How to predict failure of machinery using data science
Everyone knows how annoying mechanical breakdown can be. Production is directly successful because the equipment malfunctions. Large sums of money are lost as production resumes. It also affects OEMs and distributors based on lost reputation and business opportunity. Fortunately, the use of data science can handle this problem to a large extent.
Opportunity for machine owners
The cost of breakdown is not only the loss of opportunity (profit from production), but also the fixed cost of the machine. Also, delays in production can attract fines and lost orders. Sometimes, while other machines depend on failed machines, the cost increases through the roof. The cost of a single break can easily exceed thousands of dollars. The worst part is that this loss can never be recovered.
The figure above shows some of the components of cost of downtime.
Using predictive models, one can now estimate the probability of failure. It gives us two abilities. First, the ability to plan maintenance to minimize losses. Second, to improve inventory better. Instead of stockpiling a lot of spare parts, it is possible to keep only what you need in the future.
Advantages for machine owners
 Reduce repair time
 Avoid unplanned maintenance
 Reduce inventory cost
 Increase bottom line
Opportunity for manufacturers (OEMs)
Failures do not directly affect OEM, but it can damage reputation and end up in lost business. If an important item is not available nearby, customers will not hesitate to purchase items from the local market. Also, manpower may not be available to repair the machine immediately.
These problems can be avoided if you already have an idea of the potential breakdowns. OEMs / Distributors can then schedule a maintenance and replace parts or provide immediate support in the event of a breakdown. In addition, it will enable OEMs to introduce new revenue models of maintenance contracts. It can also ensure that customers do not buy spare parts from local markets.
Advantages for OEMS
 Avoid unplanned breakdowns
 Increase customer satisfaction (lower repair time)
 Optimize inventory
 Improve top line
 Improve product
How to implement
The process begins by identifying the problems to be solved. Usually the problem should be broad and exclusively segregated. E.g. The goal may be to reduce operating costs. One of the many ways to achieve this is by reducing idle time and improving the list of spare parts.
Once problems are identified, data should be collected for analysis. Often data is not available. As such, the infrastructure for data collection needs to be built. When creating infrastructure and processes, efforts should be made to improve the utility of such infrastructure / processes. This can be done by evaluating other uses of the collected data. If it costs somewhat less to add additional data to solve a significant problem, it should proceed.
Once the data starts to collect, it should be cleaned and visualized. This applies not only to the data science team, but also to other business partners. If possible and possible, the dashboard (s) can be built for different partners depending on the need. Predictive features of analyzes are natural advances from research analyzes. Dashboards and visualization should be tested and reviewed by creating a forecast model (s).
Example using real life data
Code heavy!!! Skip if you are not interested in the codes. However, you may like to understand how well the below model performed in results
Real life (normalized) data have been used to illustrate the possible model. The data contains a record of certain parameters taken per hour. In addition, record and maintenance of failures will be used.^{1} The parameters recorded in hours are voltage, vibration, rotation and pressure. Data were recorded from 100 machines of 4 types. Failure of 4 components has been recorded. To simplify, let us analyze the failure of ‘comp2.’
To keep this brief and to focus on the prognostic model many research activities have been avoided.
1# Following data are available
2# 1. Telemetry  Logs hourly parameters (Voltage, Pressure, Rotation and Vibration) for each machine
3# 2. Failures  Log of component failures. Contains the time slot (that matches the telemetry log) and machineID
4# 3. Maint  Log of maintainance. Contains time slot, machineID and the component replaced
5# 4. Assets  Information about the machines  machineID, Model and age
6
7# Function to calculate number of periods since last maintenance of a component
8timeslm < function(k) {
9 output < c()
10 output[1] = 0
11 for (i in 2:length(k)) {
12 if (k[i  1] == 1) {
13 output[i] = 1
14 } else {
15 output[i] = output[i  1] + 1
16 }
17 }
18 return(output)
19}
20
21# For the sake of simplicity, failures of 'comp2' will be analysed
22
23#preparing data
24failures2 <
25 failures %>% filter(failure == "comp2") #new data frame with failure of comp2
26maint2 <
27 maint %>% filter(comp == "comp2") #new data frame with maintenance of comp2
28
29df <
30 telemetry %>% left_join(failures2, by = c("machineID", "datetime")) %>% #Joining log with failure
31 mutate(failed = ifelse(is.na(failure), 0, 1)) %>% #creating column with binary (failed or not)
32 left_join(maint2, by = c("machineID" = "machineID", "datetime" = "datetime")) %>% #Joining maintenance data
33 mutate(maint = ifelse(is.na(comp), 0, 1)) %>% #New column with binary (maintained or not)
34 inner_join(assets, by = "machineID") #Joining machine details
35df$datetime <
36 parse_date_time(df$datetime, "mdy HMS p") #Changing column type to date time
37df$machineID < as.factor(df$machineID)
38df$model < as.factor(df$model)
39
40timesm < timeslm(df$maint) #Calculating periods since maintenance
41df$timesm < timesm
42
43df <
44 df %>% mutate(t = ifelse(is.na((
45 as.numeric(datetime  lag(datetime, 1))
46 )), 0, (as.numeric(
47 datetime  lag(datetime, 1)
48 )))) %>%
49 mutate(tim = cumsum(t)) #Adding time columns
50
51df < df[, c(1, 14, 15, 13, 11, 12, 2:6, 8, 10)]
52#Column details  datetime = event log time
53# machineID = Machine Identification number
54# volt, rotate, pressure, vibration are some of the parameters that are measured
55# failed and maint indicate if the component (comp2) failed. 1 indicates true.
56# age is the age of the machine
57# timesm is the time since maintenance
58# tim is the time since the beginning of event logging
59
60
61#removing dfs that are not required
62rm(telemetry)
63rm(assets)
64rm(failures)
65rm(maint)
66rm(timesm)
67
68# adding grouping to calculate cumulative parameter values.
69g < c()
70g[1] = 1
71for (i in 2:nrow(df)) {
72 if (df$timesm[i] < df$timesm[i  1]) {
73 g[i] = g[i  1] + 1
74 } else {
75 g[i] = g[i  1]
76 }
77}
78
79df$group < g
80
81# removing unwanted data
82rm(g)
83
84
85#Will add new columns with cumulative parameters  sum, mean
86
87df1 <
88 df %>% group_by(group) %>% mutate(
89 volt.cum = cumsum(volt),
90 vib.cum = cumsum(vibration),
91 pres.cum = cumsum(pressure),
92 rot.cum = cumsum(rotate),
93 volt.mean = cumsum(volt) / seq_along(volt),
94 vib.mean = cumsum(vibration) / seq_along(vibration),
95 pres.mean = cumsum(pressure) / seq_along(pressure),
96 rot.mean = cumsum(rotate) / seq_along(rotate)
97 ) %>%
98 filter(maint == 1) # filtered required data
99
100# In case you are interested to know about the transformations in detail please get in touch.
101
102#preparing test and train data
103df.train < df1 %>% filter(datetime < "20151115 06:00:00 UTC")
104df.test < df1 %>% filter(datetime > "20151115 06:00:00 UTC")
105
106#removing unwanted data
107rm(df1)
108rm(df)
109
110# Fitting Kaplan Meier
111
112kap.fit<survfit(Surv(timesm,failed)~model, data=df.train)
113
114#Plotting
115
116fig<ggsurvplot(
117 kap.fit,
118 pval = F, # show pvalue
119 break.time.by = 1000, #break X axis by 25 periods
120 #risk.table = "abs_pct", # absolute number and percentage at risk
121 #risk.table.y.text = FALSE,# show bars instead of names in text annotations
122 linetype = "strata",
123 # Change line type by groups
124 conf.int = T,
125 # show confidence intervals for
126 #conf.int.style = "step", # customize style of confidence intervals
127 #surv.median.line = "hv",
128 # Specify median survival
129 ggtheme = theme_minimal(),
130 # Change ggplot2 theme
131 legend.labs =
132 c("Model 1", "Model 2", "Model 3", "Model 4"),
133 # change legend labels
134 ncensor.plot = F,
135 # plot the number of censored subjects (outs) at time t
136 #palette = c("#000000", "#2E9FDF","#FF0000")
137
138)+
139 labs(x="Hours")
140fig
Kaplan Meier model predicts survival chances by 3000 hours of operation (post maintenance) reduces significantly. But there is a substantial amount of uncertainty in prediction, except in case of model 4. The model also shows that it is almost certain that there will be no failures till about 700 hours of operation, post maintenance.
Summary of the fit is as shown below.
1summary(kap.fit)$table
## records n.max n.start events *rmean *se(rmean) median 0.95LCL
## model=model1 103 103 103 37 2661.662 317.7212 1800 1440
## model=model2 112 112 112 32 2781.430 370.7489 2160 1489
## model=model3 257 257 257 78 2871.243 264.5345 1800 1440
## model=model4 191 191 191 70 2620.189 214.6314 2160 1800
## 0.95UCL
## model=model1 3240
## model=model2 NA
## model=model3 2880
## model=model4 2880
Since the uncertainty is high, I will not use this model and try Cox regression.
Cox regression model shows that among all the parameters used, cumulative rotation is the one that significantly impacts failure of ‘comp2.’
With this insight, OEM can think of ways to improve component quality or find out ways to keep the rotation low.
1# Cox regression
2cox.fit<coxph(Surv(timesm,failed) ~ volt.cum+vib.cum+pres.cum+rot.cum+volt.mean+vib.mean+pres.mean+rot.mean+factor(model), data=df.train)
3summary(cox.fit)
## Call:
## coxph(formula = Surv(timesm, failed) ~ volt.cum + vib.cum + pres.cum +
## rot.cum + volt.mean + vib.mean + pres.mean + rot.mean + factor(model),
## data = df.train)
##
## n= 663, number of events= 217
##
## coef exp(coef) se(coef) z Pr(>z)
## volt.cum 2.389e04 9.998e01 1.416e04 1.687 0.091529 .
## vib.cum 3.233e04 9.997e01 2.849e04 1.135 0.256382
## pres.cum 2.164e05 1.000e+00 1.557e04 0.139 0.889459
## rot.cum 1.496e04 9.999e01 4.161e05 3.594 0.000326 ***
## volt.mean 2.527e01 1.287e+00 1.687e01 1.498 0.134178
## vib.mean 5.436e01 1.722e+00 3.291e01 1.652 0.098603 .
## pres.mean 1.520e01 1.164e+00 1.851e01 0.821 0.411487
## rot.mean 4.229e02 9.586e01 4.338e02 0.975 0.329642
## factor(model)model2 4.183e01 6.582e01 2.786e01 1.501 0.133273
## factor(model)model3 1.932e01 8.243e01 2.322e01 0.832 0.405304
## factor(model)model4 9.385e02 1.098e+00 2.397e01 0.391 0.695429
## 
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(coef) lower .95 upper .95
## volt.cum 0.9998 1.0002 0.9995 1.0000
## vib.cum 0.9997 1.0003 0.9991 1.0002
## pres.cum 1.0000 1.0000 0.9997 1.0003
## rot.cum 0.9999 1.0001 0.9998 0.9999
## volt.mean 1.2875 0.7767 0.9250 1.7920
## vib.mean 1.7222 0.5807 0.9035 3.2826
## pres.mean 1.1641 0.8590 0.8100 1.6731
## rot.mean 0.9586 1.0432 0.8804 1.0437
## factor(model)model2 0.6582 1.5193 0.3813 1.1363
## factor(model)model3 0.8243 1.2132 0.5229 1.2994
## factor(model)model4 1.0984 0.9104 0.6866 1.7571
##
## Concordance= 0.98 (se = 0.004 )
## Likelihood ratio test= 1060 on 11 df, p=<2e16
## Wald test = 135.2 on 11 df, p=<2e16
## Score (logrank) test = 483.9 on 11 df, p=<2e16
So, a new model was built to include only cumulative rotation as parameter. The model was used to predict outcome on test data. Confusion matrix was built to analyze accuracy.
1# Revised cox model
2cox.fit<coxph(Surv(timesm,failed) ~ rot.cum, data=df.train)
3
4# Predicted probabilities
5pred<predict(cox.fit,newdata=filter(df.test), type = "expected")
6
7d<df.test%>%cbind(pred=pred)%>%select(12,14,23)%>%mutate(pred=ifelse(pred>0.5,1,0))
8
9table(act=d$failed,pred=d$pred)
## pred
## act 0 1
## 0 49 12
## 1 7 32
Results
 81 % accuracy was achieved *
 87 % accurate when did not predict failure *
 72 % accurate when predicted failure *
Wondering what does it mean in terms of saved cash? Or what are all possible ways to create value out of this? One needs more detail of the business and operations to answer those questions. If you are really interested, you know what to do!
For any questions and/or clarifications, please do not hesitate to contact me.
Notes

The data has been sourced from [Deepti Chevvuri’s Github] (https://github.com/DeeptiChevvuri/PredictiveMaintenanceModellingDatasets). The data contains error logs as well, which has not been used in this analysis. ↩︎