely to be. Therefore, 95% LOC is the range where the actual true population parameter lies within this interval. More accurately, the confidence interval range covers 95% of all possible means that can be obtained from multiple samples of the same MOV device population. Any calculated sample mean that is then outside of the 95% confidence interval range occurs less than or equal to 5% of the time. Therefore, the associated statistical p-value will be less than or equal to 0.05 or 5%, and it is then considered to be a significant result. The width of the confidence interval range is affected by the actual variation in the population, the selected sample size, and stated LOC. Large sample sizes of 30 or more are similar to each other because the effects of a few unusual outlier data values are evened out by the other sample values.

By using one sample and knowledge about the central limit theorem, the parameters of a sampling distribution can be determined in order to calculate the confidence interval range limits or even conduct a hypothesis test [22]. The sampling distribution of the mean statistic ($\stackrel{-}{\mathrm{X}}$) for a given $\mathrm{n}$ is the distribution of all possible calculated sample means that can be obtained from multiple samples of the same population. According to the central limit theorem, the sampling distribution parameter mean (${\mathsf{\mu }}_{\stackrel{-}{\mathrm{X}}}$) is equal to the true population mean (μ) and its standard deviation (${\mathsf{\sigma }}_{\stackrel{-}{\mathrm{X}}}$) is equal to the population standard deviation ($\mathsf{\sigma }$) divided by the square root of the sample size. However, rarely is enough known about a given population to determine its actual parameter values. Therefore, the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and the associated $\mathrm{S}$ calculation of a sample without outlier ${\mathrm{Q}}_{\mathrm{TOT}}$ data can then be used as an estimate of the population mean ($\mathsf{\mu }$) and standard deviation ($\mathsf{\sigma }).$ Therefore, the sampling distribution standard deviation is then estimated to be:

$${\mathrm{S}}_{\overline{\mathrm{x}}}=\mathrm{S}/\sqrt{\mathrm{n}}$$

(10)

where ${\mathrm{S}}_{\stackrel{-}{\mathrm{X}}}$ is the standard error of the mean; to find the confidence interval range limits, the central limit theorem underpins the following equation:

$${\mathrm{C}}_{\mathrm{I}}=\overline{{\mathrm{Q}}_{\mathrm{TOT}}}\pm \mathrm{t}\frac{\mathrm{S}}{\sqrt{\mathrm{n}}}$$

(11)

where ${\mathrm{C}}_{\mathrm{I}}$ is the confidence interval range and t is determined from the t-distribution family depending on sample n and the LOC. If the sample size is less than or equal to 30, the t-distribution that approximates a normal distribution is used as the sampling distribution of the means [22]. The $\mathrm{t}$ value can be determined from a t-distribution table by using $\mathrm{n}$ and the LOC or by using sample n and the LOS with Microsoft Excel “T.INV” function as shown:

$$\mathrm{t}=\mathrm{T}.\mathrm{INV}\left(\mathrm{LOS}/2,\mathrm{n}-1\right)=\mathrm{T}.\mathrm{INV}\left(0.05/2,30-1\right)$$

(12)

Therefore, the $\mathrm{t}\frac{\mathrm{S}}{\sqrt{\mathrm{n}}}$ part of the equation represents the margin of error, which provides the lower and upper limits of the 95 % LOC range in which the actual true population parameter lies within this interval. Equation (11) can then be used with the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and associated $\mathrm{S}$ calculation of the 2, 3, and 4 ms UV manufacturer surged samples to calculate the ${\mathrm{C}}_{\mathrm{I}}$ range limits, as shown in

Table 5. Confidence interval limits of UV average Q_TOT.

UV Average QTOT for	${\mathbf{C}}_{\mathbf{I}}\mathbf{Lower}\mathbf{Limit}$	${\mathbf{C}}_{\mathbf{I}}\mathbf{Upper}\mathbf{Limit}$
2 ms DC surge data:	9.97 C	19.65 C
3 ms DC surge data:	9.50 C	18.03 C
4 ms DC surge data:	10.22 C	17.13 C

.

The calculated sample confidence interval ranges can then be used to perform a visual statistical comparison test of the different surge degraded samples of the same MOV device population. Therefore, the ${\mathrm{C}}_{\mathrm{I}}$ range of the UV manufacturer $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ estimate for the 2, 3, and 4 ms switching DC surged samples that occurs 95% of the time and contains the actual true population mean are graphically shown together in Figure 5.

Equation (11) can also be used with $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and the associated $\mathrm{S}$ calculation of the 2, 3, and 4 ms WX manufacturer surged samples to calculate the ${\mathrm{C}}_{\mathrm{I}}$ range limits, as shown in

Table 6. Confidence interval limits of WX average Q_TOT.

WX Average QTOT for	${\mathbf{C}}_{\mathbf{I}}\mathbf{Lower}\mathbf{Limit}$	${\mathbf{C}}_{\mathbf{I}}\mathbf{Upper}\mathbf{Limit}$
2 ms DC surge data:	3.95 C	5.78 C
3 ms DC surge data:	3.85 C	5.35 C
4 ms DC surge data:	3.85 C	6.00 C

.

The ${\mathrm{C}}_{\mathrm{I}}$ range of the WX manufacturer $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ estimate for the 2, 3, and 4 ms switching DC surged samples that occur 95% of the time and contain the actual true population mean are graphically shown together in Figure 6.

Equation (11) can also be used with $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and the associated $\mathrm{S}$ calculation of the 2, 3, and 4 ms YZ manufacturer surged samples to calculate the ${\mathrm{C}}_{\mathrm{I}}$ range limits, as shown in

Table 7. Confidence interval limits of YZ average Q_TOT.

YZ Average QTOT for	${\mathbf{C}}_{\mathbf{I}}\mathbf{Lower}\mathbf{Limit}$	${\mathbf{C}}_{\mathbf{I}}\mathbf{Upper}\mathbf{Limit}$
2 ms DC surge data:	2.33 C	4.61 C
3 ms DC surge data:	2.39 C	4.22 C
4 ms DC surge data:	2.34 C	4.08 C

.

The ${\mathrm{C}}_{\mathrm{I}}$ range of YZ manufacturer $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ estimate for the 2, 3, and 4 ms switching DC surged samples that occur 95% of the time and contain the actual true population mean are graphically shown together in Figure 7.

If the 95% ${\mathrm{C}}_{\mathrm{I}}$ ranges of the three independent samples that are subjected to different treatments of 2, 3, and 4 ms switching DC surges do not overlap at all, there is a statistically significant difference and the p-value will be less than or equal to 0.05 or 5%. This then implies that the different treatments of 2, 3, and 4 ms switching DC surges have an effect on the estimated $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA}. Alternatively, if all the 95% ${\mathrm{C}}_{\mathrm{I}}$ ranges overlap completely, then there will be no effect on the estimated $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA} by the different treatments. However, if all the 95% ${\mathrm{C}}_{\mathrm{I}}$ ranges are overlapping but not completely, there will still be a chance that there is an effect on the estimated $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA} by the different treatments. Therefore, a hypothesis pairwise sample t-test using a calculated p-value should still be conducted because the 95% ${\mathrm{C}}_{\mathrm{I}}$ ranges of all three selected MOV manufacturers do not completely overlap.

3.2. Hypothesis Testing

In inferential statistics, hypothesis testing is a key procedure that is based on the idea that a conclusion can be reached on the basis of evidence and reasoning about the actual population from sample data [22]. The hypothesis is a premise that requires testing or investigation. The null hypothesis (Ho) is the currently accepted claim for a population parameter and an alternative hypothesis (Ha) is the opposite, which involves the claim to be tested [23]. The hypothesis is about the population parameters where Ho represents no effect and includes equality whereas, Ha does not include equality. Hypothesis testing of two large independent samples of $\mathrm{n}\ge 30$ from the same population is used to test for difference between the estimated mean parameters. The two large independent samples should be as much alike as possible for equivalence and this is achieved by randomly selecting MOV devices to get sample sizes of at least 30. This ensures that the MOV device sample measured data are probabilistically equivalent, implying that individual differences will cancel out. The two large independent samples must then be treated in exactly the same way, except for what may differentiate the two estimated mean parameters. In this case, it is the different applied degradation surge charge content sizes, set by different switching DC surge duration times.

The independent variable varied in this study is the different applied switching DC surge charge content sizes that can potentially provide a difference between two estimated mean parameters. The dependent variable used to see if there is a difference is the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ estimated population mean parameter of ${\mathsf{\mu }}_{\mathrm{QTOT}}$. The study is considered valid when the independent variables of the different applied switching DC surge charge content sizes is the only potential cause of difference in the dependent variable estimated mean parameter of ${\mathsf{\mu }}_{\mathrm{QTOT}}$ at 10% change in V_{1 mA}. In this study, Ha indicates a difference or an effect between the estimated mean parameters of ${\mathsf{\mu }}_{\mathrm{QTOT}}$ for any of the two sample paired degradation treatments of either 2, 3, or 4 ms switching DC surge durations. The three possible pairwise sample Ha for each selected MOV manufacturer can be mathematically expressed as follows:

• Case 1: ${\mathrm{Ha}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}\ne {\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}{\mathrm{Or}\mathrm{Ha}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}-{\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}\ne 0;$
• Case 2: ${\mathrm{Ha}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}\ne {\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}{\mathrm{Or}\mathrm{Ha}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}-{\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}\ne 0;$
• Case 3: ${\mathrm{Ha}:\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}\ne {\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}{\mathrm{Or}\mathrm{Ha}:\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}-{\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}\ne 0$.

There is a not-equal sign in Ha, which implies that there is interest in the difference from zero in both directions and this is referred to as a two-tail test or exploratory hypothesis. In this study, Ho will indicate that there is no difference or effect between the estimated mean parameters of ${\mathsf{\mu }}_{\mathrm{QTOT}}$ for any two sample paired degradation treatments of either 2, 3, or 4 ms switching DC surge durations. The three possible pairwise sample Ho for each selected MOV manufacturer can be mathematically expressed as follows:

• Case 1: ${\mathrm{Ho}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}{=\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}{\mathrm{Or}\mathrm{Ho}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}-{\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}=0;$
• Case 2: ${\mathrm{Ho}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}{=\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}{\mathrm{Or}\mathrm{Ho}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}-{\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}=0;$
• Case 3: ${\mathrm{Ho}:\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}{=\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}{\mathrm{Or}\mathrm{Ho}}_3{:\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}-{\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}=0$.

Often in inferential statistics, a 95% LOC is required before one can reject Ho and, therefore, the LOS or amount of accepted uncertainty is set to 5% (Equation (9)). The LOS is used in hypothesis t-tests to decide whether to accept or reject the Ho claim. If Ho is rejected, Ha is thought to be truer, and if not rejected, Ho is believed to be accurate. It is important to note that Ho is not proven to be true but only that its claim cannot be rejected. By using $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and associated $\mathrm{S}$ of each manufacturer sample without any ${\mathrm{Q}}_{\mathrm{TOT}}$ outlier data as population parameter estimates, a valid statistical p-value can be obtained. However, in practice, to avoid calculation errors the p-value is normally determined by using a software package. Assuming that Ho is true, the p-value is the probability of obtaining a sample more extreme than that of the current sample data. Therefore, the calculated p-value will reveal how likely it is to obtain a specific result. If the calculated p-value is less than or equal to the LOS of 0.05, there is strong evidence that Ho is wrong and must be rejected. On the other hand, if the calculated p-value is greater than the LOS of 0.05, there is not enough evidence that Ho is wrong and therefore, cannot be rejected. For a sample size of $\mathrm{n}\le 30$, the t-distribution is used to calculate the p-value. This hypothesis testing method is referred to as, two independent sample t-test for testing difference between means assuming equal variances. For the three pairwise sample mean comparisons, the software package calculated p-value results for each manufacturer are shown in

Table 8. Two sample t-test calculated p-value results.

Pairwise Comparisons	UV	WX	YZ
${\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}{\mathrm{vs}\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}$	0.74	0.65	0.82
${\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}{\mathrm{vs}\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}$	0.70	0.72	0.71
${\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}{\mathrm{vs}\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}$	0.97	0.62	0.88

.

All the calculated p-value results of each MOV manufacturer are greater than 0.05. The Ho cannot be rejected because the p-value calculations of each manufacturer pairwise sample mean comparison are greater than the LOS of 5%. Therefore, it can be believed that there is no evidence of an effect on all three estimated mean parameters of ${\mathsf{\mu }}_{\mathrm{QTOT}}$ at 10% change in V_{1 mA}, due to the different applied switching DC surge charge content sizes. However, if at least one pairwise sample t-test calculated p-value was less than or equal to 0.05, the overall Ho would then be rejected. Therefore, when testing more than two estimated mean parameters of a population, it is more appropriate to think in terms of variances. Instead of only comparing estimated mean parameters, variances obtained in all three MOV manufacturer samples should rather be analyzed.

3.3. Analysis of Variance

There is variance (${\mathrm{S}}^2$) among the three sample means of each MOV manufacturer and this is referred to as the mean square between groups (${\mathrm{MS}}_{\mathrm{B}}$). The variance within each of the three samples represents how the data vary around the calculated mean. However, variance also resides within all three samples or all 90 devices selected for each MOV manufacturer. The sample means are different from each other but the variances in each of the three samples are about the same. Therefore, variances in the three samples of each MOV manufacturer can be pooled together to create the mean square within groups (${\mathrm{MS}}_{\mathrm{W}}$). The variance between sample means can also be compared to an estimate of the population variance in order to decide on whether to accept or reject Ho [22]. The ${\mathrm{MS}}_{\mathrm{W}}$ is the best estimate of the population variance because devices are randomly selected from a given MOV manufacturer population and assigned to each sample. It can be expected that the sample variances of ${\mathrm{Q}}_{\mathrm{TOT}}$ at 10 % change in V_{1 mA} are about the same even though the calculated $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ values are different. Therefore, if ${\mathrm{MS}}_{\mathrm{B}}$ is significantly greater than ${\mathrm{MS}}_{\mathrm{W}}$, Ho must be rejected and if not, Ho cannot be rejected [21].

Alternatively, the F-ratio calculated as ${\mathrm{MS}}_{\mathrm{B}}$ divided by ${\mathrm{MS}}_{\mathrm{W}}$ is used to compare the two variances. If the F-ratio is less than or equal to one, fail to reject Ho else if greater then reject Ho. This method is referred to as analysis of variance (ANOVA) and the hypothesis is then mathematically expressed in terms of variances instead of means, as shown:

• Null Hypothesis: ${\mathrm{Ho}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}{=\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}{=\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}\mathrm{Or}\mathrm{Ho}:\frac{{\mathrm{MS}}_{\mathrm{B}}}{{\mathrm{MS}}_{\mathrm{W}}}\le 1.00,$
• Alternative Hypothesis: ${\mathrm{Ha}:\mathsf{\mu }}_{\mathrm{QTOT}\_2\mathrm{ms}}\ne {\mathsf{\mu }}_{\mathrm{QTOT}\_3\mathrm{ms}}\ne {\mathsf{\mu }}_{\mathrm{QTOT}\_4\mathrm{ms}}\mathrm{Or}\mathrm{Ha}:\frac{{\mathrm{MS}}_{\mathrm{B}}}{{\mathrm{MS}}_{\mathrm{W}}}>1.00$.

To perform a one-way or single factor ANOVA, the associated formulas with raw ${\mathrm{Q}}_{\mathrm{TOT}}$ data can be used to compute the p-value manually. However, in practice, to avoid calculation errors a software package is used instead. The ANOVA calculated results for each MOV manufacturer is shown in

Table 9. Three MOV manufacturer ANOVA results.

ANOVA Results for	p-Value	F-Ratio	F-Crit
UV samples:	0.91	0.09	3.10
WX samples:	0.81	0.14	3.10
YZ samples:	0.84	0.18	3.11

.

Again, LOS is set to 0.05 or 5% and the calculated p-value shows the probability of attaining an F-ratio this extreme or more if Ho is true. For all three MOV manufacturers, the calculated p-values are greater than 0.05. In addition, all the three MOV manufacturer F-ratio values are less than one and, therefore, Ho cannot be rejected. Alternatively, all three MOV manufacturer F-ratio values are also less than the F-crit values, which then again implies that Ho cannot be rejected. Therefore, the ANOVA results reveal that the different applied switching DC surge charge content sizes have no effect on the estimated mean parameter of ${\mathsf{\mu }}_{\mathrm{QTOT}}$ at 10% change in V_{1 mA}.

3.4. Durability Comparison

The IEC and IEEE standards state that the charge content size measured in coulombs rather than energy in joules is considered a more relevant measure of the capability to withstand an impulse for the purpose of better comparison between different MOV manufacturers [13]. The coulomb unit of measure is independent of MOV discharge voltage or voltage rating and is completely a function of the current amplitude and duration [10,14]. This study also reveals that the ${\mathrm{Q}}_{\mathrm{TOT}}$ charge that causes 10 % change in V_{1 mA} of each MOV device in a statistically significant sample is a relevant measure of durability or resilience to switching DC surges with in-between delay time intervals that allow for thermal device recovery. The $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA} with the associated confidence intervals for all three degraded MOV manufacturer samples by the different applied switching DC surge durations is shown in

Table 10. Manufacturer durability comparison.

$\mathrm{Level}\mathrm{at}85\%\mathrm{of}{\mathrm{V}}_{\mathrm{C}}$	$\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ of UV	$\overline{{\mathrm{Q}}_{\mathrm{TOT}}}\mathrm{of}\mathrm{WX}$	$\overline{{\mathrm{Q}}_{\mathrm{TOT}}}\mathrm{of}\mathrm{YZ}$
With 2 ms DC surges:	$14.8\mathrm{C}\pm 4.8\mathrm{C}$	$4.9\mathrm{C}\pm 0.9\mathrm{C}$	$3.5\mathrm{C}\pm 1.1\mathrm{C}$
With 3 ms DC surges:	$13.8\mathrm{C}\pm 4.3\mathrm{C}$	$4.6\mathrm{C}\pm 0.6\mathrm{C}$	$3.3\mathrm{C}\pm 0.9\mathrm{C}$
With 4 ms DC surges:	$13.7\mathrm{C}\pm 3.5\mathrm{C}$	$4.9\mathrm{C}\pm 1.1\mathrm{C}$	$3.2\mathrm{C}\pm 0.9\mathrm{C}$

.

This proposed durability model can be used as a more effective and relevant way of comparing resilience between different MOV manufacturer devices with similar size and electrical specifications. Therefore, because the UV manufacturer has a larger $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA}, for all three switching DC surge charge content sizes, it has the highest durability or resilience. The WX manufacturer has the next highest durability, followed by the YZ manufacturer. Even though all three manufacturers have similar datasheet device specifications, it is now clear that the MOV device durability is different when degraded by this specific type of degradation.

4. Summary

All the statistically significant MOV device samples have no outlier ${\mathrm{Q}}_{\mathrm{TOT}}$ data values at 10 % change in V_{1 mA.} Therefore, $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ and associated $\mathrm{S}$ calculations are considered as valid estimations of the MOV population parameters. It was then determined that 95% ${\mathrm{C}}_{\mathrm{I}}$ ranges of MOV degraded device samples due to the different applied switching DC surge duration treatments overlapped but not completely. Therefore, there was still a chance that there is an effect on the estimated $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA}, by different switching DC surge charge content size treatments. A pairwise hypothesis t-test between sample averages was then conducted, where Ho represents no effect between the estimated parameter means of ${\mathsf{\mu }}_{\mathrm{QTOT}}$ at 10% change in V_{1 mA} and Ha represents an effect due to the different charge content size treatments. All the calculated p-values of sample pairwise hypothesis t-tests were greater than the LOS, indicating that the Ho claim cannot be rejected. This implies that there was not a 95% LOC to reject Ho. For this reason, it can be believed that there is no evidence of an effect on the estimated ${\mathsf{\mu }}_{\mathrm{QTOT}}$ at 10% change in V_{1 mA} due to different switching DC surge charge content size treatments. However, a single-factor ANOVA was also conducted because there were more than two estimated ${\mathsf{\mu }}_{\mathrm{QTOT}}$ at 10% change in V_{1 mA} for each selected MOV manufacturer. It was then determined that the calculated ANOVA p-values for all three MOV manufacturers was greater than the LOS. This implies again that the Ho claim cannot be rejected. Therefore, it can be said that for a statistically significant sample, the determined $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA} will effectively model the MOV durability to occasional switching DC surges with in-between delay time intervals that allow for sufficient thermal device recovery.

5. Conclusions

In large DC systems, a parallel-connected MOV device is used to absorb and transfer stored line inductance energy or charge contents around an opening switch to prevent surge damage. However, occasionally induced switching DC surges degrade the MOV and reduce its energy absorption capability over time. The aim of this study was to find a more useful MOV durability model for switching DC surges with in-between delay times that allow thermal device recovery. The hypothesis proposed that could not be rejected in this study is that MOV durability for this type of degradation can be modelled by the $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ of a statistically significant sample, where the ${\mathrm{Q}}_{\mathrm{TOT}}$ of each device is obtained at 10% change in V_{1 mA}. This durability model is useful because it can more accurately estimate the number of switching DC surges a MOV device in a given DC system can handle reliably, until an unacceptable degradation level is reached. It also assists designers to more accurately determine the expected MOV lifetime protection of a DC switch. By monitoring a given DC system, the peak average surge current multiplied by the observed impulse duration will approximate the charge transfer content size that the MOV device needs. The number of switching DC surges a MOV device can withstand is obtained by dividing the specified $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA} by the observed charge transfer content surge size. The approximate expected lifetime operation of the MOV can then be estimated by multiplying the number of switching DC surges with the observed average time delay interval between surge events. Using this approach, a more adequate MOV operation lifetime protection estimation can be determined for this specific type of degradation. This validated MOV durability model has proven to be consistent across different types of MOV material microstructures that are composed of various oxide additives but have similar size and electrical specifications. Therefore, this durability model will provide a more appropriate approach to compare MOV resilience or durability between different manufacturers that have similar specified device specifications. This scientific advance has inspired us to include the estimated $\overline{{\mathrm{Q}}_{\mathrm{TOT}}}$ at 10% change in V_{1 mA} with associated 95% ${\mathrm{C}}_{\mathrm{I}}$ ranges by MOV manufacturers in their respective datasheets for this specific type of device EHC degradation.